a. A three-month T-bill selling at $97,645.

b. A coupon bond selling at par and paying a 10% coupon semiannually.

2. Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par

value. What coupon rate would they have to pay in order to sell at par if they paid their

coupons annually?

3. Two bonds have identical times to maturity and coupon rates. One is callable at 105, the

other at 110. Which should have the higher yield to maturity? Why?

4. Consider a bond with a 10% coupon and with yield to maturity 8%. If the bond™s YTM

remains constant, then in one year, will the bond price be higher, lower, or unchanged?

Why?

5. Under the expectations hypothesis, if the yield curve is upward sloping, the market must

expect an increase in short-term interest rates. True/false/uncertain? Why?

6. A “fallen angel” bond is best defined as a bond issued:

a. Below investment grade.

b. At an original issue discount.

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c. As investment grade, but declined to speculative grade.

d. As a secured bond, but the collateral value declined below par value.

7. Under the liquidity preference theory, if inflation is expected to be falling over the next

few years, long-term interest rates will be higher than short-term rates.

True/false/uncertain? Why?

8. The yield curve is upward sloping. Can you conclude that investors expect short-term

interest rates to rise? Why or why not?

9. Consider a bond paying a coupon rate of 10% per year semiannually when the market

interest rate is only 4% per half year. The bond has three years until maturity.

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

330 Part THREE Debt Securities

a. Find the bond™s price today and six months from now after the next coupon is paid.

b. What is the total rate of return on the bond?

10. A 20-year maturity bond with par value $1,000 makes semiannual coupon payments at a

coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of

the bond if the bond price is:

a. $950

b. $1,000

c. $1,050

11. Redo problem 10 using the same data, but assume that the bond makes its coupon

payments annually. Why are the yields you compute lower in this case?

12. Return to Table 9.1 and calculate both the real and nominal rates of return on the TIPS

bond in the second and third years.

13. Fill in the table below for the following zero-coupon bonds, all of which have par

values of $1,000.

Maturity Bond-Equivalent

Price (years) Yield to Maturity

$400 20 ?

$500 20 ?

$500 10 ?

? 10 10%

? 10 8%

$400 ? 8%

14. Assume you have a one-year investment horizon and are trying to choose among three

bonds. All have the same degree of default risk and mature in 10 years. The first is a

zero-coupon bond that pays $1,000 at maturity. The second has an 8% coupon rate and

pays the $80 coupon once per year. The third has a 10% coupon rate and pays the $100

coupon once per year.

a. If all three bonds are now priced to yield 8% to maturity, what are their prices?

b. If you expect their yields to maturity to be 8% at the beginning of next year, what

will their prices be then? What is your rate of return on each bond during the one-

year holding period?

15. A bond with a coupon rate of 7% makes semiannual coupon payments on January 15

and July 15 of each year. The Wall Street Journal reports the ask price for the bond on

January 30 at 100:02. What is the invoice price of the bond? The coupon period has

182 days.

16. A bond has a current yield of 9% and a yield to maturity of 10%. Is the bond selling

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above or below par value? Explain.

17. Is the coupon rate of the bond in the previous problem more or less than 9%?

18. On May 30, 1999, Janice Kerr is considering the newly issued 10-year AAA corporate

bonds shown in the following exhibit:

Description Coupon Price Callable Call Price

Sentinal, due May 30, 2009 6.00% 100 Noncallable NA

Colina, due May 30, 2009 6.20% 100 Currently callable 102

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Essentials of Investments, Companies, 2003

Fifth Edition

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9 Bond Prices and Yields

a. Suppose that market interest rates decline by 100 basis points (i.e., 1%). Contrast the

effect of this decline on the price of each bond.

b. Should Kerr prefer the Colina over the Sentinal bond when rates are expected to rise

or to fall?

c. What would be the effect, if any, of an increase in the volatility of interest rates on

the prices of each bond?

19. A newly issued 20-year maturity, zero-coupon bond is issued with a yield to maturity of

8% and face value $1,000. Find the imputed interest income in the first, second, and last

year of the bond™s life.

20. A newly issued 10-year maturity, 4% coupon bond making annual coupon payments is

sold to the public at a price of $800. What will be an investor™s taxable income from the

bond over the coming year? The bond will not be sold at the end of the year. The bond

is treated as an original-issue discount bond.

21. A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity

is 20 years, and its yield to maturity is 8%.

a. Find the holding-period return for a one-year investment period if the bond is selling

at a yield to maturity of 7% by the end of the year.

b. If you sell the bond after one year when its yield is 7%, what taxes will you owe if

the tax rate on interest income is 40% and the tax rate on capital gains income is

30%? The bond is subject to original-issue discount (OID) tax treatment.

c. What is the after-tax holding-period return on the bond?

d. Find the realized compound yield before taxes for a two-year holding period,

assuming that (i) you sell the bond after two years, (ii) the bond yield is 7% at

the end of the second year, and (iii) the coupon can be reinvested for one year

at a 3% interest rate.

e. Use the tax rates in part (b) to compute the after-tax two-year realized compound

yield. Remember to take account of OID tax rules.

