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McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
Fundamentals of Corporate
Finance
Sixth Edition
Richard A. Brealey
Stewart C. Myers
Alan J. Marcus
Slides by
Matthew Will
Chapter 5
McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved
Valuing Bonds
6- 2
Topics Covered
The Bond Market Interest Rates and Bond Prices Current Yield and Yield to Maturity Bond Rates and Returns The Yield Curve Corporate Bonds and the Risk of Default
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Bonds
Terminology Bond - Security that obligates the issuer to
make specified payments to the bondholder. Coupon - The interest payments made to the
bondholder. Face Value (Par Value or Principal Value) - Payment
at the maturity of the bond. Coupon Rate - Annual interest payment, as a
percentage of face value.
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Bonds
WARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.
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Bond Pricing
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
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Bond Cash Flows
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Bond Pricing
Example
What is the price of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.
95.081,1$
)0215.1(
050,1
)0215.1(
50
)0215.1(
50321
PV
PV
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?
37.082,1$
)01075.1(
025,1
)01075.1(
25...
)01075.1(
25
)01075.1(
256521
PV
PV
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Treasury Yields
The interest rate on 10-year U.S. Treasury bonds
0
2
4
6
8
10
12
14
1619
00
1905
1910
1915
1920
1925
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Year
Yie
ld %
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 5.0 %?
000,1$
)050.1(
050,1
)050.1(
50
)050.1(
50321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 8 %?
69.922$
)08.1(
050,1
)08.1(
50
)08.1(
50321
PV
PV
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year, instead of once
doubles the total number of cash flows to be discounted
in the PV formula.
Discount Rate
Since the time periods are now half years, the discount rate is also
changed from the annual rate to the half year rate.
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Interest Rate Risk
The value of the 5% bond falls as interest rates rise
700
800
900
1,000
1,100
1,200
0 2 4 6 8 10 12 14 16
Interest rate (%)
Bo
nd
pri
ce (
$)
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Interest Rate Risk
-
500
1,000
1,500
2,000
2,500
3,000
0 2 4 6 8 10
YTM
$ B
on
d P
ric
e
30 yr bond
3 yr bond
When the interest rate equals the 5.0% coupon rate, both
bonds sell at face value
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Bond Yields
Current Yield - Annual coupon payments divided by bond price.
Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price.
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Bond Yields
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
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Bond Yields
Example
What is the YTM of a 5.0 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95.
95.081,1$
)1(
050,1
)1(
50
)1(
50321
PV
rrrPV
YTM = 2.15%
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Bond Yields
WARNINGWARNINGCalculating YTM by hand can be very tedious.
It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.
6- 20
Bond Yields
Rate of Return - Earnings per period per dollar invested.
Rate of return =total income
investment
Rate of return =Coupon income + price change
investment
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Bond Valuation Spreadsheet
Valuing bonds using a spreadsheet
5.0 % coupon 6.0% couponmaturing Feb 2011 10-year maturity
Settlement date 2/15/08 1/1/00Maturity date 2/15/11 1/1/10Annual coupon rate 0.05 0.06Yield to maturity 0.0215 0.07Redemption value (% of face value) 100 100Coupon payments per year 1 1
Bond price (% of par) 108.195 92.976
=PRICE(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
6- 22
Interest Rate Risk
600
700
800
900
1,000
1,100
1,200
1,300
1,400
0 5 10 15 20 25 30
Bo
nd
Pri
ce
Time to Maturity
Price path for Premium Bond
Price path for Discount Bond
Today Maturity
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Bond Yield Spreadsheet
Finding yield to maturity using a spreadsheetFeb 2011 maturity bond, coupon rate = 5.0%, maturity = 3 years
Annual coupons Semiannual coupons
Settlement date 2/15/08 2/15/08Maturity date 2/15/11 2/15/11Annual coupon rate 0.05 0.05Bond price 108.195 108.195Redemption value (% of face value) 100 100Coupon payments per year 1 2
Yield to maturity (decimal) 0.0215 0.0216
=YIELD(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
6- 24
The Yield Curve
Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date.
Yield Curve - Graph of the term structure.
6- 25
The Yield Curve
0
1
2
3
4
5
61 3 5 7 9
11
13
15
17
19
21
23
25
27
29
Maturity (years)
Yie
ld %
Treasury strips are bonds that make a single payment. The yields on Treasury strips in February 2008 show that investors received a higher yield on longer term bonds.
6- 26
Corporate Bonds
Zero coupons Floating rate bonds Convertible bonds
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Nominal and Real rates
0
2
4
6
8
10
12
14
Per
cen
t
Year
Yield on UK nominal bonds
Yield on UK indexed bonds
6- 28
Default Risk
Credit risk Default premium Investment grade Junk bonds
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Default Risk
StandardMoody' s & Poor's Safety
Aaa AAA The strongest rating; ability to repay interest and principalis very strong.
Aa AA Very strong likelihood that interest and principal will berepaid
A A Strong ability to repay, but some vulnerability to changes incircumstances
Baa BBB Adequate capacity to repay; more vulnerability to changesin economic circumstances
Ba BB Considerable uncertainty about ability to repay.B B Likelihood of interest and principal payments over
sustained periods is questionable.Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
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Default Risk
0
2
4
6
8
10
12Y
ield
sp
read
%
Junk bonds
Baa-rated bonds
Aaa-rated bonds
Yield spreads between corporate and 10-year Treasury bonds
6- 31
Web Resources
