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BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1)
bull For technical issues contact GoToWebinar (GoToMeeting) at
1-800-263-6317 or
httpsupportcitrixonlinecomgotomeeting
bull Presentation slides are available to download at
httpwwwtreasurercagovcdiacwebinars2014201408
07descriptionasp
bull For MCLE credit email cdiac_educationtreasurercagov
bull Live captioning is available at
wwwstreamtextnettextaspxevent=CDIAC
August 7 2014 200 PM ndash 330 PM
BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1)
PRESENTED BY LOUIS CHOI
PUBLIC RESOURCES ADVISORY GROUP AN INDEPENDENT REGISTERED MUNICIPAL ADVISOR (IRMA)
Topics presented by
3
Bonds and Loans
How Municipal Bonds are Priced (or Valued)
Understanding Cash Flow Schedules
Debt Amortization
Bonus Using Microsoft Excel Functions
Bonds and Loans
Bond cash flows literacy intermediate bond math (Part 1)
Bonds and Loans
Bonds as Loans presented by
5
ϜϜ
π
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
Bonds and Loans
In Aggregate Bonds in an Issue Are
Equivalent to a Loan presented by
6
$120
$100 Interest
$80 $60 $40 $20 $0
$120
$100
$80
$60
$40
$20
$0
Principal
1
$120
$60
$80
$100 Interest
Principal
$40
$20
$0
5 10 15 20 25 30
$0
$20
$40
$60
$80
$100
$120
Interest
Principal
Interest
Principal
1 5 10 15 20 25 30
= 1 5 10 15 20 25 30 1 5 10 15 20 25 30
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
BOND CASH FLOWS LITERACY INTERMEDIATE BOND MATH (PART 1)
PRESENTED BY LOUIS CHOI
PUBLIC RESOURCES ADVISORY GROUP AN INDEPENDENT REGISTERED MUNICIPAL ADVISOR (IRMA)
Topics presented by
3
Bonds and Loans
How Municipal Bonds are Priced (or Valued)
Understanding Cash Flow Schedules
Debt Amortization
Bonus Using Microsoft Excel Functions
Bonds and Loans
Bond cash flows literacy intermediate bond math (Part 1)
Bonds and Loans
Bonds as Loans presented by
5
ϜϜ
π
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
Bonds and Loans
In Aggregate Bonds in an Issue Are
Equivalent to a Loan presented by
6
$120
$100 Interest
$80 $60 $40 $20 $0
$120
$100
$80
$60
$40
$20
$0
Principal
1
$120
$60
$80
$100 Interest
Principal
$40
$20
$0
5 10 15 20 25 30
$0
$20
$40
$60
$80
$100
$120
Interest
Principal
Interest
Principal
1 5 10 15 20 25 30
= 1 5 10 15 20 25 30 1 5 10 15 20 25 30
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Topics presented by
3
Bonds and Loans
How Municipal Bonds are Priced (or Valued)
Understanding Cash Flow Schedules
Debt Amortization
Bonus Using Microsoft Excel Functions
Bonds and Loans
Bond cash flows literacy intermediate bond math (Part 1)
Bonds and Loans
Bonds as Loans presented by
5
ϜϜ
π
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
Bonds and Loans
In Aggregate Bonds in an Issue Are
Equivalent to a Loan presented by
6
$120
$100 Interest
$80 $60 $40 $20 $0
$120
$100
$80
$60
$40
$20
$0
Principal
1
$120
$60
$80
$100 Interest
Principal
$40
$20
$0
5 10 15 20 25 30
$0
$20
$40
$60
$80
$100
$120
Interest
Principal
Interest
Principal
1 5 10 15 20 25 30
= 1 5 10 15 20 25 30 1 5 10 15 20 25 30
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonds and Loans
Bond cash flows literacy intermediate bond math (Part 1)
Bonds and Loans
Bonds as Loans presented by
5
ϜϜ
π
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
Bonds and Loans
In Aggregate Bonds in an Issue Are
Equivalent to a Loan presented by
6
$120
$100 Interest
$80 $60 $40 $20 $0
$120
$100
$80
$60
$40
$20
$0
Principal
1
$120
$60
$80
$100 Interest
Principal
$40
$20
$0
5 10 15 20 25 30
$0
$20
$40
$60
$80
$100
$120
Interest
Principal
Interest
Principal
1 5 10 15 20 25 30
= 1 5 10 15 20 25 30 1 5 10 15 20 25 30
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonds and Loans
Bonds as Loans presented by
5
ϜϜ
π
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
$120
$100
$80
