CHAPTER 6 Interest Rates and Bond Valuation 199
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–17)
LO 2 1. Interpreting Bond Yields Is the yield to maturity on a bond the same thing
as the required return? Is YTM the same thing as the coupon rate? Suppose
today a 10 percent coupon bond sells at par. Two years from now, the
required return on the same bond is 8 percent. What is the coupon rate on
the bond now? The YTM?
LO 2 2. Interpreting Bond Yields Suppose you buy a 7 percent coupon, 20-year
bond today when it’s first issued. If interest rates suddenly rise to 15 percent,
what happens to the value of your bond? Why?
LO 2 3. Bond Prices Vulcan, Inc., has 7 percent coupon bonds on the market that
have 13 years left to maturity. The bonds make annual payments and have a
par value of $1,000. If the YTM on these bonds is 8.4 percent, what is the
current bond price?
LO 2 4. Bond Yields The Petit Chef Co. has 7 percent coupon bonds on the market
with nine years left to maturity. The bonds make annual payments and have a
par value of $1,000. If the bonds currently sell for $1,038.50, what is the YTM?
LO 2 5. Coupon Rates Big Canyon Enterprises has bonds on the market making
annual payments, with 12 years to maturity, a par value of $1,000, and a
price of $1,030. At this price, the bonds yield 6.14 percent. What must the
coupon rate be on the bonds?
LO 2 6. Bond Prices Dufner Co. issued 15-year bonds one year ago at a coupon rate of
4.8 percent. The bonds make semiannual payments. If the YTM on these bonds
is 5.3 percent, what is the current dollar price assuming a $1,000 par value?
LO 2 7. Bond Yields Parkway Void Co. issued 15-year bonds two years ago at a
coupon rate of 5.4 percent. The bonds make semiannual payments. If these
bonds currently sell for 106 percent of par value, what is the YTM?
LO 2 8. Coupon Rates Henley Corporation has bonds on the market with 10.5
years to maturity, a YTM of 5.7 percent, a par value of $1,000, and a current
price of $945. The bonds make semiannual payments. What must the
coupon rate be on the bonds?
LO 4 9. Calculating Real Rates of Return If Treasury bills are currently paying 4.7
percent and the inflation rate is 1.9 percent, what is the approximate real rate
of interest? The exact real rate?
LO 4 10. Inflation and Nominal Returns Suppose the real rate is 1.8 percent and the
inflation rate is 3.7 percent. What rate would you expect to see on a Treasury bill?
LO 4 11. Nominal and Real Returns An investment offers a total return of 12 percent
over the coming year. Alex Hamilton thinks the total real return on this
investment will be only 9 percent. What does Alex believe the inflation rate
will be over the next year?
LO 4 12. Nominal versus Real Returns Say you own an asset that had a total return
last year of 12.1 percent. If the inflation rate last year was 3.4 percent, what
was your real return?
200 PART 4 Valuing Stocks and Bonds
LO 2 13. Using Treasury Quotes Locate the Treasury issue in Figure 6.3 maturing
in February 2029. What is its coupon rate? What is the dollar bid price for a
$1,000 par value bond? What was the previous day’s asked price for a $1,000
par value bond?
LO 2 14. Using Treasury Quotes Locate the Treasury bond in Figure 6.3 maturing in
May 2037. Is this a premium or a discount bond? What is its current yield?
What is its yield to maturity? What is the bid-ask spread for a $1,000 par
value bond?
LO 2 15. Zero Coupon Bonds You find a zero coupon bond with a par value of
$10,000 and 13 years to maturity. If the yield to maturity on this bond is 4.7
percent, what is the price of the bond? Assume semiannual compounding
periods.
LO 2 16. Valuing Bonds Lion Corp. has a $2,000 par value bond outstanding with a
coupon rate of 3.8 percent paid semiannually and 13 years to maturity. The
yield to maturity of the bond is 4.9 percent. What is the dollar price of the
bond?
LO 2 17. Valuing Bonds Union Local School District has bonds outstanding with a
coupon rate of 3.2 percent paid semiannually and 16 years to maturity. The
yield to maturity on these bonds is 3.7 percent and the bonds have a par
value of $5,000. What is the dollar price of the bonds?
