Chapter
Brealey, Myers, and Allen
Principles of Corporate Finance
11th Global Edition
VALUING BONDS
3
3-3-22
3-1 USING THE PRESENT VALUE FORMULA TO VALUE BONDS
NN
r
C
r
C
r
C
)1(
000,1...
)1()1(PV
22
11
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• Example• Today is October 1, 2010; what is the value of the
following bond? An IBM bond pays $115 every September 30 for five years. In September 2015 it pays an additional $1,000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%).
84.161,1$
075.1
115,1
075.1
115
075.1
115
075.1
115
075.1
115PV 5432
3-1 USING THE PRESENT VALUE FORMULA TO VALUE BONDS
3-3-44
• Example: France• In October 2011 you purchase 100 euros of
bonds in France which pay a 5% coupon every year. If the bond matures in 2016 and the YTM is 3.0%, what is the value of the bond?
11.112€
024.1
0.105
024.1
5
024.1
5
024.1
5
024.1
5PV
5432
3-1 USING THE PRESENT VALUE FORMULA TO VALUE BONDS
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• Another Example: Japan• In July 2010 you purchase 200 yen of bonds in
Japan which pay an 8% coupon every year. If the bond matures in 2015 and the YTM is 4.5%, what is the value of the bond?
57.243¥
045.1
216
045.1
16
045.1
16
045.1
16
045.1
16PV 5432
3-1 USING THE PRESENT VALUE FORMULA TO VALUE BONDS
3-3-66
• Example: USA• In February 2012 you purchase a three-year
U.S. government bond. The bond has an annual coupon rate of 11.25%, paid semiannually. If investors demand a 0.085% semiannual return, what is the price of the bond?
40.331,1$
00085.1
25.1056
00085.1
25.56
00085.1
25.56
00085.1
25.56
00085.1
25.56
00085.1
25.56PV 65432
3-1 USING THE PRESENT VALUE FORMULA TO VALUE BONDS
3-3-77
3-2 HOW BOND PRICES VARY WITH INTEREST RATES
• Example, Continued: USA• Take the same three-year U.S. government
bond. If investors demand a 4.0% semiannual return, what is the new price of the bond?
05.1203$
04.125.1056
04.125.56
04.125.56
04.125.56
04.125.56
04.125.56PV 65432
3-3-99
80.00
85.00
90.00
95.00
100.00
105.00
110.00
115.00
Interest rate, %
3-2 HOW BOND PRICES VARY WITH INTEREST RATES
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FIGURE 3.2 MATURITY AND PRICES
When interest rate = 11.25% coupon, both bonds sell for face value
Interest rate, %
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3-2 HOW BOND PRICES VARY WITH INTEREST RATES
PV)(PV...
PV)(PV3
PV)(PV2
PV)(PV1Duration 321 TCTCCC
yield1duration(%) volatilityduration Modified
3-3-1212
3-2 DURATION CALCULATION
Year Payment Ct
PV(Ct) at 4.0%
Fraction of Total Value
[PV(Ct)/V]
Year × fraction of total value
[t × PV(Ct)/PV]
1 $90 $86.54 0.0666 0.0666
2 90 83.21 0.0640 0.1280
3 90 80.01 0.0615 0.1846
4 90 76.93 0.0592 0.2367
5 90 73.97 0.0569 0.2845
6 90 71.13 0.0547 0.3283
7 1090 828.31 0.6371 4.4598
PV = $1300.10
Total = duration = 5.60
3-3-1313
3-3 TERM STRUCTURE OF INTEREST RATES
• Short- and long-term rates are not always parallel
• September 1992–April 2000: U.S. short-term rates rose sharply while long-term rates declined
3-3-1414
3-3 TERM STRUCTURE OF INTEREST RATES
• Spot Rate: Actual interest rate today (t = 0)
• Yield To Maturity (YTM): IRR on interest-bearing instrument
YTM (r)
Year
1981
1987 & Normal
1976
1 5 10 20 30
3-3-1616
3-3 LAW OF ONE PRICE
• All interest-bearing instruments priced to fit term structure
• Accomplished by modifying asset price
• Modified price creates new yield, which fits term structure
• New yield called yield to maturity (YTM)
3-3-1717
3-3 YIELD TO MATURITY
• Example• $1,000 Treasury bond expires in 5
years. Pays coupon rate of 10.5%. What is YTM if market price is 107.88?
Calculate IRR = 8.5%
C0 C1 C2 C3 C4 C5
−1078.80 105 105 105 105 1105
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3-4 TERM STRUCTURE
• Expectations Theory• Term Structure and Capital Budgeting
• CF should be discounted using term structure info
• When rate incorporates all forward rates, use spot rate that equals project term
• Take advantage of arbitrage
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3-5 DEBT AND INTEREST RATES
• Classical Theory of Interest Rates (Economics)• Developed by Irving Fisher:
• Nominal Interest Rate = Actual rate paid when borrowing money
• Real Interest Rate = Theoretical rate paid when borrowing money; determined by supply and demand
Supply
Demand
$ Qty
r
Real r
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3-5 DEBT AND INTEREST RATES
• Nominal r = Real r + expected inflation (approximation)
• Real r theoretically somewhat stable• Inflation is a large variable
• Term structure of interest rates shows cost of debt
3-3-2424
FIGURE 3.7 UK BOND YIELDS
10-year nominal interest rate
10-year real interest rate
Inte
rest
rat
e, %
3-3-2828
3-6 THE RISK OF DEFAULT
• Corporate Bonds and Default Risk
• Payments promised to bondholders represent best-case scenario
• Most bonds’ safety judged by bond ratings
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TABLE 3.6 PRICES AND YIELDS OF CORPORATE BONDS, 01/2011
Issuer Coupon Maturity S&P Rating Price, % of Face Value
Yield to Maturity
Johnson & Johnson 5.15% 2017 AAA 122.88% 1.27%
Walmart 5.38 2017 AA 117.99 1.74
Walt Disney 5.88 2017 A 121.00 2.07
Suntrust Banks 7.13 2017 BBB 109.76 4.04
U.S. Steel 6.05 2017 BB 97.80 6.54 American
Stores 7.90 2017 B 97.50 8.49 Caesars
Entertainment 5.75 2017 CCC 41.95 25.70
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TABLE 3.7 BOND RATINGS
Moody's Standard & Poor's
and Fitch
Investment grade bonds
Aaa AAA Aa AA A A
Baa BBB
Junk bonds
Ba BB B B
Caa CCC
Ca CC
C C
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3-6 THE RISK OF DEFAULT
• Sovereign Bonds and Default Risk
• Sovereign debt is generally less risky than corporate debt
• Inflationary policies can reduce real value of debts
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3-6 THE RISK OF DEFAULT
• Sovereign Bonds and Default Risk• Foreign Currency Debt
• Default occurs when foreign government borrows dollars
• If crisis occurs, governments may run out of taxing capacity and default
• Affects bond prices, yield to maturity
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3-6 THE RISK OF DEFAULT
• Sovereign Bonds and Default Risk• Own Currency Debt
• Less risky than foreign currency debt
• Governments can print money to repay bonds
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