$60
$40
$20
$0
Interest
Principal
1 5 10 15 20 25 30
Bonds and Loans
In Aggregate Bonds in an Issue Are
Equivalent to a Loan presented by
6
$120
$100 Interest
$80 $60 $40 $20 $0
$120
$100
$80
$60
$40
$20
$0
Principal
1
$120
$60
$80
$100 Interest
Principal
$40
$20
$0
5 10 15 20 25 30
$0
$20
$40
$60
$80
$100
$120
Interest
Principal
Interest
Principal
1 5 10 15 20 25 30
= 1 5 10 15 20 25 30 1 5 10 15 20 25 30
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonds and Loans
In Aggregate Bonds in an Issue Are
Equivalent to a Loan presented by
6
$120
$100 Interest
$80 $60 $40 $20 $0
$120
$100
$80
$60
$40
$20
$0
Principal
1
$120
$60
$80
$100 Interest
Principal
$40
$20
$0
5 10 15 20 25 30
$0
$20
$40
$60
$80
$100
$120
Interest
Principal
Interest
Principal
1 5 10 15 20 25 30
= 1 5 10 15 20 25 30 1 5 10 15 20 25 30
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonds and Loans
A Bond Issue and a Loan Are Mathematically
Similar But Not Identical presented by
77
A Loan
Principal 500 Debt
Date Balance Principal Interest Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
A Bond Issue 200 300 400 450 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 471375 550000 1886375 10936375
512016 40950000 9500000 300 285000 399000 471375 550000 1705375 11205375
512017 31450000 9975000 400 399000 471375 550000 1420375 11395375
512018 21475000 10475000 450 471375 550000 1021375 11496375
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 1885500 2750000 6583500 56583500
Interest on Principal Due
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
presented by
Bonds and Loans
Differences in Rates Across Maturities Generate a
Yield Curve 8
State Public Works Board of the State of California $152420000 Lease Revenue Bonds
(Department of Corrections and Rehabilitation) 2014 Series C
00
05
10
15
20
25
30
35
40
45
2014 2019 2024 2029 2034
Yie
ld
0
2
4
6
8
10
12$Millions
Pri
nci
pa
l
Principal
Yield
Principal Amounts and Initial Reoffering Yields as of April 10 2014
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonds and Loans
Selected Historical Yield Curves presented by
9
AAA GO MMD
0
1
2
3
4
5
6
1 5 10 15 20 25 30
8292001 (normal)12122008 (steep)2232007 (flat)1212006 (inverted)Today
PercentileDate 25th 50th 75th 82901 121208 22307 12106
1Y vs 5Y MMD 052 088 130 088 201 000 ndash005
1Y vs 10Y MMD 095 155 235 159 326 012 008
1Y vs 30Y MMD 165 250 344 250 486 044 044
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Bond cash flows literacy intermediate bond math (Part 1)
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Time-Value of Money (TVM) presented by
11
Calculates the value of Present Value Formula future-day dollars in present-day dollars and applicable to calculations for
Opportunity cost
Inflation
Investments
t
p
i
FVPV
1
ldquoPVrdquo = Present Value
ldquoFVrdquo = Future Cash Flows
ldquo i rdquo = Interest Rate
ldquo p rdquo = ompounding Periods Per Year
ldquo t rdquo = Time or Periods
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
TVM Is the Basis for Calculating Bond Prices presented by
12
A stream of future cash flows such as the periodic payment of interest and final payment of principal follows the same approach as the sum of multiple terms
Present Value Formula for Multiple Future Cash Flows
nt
n
tt
p
i
CF
p
i
CF
p
i
CFPV
111
21
21
ldquoPVrdquo = Present Value or Price
ldquoFrdquo = Future Cash Flows which for bonds include
Principal
Semi-Annual Interest
ldquo i rdquo = Interest Rate or Yield
ldquo p rdquo = ompounding Periods Per Year
(Municipal Convention = 2)
ldquo t rdquo = Time or Periods
(Municipal Convention = 180
360
30Days
)
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Bond Pricing Formula presented by
13
Municipal Standard Price Formula
RB
A
Y
R
Y
RVP
N
k E
AEk
E
AEN
^^100
21
2100
21
1 11
Principal Component
