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Chapter 7: Bonds and Their Valuation
Learning Objectives
145
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.
146
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.
148
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
150
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:
152
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
154
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
155
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:
156
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.
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.
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.
3.
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%
160
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.
162
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
163
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
