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1,400
Required Returns
Bond values and required
Market Value of Bond, B0 (\$)

1,300
returns (Mills CompanyвЂ™s
10% coupon interest rate,
1,200
10-year maturity, \$1,000 par,
1,134
January 1, 2004, issue paying 1,100
annual interest)
Par 1,000
Discount
900
887
800

700

0 2 4 6 8 10 12 14 16
Required Return, kd (%)
250 PART 2 Important Financial Concepts

Time to Maturity and Bond Values
Whenever the required return is different from the coupon interest rate, the
amount of time to maturity affects bond value. An additional factor is whether
required returns are constant or changing over the life of the bond.

Constant Required Returns When the required return is different from the
coupon interest rate and is assumed to be constant until maturity, the value of the
bond will approach its par value as the passage of time moves the bondвЂ™s value
closer to maturity. (Of course, when the required return equals the coupon inter-
est rate, the bondвЂ™s value will remain at par until it matures.)

Figure 6.6 depicts the behavior of the bond values calculated earlier and pre-
EXAMPLE
sented in Table 6.6 for Mills CompanyвЂ™s 10% coupon interest rate bond paying
annual interest and having 10 years to maturity. Each of the three required
returnsвЂ”12%, 10%, and 8%вЂ”is assumed to remain constant over the 10 years
to the bondвЂ™s maturity. The bondвЂ™s value at both 12% and 8% approaches and
ultimately equals the bondвЂ™s \$1,000 par value at its maturity, as the discount (at
12%) or premium (at 8%) declines with the passage of time.

Changing Required Returns The chance that interest rates will change and
thereby change the required return and bond value is called interest rate risk.
interest rate risk
(This was described as a shareholder-specific risk in Chapter 5, Table 5.1.) Bond-
The chance that interest rates
will change and thereby change holders are typically more concerned with rising interest rates because a rise in
the required return and bond
interest rates, and therefore in the required return, causes a decrease in bond
value. Rising rates, which result
value. The shorter the amount of time until a bondвЂ™s maturity, the less responsive
in decreasing bond values, are of
is its market value to a given change in the required return. In other words, short
greatest concern.
maturities have less interest rate risk than long maturities when all other features
(coupon interest rate, par value, and interest payment frequency) are the same.

FIGURE 6.6
Time to Maturity
Market Value of Bond, B0 (\$)

and Bond Values Premium Bond, Required Return, kd = 8%
1,200
Relationship among time to 1,134
1,115
maturity, required returns,
1,100
and bond values (Mills
1,052
CompanyвЂ™s 10% coupon inter-
Par-Value Bond, Required Return, kd = 10%
1,000 M
est rate, 10-year maturity,
\$1,000 par, January 1, 2004, 952
issue paying annual interest) 901
887
Discount Bond, Required Return, kd = 12%
800

10 9 8 7 6 5 4 3 2 1 0
Time to Maturity (years)
251
CHAPTER 6 Interest Rates and Bond Valuation

This is because of the mathematics of time value; the present values of short-term
cash flows change far less than the present values of longer-term cash flows in
response to a given change in the discount rate (required return).

The effect of changing required returns on bonds of differing maturity can be
EXAMPLE
illustrated by using Mills CompanyвЂ™s bond and Figure 6.6. If the required return
rises from 10% to 12% (see the dashed line at 8 years), the bondвЂ™s value
decreases from \$1,000 to \$901вЂ”a 9.9% decrease. If the same change in required
return had occurred with only 3 years to maturity (see the dashed line at 3 years),
the bondвЂ™s value would have dropped to just \$952вЂ”only a 4.8% decrease. Simi-
lar types of responses can be seen for the change in bond value associated with
decreases in required returns. The shorter the time to maturity, the less the impact
on bond value caused by a given change in the required return.

