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Investments

Zvi Bodie, Alex Kane, Alan J. Marcus

Chapter 14

Bond Prices and Yields - all with Video Answers

Educators

Chapter Questions

Problem 1

Define the following types of bonds:
a. Catastrophe bond
b. Eurobond
c. Zero-coupon bond
d. Samurai bond
e. Junk bond
f. Convertible bond
8. Serial bond
h. Equipment obligation bond
L. Original-issue-discount bond
f. Indexed bond
k. Callable bond
$L$ Puttable bond

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Problem 2

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?

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02:39

Problem 3

The stated yield to maturity and realized compound yield to maturity of a (defaull-free) zerocoupon bond are always equal. Why?

Narayan Hari
Narayan Hari
Numerade Educator
01:10

Problem 4

Why do bond prices go down when interest rates go up? Don't bond lenders like to receive high interest rates?

Brooke Bussoletti
Brooke Bussoletti
Numerade Educator

Problem 5

A bond with an annual coupon rate of $4.8 \%$ sells for $$\$ 970$$. What is the bond's current yield?

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03:45

Problem 6

Which security has a higher effecrive annual interest rate?
a. A 3-month T-bill selling at $$\$ 97,645$$ with par value $$\$ 100,000$$.
b. A coupon bond selling at par and paying a $10 \%$ coupon semiannually.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 7

Treasury boads 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?

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03:39

Problem 8

Consider a bond with a $10 \%$ coupon and yield to maturity $=8 \%$. If the bond's yield to maturity remains constant, then in one year, will the bond price be higher, lower, or unchanged? Why?

Narayan Hari
Narayan Hari
Numerade Educator
02:39

Problem 9

Consider an $8 \%$ coupon bond selling for $$\$ 953.10$$ with three years until maturity making annual coupon payments. The interest rates in the next three years will be, with certainty, $r_1=8 \%, r_2=$ $10 \%$, and $r_3=12 \%$. Calculate the bond's (a) yield to maturity and (b) realized compound yield.

Anand Jangid
Anand Jangid
Numerade Educator

Problem 10

Assume you have a 1-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 the prices of (i) the zerocoupon bond; (ii) the $8 \%$ coupon bond; (iii) the $10 \%$ coupon bond?
b. If you expect their yields to maturity to be $8 \%$ at the beginning of next year, what will be the price of each bond?
c. What is your before-tax holding-period return on each bond?
d. If your tax bracket is $30 \%$ on ordinary income and $20 \%$ on capital gains income, what will be the after-tax rate of return on each bond?
e. Recalculate your answers to parts $(b)$ - $(d)$ under the assumption that you expect the yields to maturity on each bond to be $7 \%$ at the beginning of next year.

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04:03

Problem 11

A 20 -year-maturity bond with par value of $$\$ 1,000$$ 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. $$\$ 1,050$$

Narayan Hari
Narayan Hari
Numerade Educator

Problem 12

Repeat Problem 11 using the same data, but now assume that the bond makes its coupon payments annually. Why are the yields you compute lower in this case?

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Problem 13

Fill in the table below for the following zero-coupon bonds, all of which have par values of $$\$ 1,000$$.
$$
\begin{array}{lcc}
\text { Price } & \text { Maturity (years) } & \begin{array}{l}
\text { Bond-Equivalent } \\
\text { Yield to Maturity }
\end{array} \\
\hline \text { a. } \$ 400 & 20 & \\
\text { b. } \$ 500 & 20 & - \\
\text { c. } \$ 500 & 10 & - \\
d- & 10 & 10 \% \\
\text { e. }- & 10 & 8 \% \\
t . \$ 400 & - & 8 \%
\end{array}
$$

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06:09

Problem 14

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.
a. Find the bond's price today and six months from now after the next coupon is paid.
b. What is the toxal ( 6 -month) rate of return on the bond?

Narayan Hari
Narayan Hari
Numerade Educator

Problem 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 100.125. What is the invoice price of the bond? The coupon period has 182 days.

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Problem 16

A bond has a current yield of $9 \%$ and a yield to maturity of $10 \%$. Is the bond selling above or below par value? Explain.

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03:39

Problem 17

Is the coupon rate of the bond in Problem 16 more or less than $9 \%$ ?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
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Problem 18

Return to Table 14.1, showing the cash flows for TIPS bonds.
a. What is the nominal rate of return on the bond in year 2 ?
b. What is the real rate of return in year 2 ?
c. What is the nominal rate of return on the bond in year 3 ?
d. What is the real rate of return in year 3 ?

