V: Debt Markets
12: Prices and Yields
Time Value of Money
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Time Value of Money
¥100
$100
£100
M 300
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Time Value of Money
100
¥100
Chapter 12: Prices and Yields
1.61
$100
£100
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Time Value of Money
$1002015
Chapter 12: Prices and Yields
3%
$1002016
4%
$1002017
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Time Line
Interest rates
between
compounding lines
Compounding lines
3%
$100
4%
$200
5%
-$100
4%
5%
$300
3%
$100
Cash flows
 Positive and negative
 at or between compounding lines
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Time Line
3%
$100
4%
$200
Chapter 12: Prices and Yields
5%
-$100
4%
5%
$300
3%
$100
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Bonds
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Bonds
 Documentary
Evidence of Debt
 Specifies
 Principal
 Coupon
 Maturity
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Discovery Café Bond
 Principal: $1,000,000
 Coupon: 6%
 Maturity: February 16, 2020
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
 Contract specifies payments over time
2/16/17
8/16/16
8/16/17
2/16/18
$30,000
$30,000
$30,000
2/16/16
Chapter 12: Prices and Yields
2/16/19
8/16/18
$30,000
$30,000
8/16/19
Start at the Maturity Date
Discovery Café Bond
2/16/20
$30,000
$30,000
$30,000
$1,000,000
Go back six months at a time
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Yield versus Coupon
$40,000
$40,000
$40,000
$40,000
$40,000
$40,000
$40,000
8% Coupon
-$1,000,000 (PV @ 8%)
$30,000
6% Coupon
Chapter 12: Prices and Yields
Market Yield:
Yield on alternative investments
$30,000
$30,000
$30,000
$40,000
$1,000,000
$30,000
$30,000
$30,000
$30,000
$1,000,000
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Yield versus Coupon
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
4% Coupon
-$1,000,000 (PV @ 4%)
$30,000
6% Coupon
Chapter 12: Prices and Yields
Market Yield:
Yield on alternative investments
$30,000
$30,000
$30,000
$20,000
$1,000,000
$30,000
$30,000
$30,000
$30,000
$1,000,000
© Oltheten & Waspi 2012
Price Yield Curve
 Prices expressed as % of face value;
100. not $100.
2n
140
Price  
t 1
120
100
Ct
 Yd 
1 

2 

t

P
 Yd 
1 

2 

2n
80
60
40
0%
3%
Chapter 12: Prices and Yields
6%
9%
12%
15%
18%
21%
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Calculator Techniques




SDT =
CPN =
RDT =
RV =
2.16 16
6 (%)
2.16 20
100 (%)
 YLD =
 PRI =
 AI =
 360 (Days in a Year)
 2/Y (2 coupons per year)
Chapter 12: Prices and Yields
7 (%)
[CPT] (%)
0.000 (%)
Coupon Rate
(Annual)
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Yields
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Nominal Yield
 Coupon Rate
Discovery Café
$1,000,000. @ 6%
due February. 16, 2020
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%.
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Income Yield
 Current or Income Yield
Yield Income
Chapter 12: Prices and Yields
Coupon

Price
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Promised Yield to Maturity
2n
Price  
t 1
Chapter 12: Prices and Yields
Ct
 Yd 
1 

2 

t

P
 Yd 
1 

2 

2n
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Promised Yield to Maturity
Yield Income=6.214%
8

t 1
$30,000
 .07 
1 

2 

t

Capital Gain=0.876%
$1,000,000
 .07 
1 

2 

8
 $965,630.22
YTM=7%
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
YTM = 7.00%
$30,000
$30,000
$30,000
$30,000
$30,000
6% Coupon
Priced to
yield 7%
SDT = 2.16 16
YLD =
PRI =
Chapter 12: Prices and Yields
CPN = 6.
360
2/Y
$30,000
$30,000
$30,000
$1,000,000
Matures @
100
RDT = 2.16 20
RV =
© Oltheten & Waspi 2012
YTM = 5.00% (Buyer)
6% Coupon
$30,000
$30,000
$30,000
Priced
to yield
5%
SDT = 2.16 17
YLD =
Chapter 12: Prices and Yields
$30,000
$30,000
$30,000
$1,000,000
Matures @
100
CPN = 6.
360
2/Y
RDT = 2.16 20
RV =
© Oltheten & Waspi 2012
Realized Yield = 12.432% (Seller)
$30,000
6% Coupon
Buy @
96.563022
YTM=7%
Sell @
102.754063
YTM=5%
RDT = 2.16 17
RV = 102.754063
CPN = 6.
360
2/Y
SDT = 2.16 16
PRI = 96.563022
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Realized Yield
2 hp
Price  
t 1
Ct
 Yd 
1 

2 

t

Selling Price
 Yd 
1 

2 

2 hp
12.4317%
2

t 1
$30,000
 .124317 
1 

2 

Chapter 12: Prices and Yields
t

$1,027,540.63
 .124317 
1 

2 

2
 $965,630.22
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Effective Annual Rate
 Including compounding
2
 0.12 
Semi  annually : 1 
 
2 

12
 0.12 
monthly : 1 
 
12 

365
 0.12 
daily : 1 
 
365 

continuously : .12 
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Bond Equivalent Yield
 Twice the semi-annual rate
12.360% annually 


2 1.1236  1  .12  12%
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
Yields
 12 – 8:
Chapter 12: Prices and Yields
© Oltheten & Waspi 2012
V: Debt Markets I