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V: Debt Markets
12: Prices and Yields
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Time Value of Money
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
$100 £100¥100
M 300
Time Value of Money
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
$100 £100¥100100 1.61
Time Value of Money
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Time Value of Money
$1002016$1002017$1002015
3% 4%
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Time Line
$100 $200 -$100 $300 $100
3% 4% 5% 4% 5% 3%
Cash flows Positive and negative at or between compounding lines
Compounding lines Interest rates between compounding lines
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Time Line
$100 $200 -$100 $300 $100
3% 4% 5% 4% 5% 3%
Chapter 12: Prices and Yields
Bonds
© Oltheten & Waspi 2012
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Bonds
DocumentaryEvidence of Debt
Specifies Principal Coupon Maturity
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Principal: $1,000,000 Coupon: 6% Maturity:
Discovery Café Bond
February 17, 2019
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Contract specifies payments over time
$30,000
Discovery Café BondS
tart at the M
aturity D
ate
$30,000$1,000,000
Go back six months at a time2/17/15
$30,000$30,000$30,000 $30,000 $30,000 $30,000
8/17/15 8/17/16 8/17/17 8/17/182/17/16 2/17/17 2/17/18 2/17/19
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Yield versus Coupon
$30,000$1,000,000
$30,000$30,000
$30,000 $30,000
$30,000$30,000
$30,000
6% Coupon
$40,000$1,000,000
$40,000$40,000
$40,000 $40,000
$40,000$40,000
$40,0008% Coupon
-$1,000,000 (PV @ 8%)Market Yield:
Yield on alternative investments
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Yield versus Coupon
$30,000$1,000,000
$30,000$30,000
$30,000 $30,000
$30,000$30,000
$30,000
6% Coupon
$20,000$1,000,000
$20,000$20,000
$20,000 $20,000
$20,000$20,000
$20,0004% Coupon
-$1,000,000 (PV @ 4%)
Market Yield:Yield on alternative investments
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Price Yield Curve
40
60
80
100
120
140
0% 3% 6% 9% 12% 15% 18% 21%
n
n
tt 2
2
1
t
2Yd
1
P
2Yd
1
CPrice
Prices expressed as % of face value;100. not $100.
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Calculator Techniques
SDT = CPN = 6 (%) RDT = RV = 100 (%)
360 (Days in a Year) 2/Y (2 coupons per year)
YLD = 7 (%) PRI = [CPT] (%) AI = 0.000 (%)
Coupon Rate(Annual)
2.17 15
2.17 19
Chapter 12: Prices and Yields
Yields
© Oltheten & Waspi 2012
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Nominal Yield
Coupon Rate
Discovery Café$1,000,000. @ 6%
.Discovery Café Inc, incorporated in the State of Illinois (herein called the Company) for value received hereby promises to pay to the registered owner hereof on February 20, 2013 the sum of one million dollars and to pay interest semi-annually on August and February 20 of each year the sum of one half the annual interest thereon calculated at a semi-annual rate of half the stated annual interest of 6%.
due February 17, 2019
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Income Yield
Current or Income Yield
Price
CouponYield Income
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Promised Yield to Maturity
n
n
tt 2
2
1
t
2Yd
1
P
2Yd
1
CPrice
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Promised Yield to Maturity
22.630,965$
207
1
0000001$
207
1
00030$8
8
1
.
,,
.
,
tt
YTM=7%
Yield Income=6.214%Capital Gain=0.876%
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
YTM = 7.00%
$30,000$1,000,000
$30,000$30,000
$30,000 $30,000
$30,000$30,000
$30,000
6% Coupon
Priced to yield 7%
Matures @ 100
SDT =YLD =PRI =
RDT =RV =
CPN = 6.3602/Y
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
$30,000$1,000,000
6% Coupon
$30,000 $30,000
$30,000$30,000
$30,000
YTM = 5.00% (Buyer)
Priced to yield 5%
Matures @ 100
SDT =YLD =
RDT =RV =
CPN = 6.3602/Y
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Realized Yield = 12.432% (Seller)
$30,000
6% Coupon
Buy @ 96.563022YTM=7%
Sell @ 102.754063YTM=5%
SDT =PRI = 96.563022
RDT =RV = 102.754063
CPN = 6.3602/Y
2.17 16
2.17 15
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Realized Yield
hp
hp
tt 2
2
1
t
2Yd
1
Price Selling
2Yd
1
CPrice
22.630,965$
2124317
1
63.540,027,1$
2124317
1
00030$2
2
1
..
,
tt
12.4317%
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Effective Annual Rate
Including compounding
2
2
0.121 :annuallySemi
12
12
0.121 :monthly
365
365
0.121 :daily
12. :lycontinuous
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Bond Equivalent Yield
Twice the semi-annual rate
12% .1211.12362
annually 12.360%
Chapter 12: Prices and Yields © Oltheten & Waspi 2012
Yields
12 – 8:
V: Debt Markets I
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