Interest Component
Accrued Interest
Component
ldquordquo = 30360 days from dated date to settlement date
ldquordquo = Days in the year (usually 360)
ldquoErdquo = Days in semi-annual period (usually 180)
ldquoNrdquo = Interest payments between settlement and redemption dates Expressed as a percentage
ldquoPrdquo = Dollar price (as a ) of the principal amount
ldquoRrdquo = nnual coupon (as decimal)
ldquoRVrdquo = Redemption value including premiums if any
ldquoYrdquo = Yield (as decimal)
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Prices Can Vary Greatly with Different Coupons
and Maturities presented by
14
10-year bond with a 3 coupon at yield of 315
10-year bond with a 5 coupon at yield of 315
10-year bond with a 5 coupon at yield of 5165
721983360
0100
2
1531
2
3100
2
1531
100 20
1 180
01801
180
0180120
k k^^
7641155360
0100
2
1531
2
5100
2
1531
100 20
1 180
01801^
180
0180120^
k k
721985360
0100
2
16551
2
5100
2
16551
100 20
1 180
01801^
180
0180120^
k k
Terminology
Par Price = 100 Discount Price lt 100 Premium Price gt 100
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Bond Prices are Commonly Expressed in Yields
for Ease of Comparison presented by
15
Yields help to inform consistency of pricing as terms vary
7252014 AAA GO MMD
00
05
10
15
20
25
1 2 3 4 5 6 7 8 9 10
Yield gtgt 011 031 054 087 121 145 169 191 207 219
Co
up
on 300 102887 105359 107310 108355 108659 108876 108614 108050 107600 107239
400 103886 107351 110282 112278 113496 114602 115189 115437 115773 116176
500 104885 109343 113254 116201 118334 120329 121765 122823 123946 125113
C 5 P 109500 Y 0236
C 4 P 109000 Y 0950
C 3 P 108500 Y 0835
C 5 P 124000 Y 2064 C 3
P 108000 Y 1779
C 4 P 116500 Y 1778
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Bond Pricing Conventions presented by
16
Using the price formula when coupon equals yield may result in a calculated price of 99998 or 99999
Guarantees investors that the stated yield would be achieved regardless of whether or when the issuer exercises its option
Prices do not have to calculated for every date instead only first dates when redemption prices change must be checked
Bonds where coupon equals yield are priced at 100000 (or par)
Prices are truncated to third place after decimal
E΄ ώϜ Ϧ ΫΪαΫβΰάήέ ύϜώϜ ΫΪαΫβΰ
E΄ ώϜ Ϧ γβίέάγέ ύϜώϜ γβίέά
Yields are rounded to the nearest third place after decimal
E΄ ΅ϜϘ Ϧ ίΫΰήέί ύϜώϜ ίΫΰή
E΄ ΅ϜϘ Ϧ έΫβγβα ύϜώϜ έΫγΪ
For optionally callable premium bonds (ie coupon gt yield) bonds are priced to that call date which results in the lowest price
Ex 1112028 maturity 42 coupon 315 yield callable on 1112024 at 102 on 1112025 at 101 and on 1112026 at 100 and settled on 1112014
Assumed
Redemption Date
No of interest
periods (N)
Redemption
value (RV) Price (P)
1112024 20 102 110410
1112025 22 101 110406
1112026 24 100 110424
1112028 28 100 111813
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Capital Appreciation Bonds (CAB) presented by
17
Also based on TVM formula
Note Prices may be expressed as percentage of delivery date principal amount or final maturity amount depending on how issuance principal is expressed
Interest is compounded and paid at maturity
Growth in value of a CAB is expressed as an accreted value
2^
21
n
nY
PRAV
ldquoAVnrdquo = ccreted value at period n
ldquoPRrdquo = Initial price (generally par)
ldquoYrdquo = Yield
Generally not subject to optional redemption
Sold in denominations such that the final accreted value of each denomination is $5000
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Calculating Bond Prices
Capital Appreciation Bonds (Contrsquod) presented by
18
Solving for an accretion tablehellip
2^
21
nM
n
Y
DNAV
ldquoAVnrdquo = ccreted value at period n
ldquoYrdquo = Yield
ldquoMrdquo = Maturity
Example Delivery Date 5142014 Maturity 512019 Yield 350 Effective Denomination $5000
