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Financial Management: Theory and Practice

Eugene F. Brigham, Michael C. Ehrhardt

Chapter 5

Bonds, Bond Valuation, and Interest Rates - all with Video Answers

Educators

Chapter Questions

04:46

Problem 1

Jackson Corporation's bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $\$ 1,000$ par value, and the coupon interest rate is $8 \% .$ The bonds have a yield to maturity of $9 \% .$ What is the current market price of these bonds?

Narayan Hari
Narayan Hari
Numerade Educator
02:04

Problem 2

Wilson Wonders' bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $\$ 1,000$ par value, and the coupon interest rate is $10 \%$ The bonds sell at a price of $\$ 850 .$ What is their yield to maturity?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
04:46

Problem 3

Heath Foods' bonds have 7 years remaining to maturity. The bonds have a face value of $\$ 1,000$ and a yield to maturity of $8 \% .$ They pay interest annually and have a $9 \%$ coupon rate. What is their current yield?

Narayan Hari
Narayan Hari
Numerade Educator
01:44

Problem 4

The real risk-free rate of interest is $4 \% .$ Inflation is expected to be $2 \%$ this year and $4 \%$ during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities?

Achintya Suden
Achintya Suden
Numerade Educator
02:38

Problem 5

A Treasury bond that matures in 10 years has a yield of $6 \% .$ A 10 -year corporate bond has a yield of $9 \%$. Assume that the liquidity premium on the corporate bond is $0.5 \% .$ What is the default risk premium on the corporate bond?

Sarah Vo
Sarah Vo
Numerade Educator
01:44

Problem 6

The real risk-free rate is $3 \%$, and inflation is expected to be $3 \%$ for the next 2 years. A 2 -year Treasury security yields $6.3 \% .$ What is the maturity risk premium for the 2-year security?

Achintya Suden
Achintya Suden
Numerade Educator
02:08

Problem 7

Renfro Rentals has issued bonds that have a $10 \%$ coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $\$ 1,000$, and a yield to maturity of $8.5 \% .$ What is the price of the bonds?

Narayan Hari
Narayan Hari
Numerade Educator
03:10

Problem 8

Thatcher Corporation's bonds will mature in 10 years. The bonds have a face value of $\$ 1,000$ and an $8 \%$ coupon rate, paid semiannually. The price of the bonds is $\$ 1,100 .$ The bonds are callable in 5 years at a call price of $\$ 1,050 .$ What is their yield to maturity? What is their yield to call?

Narayan Hari
Narayan Hari
Numerade Educator
01:27

Problem 9

The Garraty Company has two bond issues outstanding. Both bonds pay $\$ 100$ annual interest plus $\$ 1,000$ at maturity. Bond L has a maturity of 15 years, and Bond S a maturity of 1 year.
a. What will be the value of each of these bonds when the going rate of interest is $(1) 5 \%,(2) 8 \%,$ and (3) $12 \% ?$ Assume that there is only one more interest payment to be made on Bond S.
b. Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?

Vikash Ranjan
Vikash Ranjan
Numerade Educator
02:39

Problem 10

The Brownstone Corporation bonds have 5 years remaining to maturity. Interest is paid annually; the bonds have a $\$ 1,000$ par value; and the coupon interest rate is $9 \%$
a. What is the yield to maturity at a current market price of (1)$\$ 829$ or $(2) \$ 1,104 ?$
b. Would you pay $\$ 829$ for one of these bonds if you thought that the appropriate rate of interest was $12 \%-$ that is, if $\mathrm{r}_{\mathrm{d}}=12 \% ?$ Explain your answer.

Anand Jangid
Anand Jangid
Numerade Educator
02:36

Problem 11

Seven years ago, Goodwynn \& Wolf Incorporated sold a 20 -year bond issue with a $14 \%$ annual coupon rate and a $9 \%$ call premium. Today, G\&W called the bonds. The bonds originally were sold at their face value of $\$ 1,000$. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.

Andrew Davis
Andrew Davis
Numerade Educator
02:39

Problem 12

A 10 -year, $12 \%$ semiannual coupon bond with a par value of $\$ 1,000$ may be called in 4 years at a call price of $\$ 1,060$. The bond sells for $\$ 1,100$. (Assume that the bond has just been issued.)
a. What is the bond's yield to maturity?
b. What is the bond's current yield?
c. What is the bond's capital gain or loss yield?
d. What is the bond's yield to call?

Anand Jangid
Anand Jangid
Numerade Educator
01:23

Problem 13

You just purchased a bond that matures in 5 years. The bond has a face value of $\$ 1,000$ and has an $8 \%$ annual coupon. The bond has a current yield of $8.21 \% .$ What is the bond's yield to maturity?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
02:39

Problem 14

A bond that matures in 7 years sells for $\$ 1,020$. The bond has a face value of $\$ 1,000$ and a yield to maturity of $10.5883 \%$. The bond pays coupons semiannually. What is the bond's current yield?

