Economics Chapter 7 Homework The price of the bond will fall and its YTM will rise

Chapter 7: Bonds and Their Valuation

Learning Objectives

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Chapter 7

Bonds and Their Valuation

Learning Objectives

After reading this chapter, students should be able to:

◆ Identify the different features of corporate and government bonds.

◆ Discuss how bond prices are determined in the market, what the relationship is between interest

rates and bond prices, and how a bond’s price changes over time as it approaches maturity.

◆ Calculate a bond’s yield to maturity and yield to call if it is callable, and determine the “true” yield.

◆ Explain the different types of risk that bond investors and issuers face, and discuss how a bond’s

terms and collateral can be changed to affect its interest rate.

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Lecture Suggestions

Chapter 7: Bonds and Their Valuation

Lecture Suggestions

This chapter serves two purposes. First, it provides important and useful information on bonds per se.

Second, it provides a good example of the use of time value concepts, so it reinforces the topics covered

in Chapter 5.

DAYS ON CHAPTER: 3 OF 56 DAYS (50-minute periods)

Chapter 7: Bonds and Their Valuation

Answers and Solutions

147

Answers to End-of-Chapter Questions

7-1 From the corporation’s viewpoint, one important factor in establishing a sinking fund is that its

own bonds generally have a higher yield than do government bonds; hence, the company saves

7-4 The price of the bond will fall and its YTM will rise if interest rates rise. If the bond still has a

long term to maturity, its YTM will reflect long-term rates. Of course, the bond’s price will be less

affected by a change in interest rates if it has been outstanding a long time and matures soon.

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Answers and Solutions

Chapter 7: Bonds and Their Valuation

7-7 As an investor with a short investment horizon, you would view the 20-year Treasury security as

being more risky than the 1-year Treasury security. If you bought the 20-year security, you

7-9 If a company sold bonds when interest rates were relatively high and the issue is callable, then

7-10 A sinking fund provision facilitates the orderly retirement of the bond issue. Although sinking

funds are designed to protect investors by ensuring that the bonds are retired in an orderly

7-11 A call for sinking fund purposes is quite different from a refunding call. A sinking fund call

requires no call premium, and only a small percentage of the issue is normally callable in a given

7-12 Convertibles and bonds with warrants are offered with lower coupons than similarly-rated straight

Chapter 7: Bonds and Their Valuation

Answers and Solutions

149

7-13 This statement is false. Extremely strong companies can use debentures because they simply do

7-14 The yield spread between a corporate bond over a Treasury bond with the same maturity reflects

7-15 Assuming a bond issue is callable, the YTC is a better estimate of a bond’s expected return when

7-16 d. The 15-year zero coupon bonds have the most price risk. Longer-maturity bonds have a high

7-17 b. The 1-year bonds with a 12% coupon have the most reinvestment risk. Shorter-maturity

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Answers and Solutions

Chapter 7: Bonds and Their Valuation

Solutions to End-of-Chapter Problems

7-1 With your financial calculator, enter the following:

7-3 The problem asks you to find the price of a bond, given the following facts: N = 2  8 = 16; I/YR =

7-4 With your financial calculator, enter the following to find YTM:

Chapter 7: Bonds and Their Valuation

Answers and Solutions

151

7-6 a. Time Years to Maturity Price of Bond C Price of Bond Z

t = 0 4 $1,012.79 $ 693.04

b.

7-7 Percentage

Price at 8% Price at 7% Change

10-year, 10% annual coupon $1,134.20 $1,210.71 6.75%

7-8 The rate of return is approximately 15.03%, found with a calculator using the following inputs:

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Answers and Solutions

Chapter 7: Bonds and Their Valuation

7-9 a. VB =



=+

+

N

1t

N

d

t

d)r1(

M

)r1(

INT

7-10 a. Solving for YTM:

b. The current yield is defined as the annual coupon payment divided by the current price.

7-11 a. Using a financial calculator, input the following to solve for YTM:

Chapter 7: Bonds and Their Valuation

Answers and Solutions

153

c. YTM = Current yield + Capital gains (loss) yield

7-12 a. Yield to maturity (YTM):

Yield to call (YTC):

b. Knowledgeable investors would expect the return to be closer to 6.1% than to 8%. If interest

7-13 The problem asks you to solve for the YTM and Price, given the following facts:

7-14 a. The bond is selling at a large premium, which means that its coupon rate is much higher than the

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Answers and Solutions

Chapter 7: Bonds and Their Valuation

b. Since the bonds are likely to be called, they will probably provide a return equal to the YTC rather

than the YTM. So, there is no point in calculating the YTM—just calculate the YTC. Enter these

values:

7-15 First, we must find the amount of money we can expect to sell this bond for in 5 years. This is found

using the fact that in five years, there will be 15 years remaining until the bond matures and that the

expected YTM for this bond at that time will be 8.5%.