ldquoDNrdquo = ccreted value at maturity (effective denomination)
Date
Accreted
Value
5142014 $420891
1112014 427721
512015 435206
1112015 442822
512016 450571
1112016 458456
512017 466479
1112017 474643
512018 482949
1112018 491400
512019 500000
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
Bond cash flows literacy intermediate bond math (Part 1)
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
Describing a Bond Issue with Numbers presented by
20
Goal to understand how the numbers that describe individual bonds and a bond issue work
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
Start with a Basic Loanhellip presented by
21
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9048740 2500000 11548740
512016 40951260 9501177 2047563 11548740
512017 31450083 9976236 1572504 11548740
512018 21473847 10475048 1073692 11548740
512019 10998800 10998800 549940 11548740
Total 50000000 7743700 57743700
Assumptions ndash
bull $50000000 borrowed
bull Repaid in 5 years
bull Interest rate of 500
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipRound by Denominationshellip presented by
22
500
Principal Interest on Debt
Date Balance Principal Balance Service
512014 50000000
512015 50000000 9050000 2500000 11550000
512016 40950000 9500000 2047500 11547500
512017 31450000 9975000 1572500 11547500
512018 21475000 10475000 1073750 11548750
512019 11000000 11000000 550000 11550000
Total 50000000 7743750 57743750
Municipal bonds are generally sold (and therefore repaid) in denominations of $5000
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipReflect Different Interest Rates (Coupons) for Each Maturityhellip presented by
23
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9050000 200 181000 285000 399000 523750 550000 1938750 10988750
512016 40950000 9500000 300 285000 399000 523750 550000 1757750 11257750
512017 31450000 9975000 400 399000 523750 550000 1472750 11447750
512018 21475000 10475000 500 523750 550000 1073750 11548750
512019 11000000 11000000 500 550000 550000 11550000
Total 50000000 181000 570000 1197000 2095000 2750000 6793000 56793000
Interest on Principal Due
Or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9050000 200 1938750 10988750
512016 40950000 9500000 300 1757750 11257750
512017 31450000 9975000 400 1472750 11447750
512018 21475000 10475000 500 1073750 11548750
512019 11000000 11000000 500 550000 11550000
Total 50000000 6793000 56793000
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipAdjust Principal of Each Maturity to Achieve Debt Service Patternhellip presented by
24
200 300 400 500 500
Principal Total Debt
Date Balance Principal Coupon 512015 512016 512017 512018 512019 Interest Service
512014 50000000
512015 50000000 9415000 200 188300 288150 395600 514500 540000 1926550 11341550
512016 40585000 9605000 300 288150 395600 514500 540000 1738250 11343250
512017 30980000 9890000 400 395600 514500 540000 1450100 11340100
512018 21090000 10290000 500 514500 540000 1054500 11344500
512019 10800000 10800000 500 540000 540000 11340000
Total 50000000 188300 576300 1186800 2058000 2700000 6709400 56709400
Interest on Principal Due
Once again or in the more familiar form below
Principal Total Debt
Date Balance Principal Coupon Interest Service
512014 50000000
512015 50000000 9415000 200 1926550 11341550
512016 40585000 9605000 300 1738250 11343250
512017 30980000 9890000 400 1450100 11340100
512018 21090000 10290000 500 1054500 11344500
512019 10800000 10800000 500 540000 11340000
Total 50000000 6709400 56709400
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipIntroduce Prices Yields and Proceedshellip presented by
25
Principal Total Debt
Date Balance Principal Coupon Interest Service Yield Price Proceeds
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254