Anand Jangid
Anand Jangid
Numerade Educator
02:39

Problem 15

Absolom Motors' $14 \%$ coupon rate, semiannual payment, $\$ 1,000$ par value bonds that mature in 30 years are callable 5 years from now at a price of $\$ 1,050 .$ The bonds sell at a price of $\$ 1,353.54$, and the yield curve is flat. Assuming that interest rates in the economy are expected to remain at their current level, what is the best estimate of the nominal interest rate on new bonds?

Anand Jangid
Anand Jangid
Numerade Educator
03:08

Problem 16

A bond trader purchased each of the following bonds at a yield to maturity of $8 \%$ Immediately after she purchased the bonds, interest rates fell to $7 \% .$ What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table:

Jessica Bisagno
Jessica Bisagno
Numerade Educator
01:41

Problem 17

An investor has two bonds in his portfolio. Each bond matures in 4 years, has a face value of $\$ 1,000$, and has a yield to maturity equal to $9.6 \%$. One bond, Bond $C$, pays an annual coupon of $10 \% ;$ the other bond, Bond $Z$, is a zero coupon bond. Assuming that the yield to maturity of each bond remains at $9.6 \%$ over the next 4 years, what will be the price of each of the bonds at the following time periods? Fill in the following table:

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:44

Problem 18

The real risk-free rate is $2 \% .$ Inflation is expected to be $3 \%$ this year, $4 \%$ next year, and then $3.5 \%$ thereafter. The maturity risk premium is estimated to be $0.0005 \times$ $(t-1),$ where $t-$ number of years to maturity. What is the nominal interest rate on a 7 -year Treasury security?

Achintya Suden
Achintya Suden
Numerade Educator
01:44

Problem 19

Assume that the real risk-free rate, $r^{*},$ is $3 \%$ and that inflation is expected to be $8 \%$ in Year $1,5 \%$ in Year $2,$ and $4 \%$ thereafter. Assume also that all Treasury securities are highly liquid and free of default risk. If 2 -year and 5 -year Treasury notes both yield $10 \%,$ what is the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is $\mathrm{MRP}_{5}$ minus $\mathrm{MRP}_{2}$ ?

Achintya Suden
Achintya Suden
Numerade Educator
00:56

Problem 20

Due to a recession, the inflation rate expected for the coming year is only $3 \%$ However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above $3 \%$. Assume that the real risk-free rate is $\mathrm{r}^{*}=2 \%$ for all maturities and that there are no maturity premiums. If 3 -year Treasury notes yield 2 percentage points more than 1-year notes, what inflation rate is expected after Year $1 ?$

Neel Faucher
Neel Faucher
Numerade Educator
01:33

Problem 21

Suppose Hillard Manufacturing sold an issue of bonds with a 10 -year maturity, a $\$ 1,000$ par value, a $10 \%$ coupon rate, and semiannual interest payments.
a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to $6 \%$. At what price would the bonds sell?
b. Suppose that, 2 years after the initial offering, the going interest rate had risen to $12 \% .$ At what price would the bonds sell?.
c. Suppose that the conditions in part a existed-that is, interest rates fell to $6 \% 2$ years after the issue date. Suppose further that the interest rate remained at $6 \%$ for the next 8 years. What would happen to the price of the bonds over time?

Carson Merrill
Carson Merrill
Numerade Educator
01:27

Problem 22

Arnot International's bonds have a current market price of $\$ 1,200$. The bonds have an $11 \%$ annual coupon payment, a $\$ 1,000$ face value, and 10 years left until maturity. The bonds may be called in 5 years at $109 \%$ of face value (call price $=$ $\$ 1,090)$
a. What is the yield to maturity?
b. What is the yield to call, if they are called in 5 years?
c. Which yield might investors expect to earn on these bonds, and why?
d. The bond's indenture indicates that the call provision gives the firm the right to call them at the end of each year beginning in Year $5 .$ In Year 5 , they may be called at $109 \%$ of face value, but in each of the next 4 years the call percentage will decline by 1 percentage point. Thus, in Year 6 they may be called at $108 \%$ of face value, in Year 7 they may be called at $107 \%$ of face value, and so on. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?

Vikash Ranjan
Vikash Ranjan
Numerade Educator
06:21

Problem 23

Start with the partial model in the file $F M 12$ Ch 05 P24 Build a Model.xis from the textbook's Web site. Rework Problem $5-12$. After completing parts a through $\mathrm{d}$ answer the following related questions.
e. How would the price of the bond be affected by changing interest rates? (Hint:
Conduct a sensitivity analysis of price to changes in the yield to maturity, which is also the going market interest rate for the bond. Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an oversimplification, but assume it anyway for purposes of this problem.)
f. $\quad$ Now assume that the date is October 25,2007 . Assume further that our $12 \%$ 10-year bond was issued on July $1,2007,$ is callable on July $1,2011,$ at $\$ 1,060,$ will mature on June $30,2017,$ pays interest semiannually (January 1 and July 1 ), and sells for $\$ 1,100$. Use your spreadsheet to find (1) the bond's yield to maturity and (2) its yield to call.

Heather Duong
Heather Duong
Numerade Educator