Chapter

Brealey, Myers, and Allen

Principles of Corporate Finance

11th Global Edition

VALUING BONDS

3

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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

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• 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

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• 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

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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

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FIGURE 3.1 INTEREST RATE ON 10-YEAR TREASURIES

Yie

ld,

%

Year

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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

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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

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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

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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

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FIGURE 3.4 SPOT RATES ON U.S. TREASURY STRIPS, 02/2012

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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)

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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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FIGURE 3.5 ANNUAL U.S. INFLATION RATES, 1900-2011

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FIGURE 3.6 GLOBAL INFLATION RATES, 1900-2011

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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

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3-5 DEBT AND INTEREST RATES

• Debt and Interest Formula:

)1)(1(1 realnominal irr

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FIGURE 3.7 UK BOND YIELDS

10-year nominal interest rate

10-year real interest rate

Inte

rest

rat

e, %

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FIGURE 3.8 GOVT. BILLS VS. INFLATION, 1953-2011

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FIGURE 3.8 GOVT. BILLS VS. INFLATION, 1953-2011

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FIGURE 3.8 GOVT. BILLS VS. INFLATION, 1953-2011

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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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3-6 THE RISK OF DEFAULT

• Sovereign Bonds and Default Risk• Eurozone Debt

• Can’t print money to service domestic debts

• Money supply controlled by European Central Bank