512019 10800000 10800000 500 540000 11340000 310 108737 11743596
Total 50000000 6709400 56709400 52642532
Each maturity generates proceeds equal to the product of its price and its principal
Note Prices are calculated following all of the rules discussed above
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipCalculate Purchase Pricehellip presented by
26
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Principal 50000000
Net Original Issue Premium(Discount) 2642532
Production 52642532
Underwriters Discount -162052
Purchase Price 52480479
Underwriters Discount
Takedown 137240
Underwriters Counsel 15000
CDIAC 3000
CUSIP 600
Day Loan 1462
Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
The purchase price paid to the issuer is net of both compensation and expenses withheld by the underwriter
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipAdd in Sources and Uses Componentshellip presented by
27
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9415000 200 1926550 11341550 100 100992 9508397 100 9415
512016 40585000 9605000 300 1738250 11343250 175 102446 9839938 250 24013
512017 30980000 9890000 400 1450100 11340100 225 105049 10389346 250 24725
512018 21090000 10290000 500 1054500 11344500 275 108467 11161254 375 38588
512019 10800000 10800000 500 540000 11340000 310 108737 11743596 375 40500
Total 50000000 6709400 56709400 52642532 137240
Sources of Funds Principal 50000000
Principal 50000000 Net Original Issue Premium(Discount) 2642532
Net OIP (OID) 2642532 Production 52642532
Funds on Hand 1000000 Underwriters Discount -162052
Total Sources of Funds 53642532 Purchase Price 52480479
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 137240
Reserve Fund 5264253 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 162052 CUSIP 600
Contingency -2023774 Day Loan 1462
Total Uses of Funds 53642532 Dalcomp 3750
Dalnet 500
DTC 500
Total Uses of Funds 162052
Project deposit represents target amount to be borrowed
Notes Reserve fund is generally equal to the least of 10 of proceeds maximum annual debt service (MADS) and 125 of average annual debt service Contingency is a positive number that is less than the minimum denomination adjusted by the prices of the bonds
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
hellipand Readjust Principal of Each Maturity to Target Proceeds
presented by
28
Principal Total Debt Takedown Takedown
Date Balance Principal Coupon Interest Service Yield Price Proceeds ($$1000) ($)
512014 50000000
512015 50000000 9820000 200 2009200 11829200 100 100992 9917414 100 9820
512016 40180000 10015000 300 1812800 11827800 175 102446 10259967 250 25038
512017 30165000 10315000 400 1512350 11827350 225 105049 10835804 250 25788
512018 19850000 10730000 500 1099750 11829750 275 108467 11638509 375 40238
512019 9120000 11265000 500 563250 11828250 310 108737 12249223 375 42244
Total 52145000 6997350 59142350 54900918 143126
Sources of Funds Principal 52145000
Principal 52145000 Net Original Issue Premium(Discount) 2755918
Net OIP (OID) 2755918 Production 54900918
Funds on Hand 1000000 Underwriters Discount -168162
Total Sources of Funds 55900918 Purchase Price 54732756
Uses of Funds Underwriters Discount
Project Deposit 50000000 Takedown 143126
Reserve Fund 5490092 Underwriters Counsel 15000
Costs of Issuance 240000 CDIAC 3000
Underwriters Discount 168162 CUSIP 600
Contingency 2664 Day Loan 1525
Total Uses of Funds 55900918 Dalcomp 3911
Dalnet 500
DTC 500
Total Uses of Funds 168162
Note Contingency should be greater than zero but less than one denomination of the issued bond after accounting for the prices of the bonds
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Principal Total Debt
Date Balance Principal Coupon Interest Service 255204 265880 281677
512014 50000000
512015 50000000 9820000 200 2009200 11829200 11545493 11533854 11516666
