CF

473.32

7

Winter 2014

Bonds & Beyond

ch 7

What’s a Bond, Again?

“bond” = “note” = “debenture”

a loan a promise to pay

• certain amount

• on a certain day

• regular payments before that usually

What’s a Bond, Again?

no• ownership interest

• voting rights

interest• a cost of doing business

• tax deductible

bondholders have legal recourse• can lead to financial distress

Bonds Definitions

definitions Maturity date Face value aka: par value

Coupon payment Coupon rate Yield aka: yield to maturity

rate implied by market price & payments

amount paid per installment

coupon payment

face value

Purposes of Bond Pricing

not just to figure out bond prices

bond as benchmark explicit

• can develop formulas

Which projects should we choose?

Where should we get the money?

Purposes of Bond Pricing

because everything “has a price” all investments

• can be weighed together

can compare & separate out• risk

• return

• attractiveness

Bond Pricing “Theorems”

bonds of similar risk & maturity will yield about the same return

• regardless of the coupon rate

if open market

• flexible prices

• multiple participants

all information available

Real-World Bonds

The Bond Indenture• contract between company & bondholders

basic terms total amount of bonds issued description of security (property) sinking fund provisions call provisions details of protective covenants

Real-World Bonds

main types Government Bond Municipal Bond Corporate Bond

Real-World Bonds

Required Returns perceived risk = required return

flexibility = required return

Real-World Bonds

variations secured vs debenture senior debt vs subordinated sinking fund vs without convertible vs non-convertible registered vs bearer (aka coupon) time to maturity callable vs non-callable

Real-World Bonds

more variations disaster bonds income bonds put bond

• aka retractable bond

LYON bond

Real-World Bonds

still more variations call provisions

• call premium

• deferred call

• call protected

• Canada plus call

Real-World Bonds

one more variation Stripped bonds

» “Zero-coupon bonds”» “Zeroes”» “Deep discount bonds”

• coupon rate = 0 no interest payments YTM = par value - purchase price

Real-World Bonds

ratings High Grade

• AAA, AA strong ability to pay

Medium Grade• A, BBB

ability may be affected by circumstances

Real-World Bonds

ratings Low Grade

• BB, B, CCC, CC speculative

Very Low Grade• C

immediate danger of default

• D in default

Real-World Bond Markets

mainly OTC many issues little trading

• so prices may not be up to date

both primary market secondary market

exception: Treasury securities

Real-World Bond Markets

Secondary market once bond issued, price can vary

If market value < face value

• “discount bond” selling at a discount

• YTM > coupon rate

Real-World Bond Markets

Secondary market once bond issued, price can vary

If market value > face value

• “premium bond” selling at a premium

• YTM < coupon rate

Idealized Bonds

calculations assume idealized bond no

• default risk

• contract constraints

• “external” events markets exchange rates interest rates yield curve

• rational buyers & sellers

Bond Calculation Symbols

t number of periods

f bond’s face value• par value

c coupon (amount) paid each period

r rate per period converted into annual rate:

• “Yield”

• “YTM” “Yield To Maturity”

Bond Pricing

par valuecoupons PV PV Value Bond

lump sumannuity PVPV Value Bond

fcb PV PV PV

Bond-Pricing Equation

t

t

br

f

rr

-

c PV

1

1

11

Example 1

par value $1,000

coupon rate of 10% paid annually

years to maturity 5

Yield to Maturity (YTM) 11%

price?

f = $1,000.00

c = $100.00

t = 5

r = 0.11

PVb = ?

Example 1

t

t

br

f

rr

-

c PV

1

1

11

Example 1

5

5

1101

000001

1101101

11

00100).(

.,

.).(

-

.PVb

04963.PVb

Example 2

par value $1,000

coupon rate of 10% paid annually

years to maturity 20

Yield to Maturity (YTM) 8%

price?

f = $1,000.00

c = $100.00

t = 20

r = 0.08

PVb = ?

Example 2

5

0801

000001

0800801

11

0010020

).(

.,$

.).(

-

. $ PVb

361961 ., $ PVb

Example 3

par value $1,000

coupon rate of 8% paid semi-annually

years to maturity 7

Yield to Maturity (YTM) 5%

price?

f = $1,000.00

c = $40.00

t = 14

r = 0.05

PVb = ?

Semi-Annual Coupon

Example 3

14

14

0501

000001

0500501

11

0040).(

.,$

.).(

-

. $ PVb

01901. $ PVb

Semi-Annual Coupon

The Fisher Effect

connects together real rates nominal rates inflation

r

R

h

))(11( 1 hrR

111 h)r)((R

11

1

h

Rr

11

1

r

Rh

The Fisher Effect

connects together real rates nominal rates inflation

rr

rn

ri

r

R

h

111 )r)(r(r irn

11

1

i

nr r

rr

11

1

i

ni r

rr

The Fisher Effect

connects together real rates nominal rates inflation

r

R

h

))(11( 1 hrR

111 h)r)((R

11

1

h

Rr

11

1

r

Rh

Applied

we’re considering a project that will cost us $5,000 to start up generate $500/year in “profit”

equipment can be sold after 10 years for $1,000

What’s our return?

Applied

ProjectPV = -$5,000.00

c = $500.00

t = 10

f = $1,000.00

r = ?

t

t

br

f

rr

-

c PV

1

1

11

= 3.03%

Applied

we can borrow money 7%

we’re considering a project that will have $2,000 in start-up costs generate $600/year in “profit”

equipment sold for scrap after 15 years for $500

Should we do this?

Applied

ProjectPV = -$2,000.00

c = $600.00

t = 15

f = $500.00

r > 7%?

t

t

br

f

rr

-

c PV

1

1

11

= 8.90%

Applied

we have a line of credit 9%

we’re considering a project that will generate $300/year in “profit”

can re-sell equipment after 5 years for $2,000.00

What’s the most we should spend at start-up?

Applied

Projectc = $300.00

t = 5

f = $2.000.00

r = 9.00?

PV =?

t

t

br

f

rr

-

c PV

1

1

11

spend no more than $2,466.76 on start-up

Need to know

bonds different kinds how to use formulas keeping semi-annual & annual straight

projects how to apply bond formulas what the answers mean