INTERMEDIATE (Questions 18–33)
LO 2 18. Bond Price Movements Bond X is a premium bond making semiannual
payments. The bond has a coupon rate of 7.5 percent, a YTM of 6 percent,
and 13 years to maturity. Bond Y is a discount bond making semiannual
payments. This bond has a coupon rate of 6 percent, a YTM of 7.5 percent,
and also 13 years to maturity. What are the prices of these bonds today
assuming both bonds have a $1,000 par value? If interest rates remain
unchanged, what do you expect the prices of these bonds to be in 1 year?
In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here?
Illustrate your answers by graphing bond prices versus time to maturity.
LO 2 19. Interest Rate Risk Both Bond Bill and Bond Ted have 5.8 percent coupons,
make semiannual payments, and are priced at par value. Bond Bill has 5
years to maturity, whereas Bond Ted has 25 years to maturity. If interest
rates suddenly rise by 2 percent, what is the percentage change in the price
of Bond Bill? Of Bond Ted? Both bonds have a par value of $1,000. If rates
were to suddenly fall by 2 percent instead, what would the percentage change
in the price of Bond Bill be then? Of Bond Ted? Illustrate your answers by
graphing bond prices versus YTM. What does this problem tell you about
the interest rate risk of longer-term bonds?
LO 2 20. Interest Rate Risk Bond J has a coupon rate of 4 percent. Bond K has a
coupon rate of 14 percent. Both bonds have 17 years to maturity, a par value
of $1,000, and a YTM of 8 percent, and both make semiannual payments. If
interest rates suddenly rise by 2 percent, what is the percentage price change
of these bonds? What if rates suddenly fall by 2 percent instead? What does
this problem tell you about the interest rate risk of lower-coupon bonds?
CHAPTER 6 Interest Rates and Bond Valuation 201
LO 2 21. Bond Yields Bart Software has 5.7 percent coupon bonds on the market
with 22 years to maturity. The bonds make semiannual payments and
currently sell for 97 percent of par. What is the current yield? The YTM?
The effective annual yield?
LO 2 22. Bond Yields BDJ Co. wants to issue new 25-year bonds for some
much-needed expansion projects. The company currently has 4.8 percent
coupon bonds on the market that sell for $1,028, make semiannual
payments, have a $1,000 par value, and mature in 25 years. What coupon
rate should the company set on its new bonds if it wants them to sell at
par?
LO 2 23. Accrued Interest You purchase a bond with an invoice price of $1,043. The
bond has a coupon rate of 4.7 percent, semiannual coupons, and a $1,000
par value, and there are five months to the next coupon date. What is the
clean price of the bond?
LO 2 24. Accrued Interest You purchase a bond with a coupon rate of 5.2 percent,
semiannual coupons, and a clean price of $993. If the next coupon payment
is due in two months, what is the invoice price?
LO 2 25. Using Bond Quotes Suppose the following bond quote for IOU
Corporation appears in the financial page of today’s newspaper. Assume the
bond has a face value of $1,000, and the current date is April 15, 2019. What
is the yield to maturity of the bond? What is the current yield?
Company Last Last EST Vol
(Ticker) Coupon Maturity Price Yield (000s)
IOU (IOU) 7.60 Apr 15, 2031 91.645 ?? 1,827
LO 2 26. Zero Coupon Bonds Suppose your company needs to raise $40 million
and you want to issue 20-year bonds for this purpose. Assume the required
return on your bond issue will be 5.7 percent, and you’re evaluating two issue
alternatives: a 5.7 percent semiannual coupon bond and a zero coupon bond.
Your company’s tax rate is 21 percent.
a. How many of the coupon bonds would you need to issue to raise the $40
million? How many of the zeroes would you need to issue?
b. In 20 years, what will your company’s repayment be if you issue the
coupon bonds? What if you issue the zeroes?
c. Based on your answers in parts (a) and (b), why would you ever want to
issue the zeroes? To answer, calculate the firm’s aftertax cash outflows
for the first year under the two different scenarios. Assume that the IRS
amortization rules apply for the zero coupon bonds.
LO 2 27. Finding the Maturity You’ve just found a 10 percent coupon bond on the
market that sells for par value. What is the maturity on this bond? (Warning:
possible trick question.)
Use the following Treasury bond quotes to answer Questions 28–30: To calculate the
number of years until maturity, assume that it is currently May 2019. All of the
bonds have a $1,000 par value and pay semiannual coupons.