512016 40180000 10015000 300 1812800 11827800 11253871 11230634 11196363
512017 30165000 10315000 400 1512350 11827350 10969879 10935624 10885168
512018 19850000 10730000 500 1099750 11829750 10694982 10650256 10584464
512019 9120000 11265000 500 563250 11828250 10422842 10368195 10287917
Total 52145000 6997350 59142350 54887069 54718564 54470579
Sources of Funds True All-in True
Principal 52145000 Arbitrage Interest Interest
Net OIP (OID) 2755918 Yield Cost Cost
Funds on Hand 1000000 Proceeds 54900918 54900918 54900918
Total Sources of Funds 55900918 Costs of Issuance -240000
Underwriters Discount -168162 -168162
Uses of Funds Arbitrage Adjustments
Project Deposit 50000000 Target Value 54900918 54732756 54492756
Reserve Fund 5490092
Costs of Issuance 240000
Underwriters Discount 168162
Contingency 2664
Total Uses of Funds 55900918
Present Value of Debt Service at
Cash Flow Schedules
presented by How to Calculate the ldquoYieldrdquo of a Bond Issue 29
Arbitrage yield true interest cost (TIC) and all-in TIC each represent a way to express the cost of
Find the rate as the internal rate of return (IRR) of debt service to the target value
Note Debt service may be required to be adjusted for bonds subject to redemption when calculating the arbitrage yield
capital for a bond issue
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Cash Flow Schedules
How to Calculate an ldquoAveragerdquo presented by
30
Principal x
Principal Princpial x Total Debt Years to Years to
Date Balance Principal Coupon Coupon Interest Service Maturity Maturity
512014 50000000
512015 50000000 9820000 200 196400 2009200 11829200 100000 9820000
512016 40180000 10015000 300 300450 1812800 11827800 200000 20030000
512017 30165000 10315000 400 412600 1512350 11827350 300000 30945000
512018 19850000 10730000 500 536500 1099750 11829750 400000 42920000
512019 9120000 11265000 500 563250 563250 11828250 500000 56325000
Total 52145000 2009200 6997350 59142350 160040000
Weighted
Average Average
Coupon Maturity
2009200 160040000
ndashndashndashndashndashndashndashndashndashndash ndashndashndashndashndashndashndashndashndashndash
52145000 52145000
385 306913
In general averages are calculated as weighted averages by principal
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Bond cash flows literacy intermediate bond math (Part 1)
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
32
Level Principal
Ease of calculation
Common for bank product term-out provisions and GOs
Interestprincipal ratio 077 (based on 5 rate)
Level Debt Service
Even distribution of cost
Simplify long-term budget preparation
Interestprincipal ratio 095 (based on 5 rate)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
33
Deferred Principal
Revenues or operational cost savings become available at the later date (eg upon project completion)
Interestprincipal ratio 099 (based on 5 rate)
Ascending Debt Service
Growing revenues
Cost-recovery mechanism is subject to inflation
Interestprincipal ratio 110 (based on 5 rate and 2 annual growth)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
34
Backloaded Principal
Type of bond has the lowest expected cost of funds (eg floating rate or tax credit bonds)
Interestprincipal ratio 125 (based on 5 rate for THIS example)
Wrapped Debt Service
Profile of aggregate debt service is level
Extends useful life of existing debt-funded asset
Interestprincipal ratio 109 (based on 5 rate for THIS example)
presented by Common Amortization Structures
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
InterestPrincipal
0
2
4
6
8
10
12
1 5 10 15 20 25 30
($mm)
Principal Interest Existing
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Solving for Amortization Structure presented by
35
Debt Service for a given year Debt service is equal to the sum of