Rashmi Sinha
Rashmi Sinha
Numerade Educator

Problem 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 (a) the first year; (b) the second year, and (c) the last year of the bond's life.

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Problem 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 originalissue-discount bond.

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Problem 21

A 30 -year-maturity. $7 \%$ 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 $6 \%$ ( $3 \%$ 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?

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Problem 22

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 (a) the stated and (b) the expected yield to maturity of the bonds? The bond makes its coupon payments annually.

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Problem 23

A 2-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 1 -year interest rate next year turns out to be (a) $8 \%$, (b) $10 \%$, (c) $12 \%$ ?

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Problem 24

Suppose that today's date is April 15. A bond with a $10 \%$ coupon paid semiannually every January 15 and July 15 is quored as selling at an ask price of 101.25 . If you buy the bond from a dealer today, what price will you pay for it?

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Problem 25

Assume that two firms issue bonds with the following characteristics. Both bonds are issued at par.
Ignoring credit quality, identify four features of these issues that might account for the lower coupon on the ABC debt. Explain.

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Problem 26

An investor believes that a bond may temporarily increase in credit risk. Which of the following woald be the most liquid method of exploiting this?
a. The purchase of a credit default swap.
b. The sale of a credit default swap.
c. The short sale of the bond.

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Problem 27

Which of the following most accurately describes the behavior of credit default swaps?
a. When credit risk increases, swap premiums increase.
b. When credit and interest rate risk increase, swap premiums increase.
c. When credit risk increases, swap premiums increase, but when interest rate risk increases, swap premiums decrease.

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Problem 28

Describe the likely effect on the yield to maturity of a bond resulting from:
a. An increase in the issuing firm's times-interest-earned ratio.
b. An increase in the issuing firm's debt-to-equity ratio.
c An increase in the issuing firm's quick ratio.

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Problem 29

These two bonds were issued five years ago, with terms given in the following table:
$$
\begin{array}{|c|c|c|}
\hline & 6 \% \text { Coupon } & \text { Floating-Rate } \\
\hline \text { Issue size } & \$ 250 \text { million } & \$ 280 \text { million } \\
\hline \text { Origina maturity } & 20 \text { years } & 15 \text { years } \\
\hline \text { Current price (\% of par) } & 93 & 98 \\
\hline \text { Current coupon } & 6 \% & 4 \% \\
\hline \text { Coupon adjusts } & \text { Fxed coupan } & \text { Every year } \\
\hline \text { Coupon reset nule } & - & 1 \text {-year T-bil rate }+2 \% \\
\hline \text { Callabe } & 10 \text { yesrs after issue } & 10 \text { years after issue } \\
\hline \text { Call price } & 106 & 102.50 \\
\hline \text { Sinking fund } & \text { None } & \text { None } \\
\hline \text { Yeld to maturity } & 6.9 \% & - \\
\hline \text { Price range since issued } & \$ 85-\$ 112 & \$ 97-\$ 102 \\
\hline
\end{array}
$$
a. Why is the price range greater for the $6 \%$ coupon bond than the floating-rate bond?
b. What factors could explain why the floating-rate bond is not always sold at par value?
c. Why is the call price for the floating-rate bond not of great importance to investors?
d. Is the probability of a call for the fixed-rate bond high or low?
e. If the firm were to issue a fixed-rate bond with a 15 -year maturity, what coupon rate would it need to offer to issue the bond at par value?
$f$. Why is an entry for yield to maturity for the floating-rate boad not appropriate?

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Problem 30

FinCorp issued two bonds with 20 -year maturities. Both bonds are callable at $$\$ 1,050$$. The first bond was issued at a deep discount with a coupon rate of $4 \%$ and a price of $$\$ 580$$ to yield $8.4 \%$. The second bond was issued at par value with a coupon rate of $8.75 \%$.
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 has the higher expected rate of return?
c. In what sense does the discount bond offer "implicit call protection"?

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Problem 31

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 I-year investment period if the bond is selling at a yield to maturity of $7 \%$ by the end of the ycar.
b. If you sell the bond after one year, 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-issuediscount tax treatment.
c. What is the after-tax holding-period return on the bond?
d. Find the realized compound yield before taxes for a 2 -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 2-year realized compound yield. Remember to take account of OID tax rules.

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