7-16 Before you can solve for the price, we must find the appropriate semiannual rate at which to evaluate

this bond.

7-17 First, we must find the price Joan paid for this bond.

Chapter 7: Bonds and Their Valuation

Answers and Solutions

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7-18 a. Find the YTM as follows:

d. Similarly from above, YTC can be found, if called in each subsequent year.

If called in Year 6:

If called in Year 7:

If called in Year 8:

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Comprehensive/Spreadsheet Problem

Chapter 7: Bonds and Their Valuation

Comprehensive/Spreadsheet Problem

Note to Instructors:

The solution to this problem is not provided to students at the back of their text. Instructors

can access the

Excel

file on the textbook’s website.

7-19 a. Bond A is selling at a discount because its coupon rate (7%) is less than the going interest rate

b.

c.

d.

Current yield = Annual coupon / Price

Basic Input Data Bond A Bond B Bond C

Years to maturity 12 12 12

Basic Input Data Bond A Bond B Bond C

Years to maturity 11 11 11

Chapter 7: Bonds and Their Valuation

Comprehensive/Spreadsheet Problem

157

e.

f.

 A 5–year bond with a zero coupon $649.93 $620.92 -4.46%

 A 10–year bond with a zero coupon

Basic Input Data Bond D

Years to maturity 9

9% 10%

% Price

Chge

 A 1–year bond with a 9% annual coupon $1,000.00 $990.91 -0.91%

158

Comprehensive/Spreadsheet Problem

Chapter 7: Bonds and Their Valuation

g.

1.

8.10% 9.00% 9.68%

8.03% 9.00% 9.75%

7.87% 9.00% 9.90%

7.78% 9.00% 9.99%

Years Remaining Until Maturity Bond A Bond B Bond C

12 $856.79 $1,000.00 $1,143.21

Time Paths of Bonds A, B, and C

$1,400.00

Bond Value

Years Remaining Until Maturity Bond A Bond B Bond C

12

8.17% 9.00% 9.62%

Chapter 7: Bonds and Their Valuation

Comprehensive/Spreadsheet Problem

159

2.

0.97% 0.00% -0.75%

1.13% 0.00% -0.90%

1.22% 0.00% -0.99%

1.31% 0.00% -1.09%

1.52% 0.00% -1.33%

1.63% 0.00% -1.47%

1.74% 0.00% -1.63%

1.87% 0.00% -1.80%

3.

9.00% 9.00% 9.00%

Years Remaining Until Maturity Bond A Bond B Bond C

12

0.83% 0.00% -0.62%

11

0.90% 0.00% -0.68%

Years Remaining Until Maturity Bond A Bond B Bond C

12

9.00% 9.00% 9.00%

11

9.00% 9.00% 9.00%

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Integrated Case

Chapter 7: Bonds and Their Valuation

Integrated Case

7-20

Western Money Management Inc.

Bond Valuation

Robert Black and Carol Alvarez are vice presidents of Western Money

Management and codirectors of the company’s pension fund management

division. A major new client, the California League of Cities, has requested

that Western present an investment seminar to the mayors of the represented

cities. Black and Alvarez, who will make the presentation, have asked you to

help them by answering the following questions.

A. What are a bond’s key features?

Answer: [Show S7-1 through S7-4 here.] Here is a list of key features:

Chapter 7: Bonds and Their Valuation

Integrated Case

161

B. What are call provisions and sinking fund provisions? Do these

provisions make bonds more or less risky?

Answer: [Show S7-5 through S7-7 here.] A call provision is a provision in a

bond contract that gives the issuing corporation the right to redeem

the bonds under specified terms prior to the normal maturity date.

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Integrated Case

Chapter 7: Bonds and Their Valuation

C. How is the value of any asset whose value is based on expected

future cash flows determined?

Answer: [Show S7-8 through S7–10 here.]

0 1 2 3 N

| | | | • • • |

Chapter 7: Bonds and Their Valuation

Integrated Case

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D. How is a bond’s value determined? What is the value of a 10–year,

$1,000 par value bond with a 10% annual coupon if its required

return is 10%?

Answer: [Show S7–11 and S7–12 here.] A bond has a specific cash flow

pattern consisting of a stream of constant interest payments plus the