Principal
Interest on principal
1
)1(ni
iinnn CPPCDS
due and ldquoDSn rdquo = Debt service for year n
ldquoP rdquo = Principal amount for maturity n Interest on principal still n
outstanding ldquoC rdquo = oupon for maturity n n
Solving algebraically for principal results in the following
n
ni
iin
n
C
CPDS
P
11
Given target debt service numbers each principal amount can be solved
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Solving for Amortization Structure presented by
36
No unknowns egin from the last maturityhellip Example
Target debt service $5000000 Coupon for 2024 (last maturity) 500
000007604$
809047614$0051
0$0000005$
2018
2018
2018
P
P
P
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 238000 238000 4762000
2016 $5000000 300 238000 238000 4762000
2017 $5000000 350 238000 238000 4762000
2018 $5000000 500 238000 238000 4762000
2019 $5000000 500 238000 238000 4762000
2020 $5000000 500 238000 238000 4762000
2021 $5000000 500 238000 238000 4762000
2022 $5000000 475 238000 238000 4762000
2023 $5000000 475 238000 238000 4762000
2024 $5000000 4760000 500 238000 4998000 2000
Total $50000000 4760000 2380000 7140000 42860000
Rounding based on
denomination
or round down to
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
37
΅ Ϝ ͳͿ hellipontinue with next to last maturityhellip Example
Target debt service $5000000 Coupon for 2023 (next to last maturity) 475 Principal for 2024 (last maturity) $4760000 Coupon for 2024 (last maturity) 500
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 300 $453888 $453888 $4546113
2016 $5000000 300 $453888 $453888 $4546113
2017 $5000000 350 $453888 $453888 $4546113
2018 $5000000 500 $453888 $453888 $4546113
2019 $5000000 500 $453888 $453888 $4546113
2020 $5000000 500 $453888 $453888 $4546113
2021 $5000000 500 $453888 $453888 $4546113
2022 $5000000 475 $453888 $453888 $4546113
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $9305000 $4322988 $13627988 $36372013
000005454$
050625464$7541
0050007604$0000005$
2017
2017
2017
P
P
P
or round down to
Ϳώ Ϳπ ͳ ϜϘ in the last step
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Solving for Amortization Structure (Contrsquod) presented by
38
Remaining unknowns hellipnd so forth will be solved just in time as well
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Adjusting for Target Proceeds presented by
39
If there is too much principal (or if there are too many proceeds) reduce target debt service
If there is too little principal (or if there are too few proceeds) increase target debt service
To solve for a target par or proceeds amount
Make an initial guess for target debt service
Rescale accordingly
0
01
P
PDSDS
TTT
ldquoDST1rdquo = New target debt service
ldquoDSTT0rdquo = Initial target debt service
ldquoPTrdquo = Target par amount
ldquoP0rdquo = Par amount from initial target debt service
Iterate if necessary
1
1
n
TnTnT
P
PDSDS
It may be necessary to adjust by taking the average when within one denomination
22
2
1
1
T
n
nT
n
nTnT
P
P
DS
P
DSDS
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
40
Example Target principal $40000000 Coupons As shown below Initial target debt service $5000000
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5000000 $3250000 300 $1747400 $4997400 $2600
2016 $5000000 $3345000 300 $1649900 $4994900 $5100
2017 $5000000 $3450000 350 $1549550 $4999550 $450
2018 $5000000 $3570000 500 $1428800 $4998800 $1200
2019 $5000000 $3745000 500 $1250300 $4995300 $4700
2020 $5000000 $3935000 500 $1063050 $4998050 $1950
2021 $5000000 $4130000 500 $866300 $4996300 $3700
2022 $5000000 $4335000 475 $659800 $4994800 $5200
2023 $5000000 $4545000 475 $453888 $4998888 $1113
2024 $5000000 $4760000 500 $238000 $4998000 $2000
Total $50000000 $39065000 $10906988 $49971988 $28013
346721195$
00006539$
00000040$0000005$
1
1
T
T
DS
DS