22. A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five

years at a call price of $1,100. The bond currently sells at a yield to maturity of 7%

(3.5% per half year).

a. What is the yield to call?

b. What is the yield to call if the call price is only $1,050?

c. What is the yield to call if the call price is $1,100, but the bond can be called in

two years instead of five years?

23. A 10-year bond of a firm in severe financial distress has a coupon rate of 14% and sells

for $900. The firm is currently renegotiating the debt, and it appears that the lenders will

allow the firm to reduce coupon payments on the bond to one-half the originally

contracted amount. The firm can handle these lower payments. What are the stated and

expected yields to maturity of the bonds? The bond makes its coupon payments

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annually.

24. A two-year bond with par value $1,000 making annual coupon payments of $100 is

priced at $1,000. What is the yield to maturity of the bond? What will be the realized

compound yield to maturity if the one-year interest rate next year turns out to be (a) 8%,

(b) 10%, (c) 12%?

25. The stated yield to maturity and realized compound yield to maturity of a (default-free)

zero-coupon bond will always be equal. Why?

26. Suppose that today™s date is April 15. A bond with a 10% coupon paid semiannually

every January 15 and July 15 is listed in The Wall Street Journal as selling at an ask

price of 101:04. If you buy the bond from a dealer today, what price will you pay for it?

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

332 Part THREE Debt Securities

27. Assume that two firms issue bonds with the following characteristics. Both bonds are

issued at par.

ABC Bonds XYZ Bonds

Issue size $1.2 billion $150 million

Maturity 10 years* 20 years

Coupon 9% 10%

Collateral First mortgage General debenture

Callable Not callable In 10 years

Call price None 110

Sinking fund None Starting in 5 years

*Bond is extendible at the discretion of the bondholder for an additional

10 years.

Ignoring credit quality, identify four features of these issues that might account for the

lower coupon on the ABC debt. Explain.

28. A large corporation issued both fixed and floating-rate notes five years ago, with terms

given in the following table:

9% Coupon Notes Floating-Rate Note

Issue size $250 million $280 million

Maturity 20 years 15 years

Current price (% of par) 93 98

Current coupon 9% 8%

Coupon adjusts Fixed coupon Every year

Coupon reset rule ” 1-year T-bill rate 2%

Callable 10 years after issue 10 years after issue

Call price 106 102

Sinking fund None None

Yield to maturity 9.9% ”

Price range since issued $85“$112 $97“$102

a. Why is the price range greater for the 9% coupon bond than the floating-rate note?

b. What factors could explain why the floating-rate note is not always sold at par

value?

c. Why is the call price for the floating-rate note not of great importance to investors?

d. Is the probability of call for the fixed-rate note high or low?

e. If the firm were to issue a fixed-rate note with a 15-year maturity, what coupon rate

would it need to offer to issue the bond at par value?

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f. Why is an entry for yield to maturity for the floating-rate note not appropriate?

29. Bonds of Zello Corporation with a par value of $1,000 sell for $960, mature in five

years, and have a 7% annual coupon rate paid semiannually.

a. Calculate the:

(1) Current yield.

(2) Yield-to-maturity.

(3) Horizon yield (also called realized compound yield) for an investor with a three-

year holding period and a reinvestment rate of 6% over the period. At the end of

three years the 7% coupon bonds with two years remaining will sell to yield 7%.

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Essentials of Investments, Companies, 2003

Fifth Edition

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9 Bond Prices and Yields

b. Cite one major shortcoming for each of the following fixed-income yield measures:

(1) Current yield.

(2) Yield to maturity.

(3) Horizon yield (also called realized compound yield).

30. Masters Corp. issues two bonds with 20-year maturities. Both bonds are callable at

$1,050. The first bond is issued at a deep discount with a coupon rate of 4% and a

price of $580 to yield 8.4%. The second bond is issued at par value with a coupon

rate of 83„4%.

a. What is the yield to maturity of the par bond? Why is it higher than the yield of the

discount bond?

b. If you expect rates to fall substantially in the next two years, which bond would you

prefer to hold?

c. In what sense does the discount bond offer “implicit call protection”?

31. A convertible bond has the following features:

Coupon 5.25%

Maturity June 15, 2017

Market price of bond $77.50

Market price of underlying common stock $28.00

Annual dividend $ 1.20

Conversion ratio 20.83 shares

Calculate the conversion premium for this bond.

32. a. Explain the impact on the offering yield of adding a call feature to a proposed bond

issue.

b. Explain the impact on the bond™s expected life of adding a call feature to a proposed

bond issue.

c. Describe one advantage and one disadvantage of including callable bonds in a

portfolio.

33. The yield to maturity on one-year zero-coupon bonds is 8%. The yield to maturity on

two-year zero-coupon bonds is 9%.

a. What is the forward rate of interest for the second year?

b. If you believe in the expectations hypothesis, what is your best guess as to the

expected value of the short-term interest rate next year?

c. If you believe in the liquidity preference theory, is your best guess as to next year™s

short-term interest rate higher or lower than in (b)?

34. Following are the spot rates and forward rates for three years. However, the labels got

mixed up. Can you identify which row of the interest rates represents spot rates and