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Year
Target Debt
Service Principal Coupon Interest Debt Service
Difference
between
Target and
Actual DS
2015 $5119672 $3330000 300 $1789375 $5119375 $297
2016 $5119672 $3430000 300 $1689475 $5119475 $197
2017 $5119672 $3530000 350 $1586575 $5116575 $3097
2018 $5119672 $3655000 500 $1463025 $5118025 $1647
2019 $5119672 $3835000 500 $1280275 $5115275 $4397
2020 $5119672 $4030000 500 $1088525 $5118525 $1147
2021 $5119672 $4230000 500 $887025 $5117025 $2647
2022 $5119672 $4440000 475 $675525 $5115525 $4147
2023 $5119672 $4650000 475 $464625 $5114625 $5047
2024 $5119672 $4875000 500 $243750 $5118750 $922
Total $51196723 $40005000 $11168175 $51173175 $23548
Debt Amortization
Adjusting for Target Proceeds (Contrsquod) presented by
41
Example (contrsquod) Target principal $40000000 Coupons As shown below Initial target debt service $5000000 Second target debt service $511967234
Attempt Target Debt Service Resultant Principal Solution Method
1 $500000000 $3906500000 Rescale
2 511967234 4000500000 Rescale
3 511903246 3999500000 Rescale
4 511935240 4000000000 Average
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonus Excel Functions
Bond cash flows literacy intermediate bond math (Part 1)
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonus Excel Functions
Using PRICE() presented by
43
Needs to be supplemented for
Par bonds
Rounding and
Call provisions for premium bonds
Effective form for bonds callable at
par is as follows
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 100
=IF(B3=B4100TRUNC(PRICE(B1IF(AND(B3gtB4B2gtB5)B5B2)B3B41002)3))
Check for par bond
Round down to 3 decimal
places Check for premium coupon using
call date as maturity if needed
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonus Excel Functions
Using PRICE() presented by
44
For bonds with multiple call prices must evaluate result for
each case
=IF(B3=B4100TRUNC(MIN(
PRICE(B1 B2B3B41002) PRICE(B1
B5B3B4B62) PRICE(B1 B7B3B4B82) PRICE(B1 B9B3B4B102)
)3))
A B
1 Delivery 5142014
2 Maturity 512028
3 Coupon 500
4 Yield 365
5 Call Date1 512024
6 Call Price1 102
7 Call Date2 512025
8 Call Price2 101
9 Call Date3 512026
10 Call Price3 100
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
3
7
Bonus Excel Functions
Using EDATE() and EOMONTH() presented by
45
Used to create regularly aligned dates for principal
amortization or debt service schedules
=EOMONTH(A25)+1
=EDATE(A66)
A B C D
1 Date Principal Coupon Interest
2 5142014
1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
1112016 2210000
8 512017 1105000 400 2210000
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonus Excel Functions
Using SUMPRODUCT() presented by
46
Used to calculate interest for entire bond series (with multiple
coupons and principal amounts)
Tip Values
in last cells
must not be
blank
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B6B$8C6C$8)2
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Bonus Excel Functions
Using YEARFRAC() presented by
47
Used to calculate interest for irregular periods and for
ACTACT day count basis
Tip Allows
for the same
formula to
be used the
cash flow
schedule
A B C D
1 Date Principal Coupon Interest
2 5142014
3 1112014 $4439417
4 512015 $1000000 200 4785000
5 1112015 3785000
6 512016 1050000 300 3785000
7 1112016 2210000
8 512017 1105000 400 2210000
=SUMPRODUCT(B3B$8C3C$8)YEARFRAC(A2A3)
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Questions presented by
48
Thank you for your participation
A Certificate of Attendance will be emailed to you within a week
For MCLE credit please email cdiac_educationtreasurercagov
The video and transcript of this webinar will be available on CDIACrsquos website in the near future Please contact CDIAC if you would like to be notified when they are posted
Recommended