Yield to Maturity (YTM)
When investors evaluate bonds, they commonly consider yield to maturity
yield to maturity (YTM)
The rate of return that investors (YTM). This is the rate of return that investors earn if they buy the bond at a spe-
earn if they buy a bond at a cific price and hold it until maturity. (The measure assumes, of course, that the
specific price and hold it until
issuer makes all scheduled interest and principal payments as promised.) The
maturity. (Assumes that the
yield to maturity on a bond with a current price equal to its par value (that is,
issuer makes all scheduled
B0 M) will always equal the coupon interest rate. When the bond value differs
interest and principal payments
as promised.) from par, the yield to maturity will differ from the coupon interest rate.
Assuming that interest is paid annually, the yield to maturity on a bond can
be found by solving Equation 6.3 for kd. In other words, the current value, the
annual interest, the par value, and the years to maturity are known, and the
required return must be found. The required return is the bondвЂ™s yield to matu-
rity. The YTM can be found by trial and error or by use of a financial calculator.
The calculator provides accurate YTM values with minimum effort.

The Mills Company bond, which currently sells for \$1,080, has a 10% coupon
EXAMPLE
interest rate and \$1,000 par value, pays interest annually, and has 10 years to
maturity. Because B0 \$1,080, I \$100 (0.10 \$1,000), M \$1,000, and
n 10 years, substituting into Equation 6.3a yields
\$1,080 \$100 (PVIFAk ) \$1,000 (PVIFk )
d,10yrs d,10yrs
Our objective is to solve the equation for kd, the YTM.

Trial and Error Because we know that a required return, kd, of 10% (which
equals the bondвЂ™s 10% coupon interest rate) would result in a value of \$1,000,
the discount rate that would result in \$1,080 must be less than 10%. (Remember
that the lower the discount rate, the higher the present value, and the higher the
discount rate, the lower the present value.) Trying 9%, we get
\$100 (PVIFA9%,10yrs) \$1,000 (PVIF9%,10yrs)
\$100 (6.418) \$1,000 (0.422)
\$641.80 \$422.00
\$1,063.80
252 PART 2 Important Financial Concepts

Because the 9% rate is not quite low enough to bring the value up to \$1,080, we
next try 8% and get
\$100 (PVIFA8%,10yrs) \$1,000 (PVIF8%,10yrs)
\$100 (6.710) \$1,000 (0.463)
\$671.00 \$463.00
\$1,134.00
Input Function Because the value at the 8% rate is higher than \$1,080 and the value at the 9%
10 N
rate is lower than \$1,080, the bondвЂ™s yield to maturity must be between 8% and
1080 PV
9%. Because the \$1,063.80 is closer to \$1,080, the YTM to the nearest whole
100 PMT
percent is 9%. (By using interpolation, we could eventually find the more precise
FV
1000 YTM value to be 8.77%.)7
CPT
Calculator Use [Note: Most calculators require either the present value (B0 in
I
this case) or the future values (I and M in this case) to be input as negative num-
Solution
bers to calculate yield to maturity. That approach is employed here.] Using the
8.766
inputs shown at the left, you should find the YTM to be 8.766%.

Semiannual Interest and Bond Values
The procedure used to value bonds paying interest semiannually is similar to that
shown in Chapter 4 for compounding interest more frequently than annually,
except that here we need to find present value instead of future value. It involves

1. Converting annual interest, I, to semiannual interest by dividing I by 2.
2. Converting the number of years to maturity, n, to the number of 6-month
periods to maturity by multiplying n by 2.
3. Converting the required stated (rather than effective) annual return for simi-
lar-risk bonds that also pay semiannual interest from an annual rate, kd, to a
semiannual rate by dividing kd by 2.

Substituting these three changes into Equation 6.3 yields
2n
I 1 1
B0 M (6.4)
t 2n
kd kd
2 i1
1 1
2 2
I
(PVIFAkd/2,2n) M (PVIFkd/2,2n) (6.4a)
2

Assuming that the Mills Company bond pays interest semiannually and that the
EXAMPLE
required stated annual return, kd, is 12% for similar-risk bonds that also pay
semiannual interest, substituting these values into Equation 6.4a yields
\$100
B0 (PVIFA12%/2,2 10yrs) \$1,000 (PVIF12%/2,2 10yrs)
2

WW 7. For information on how to interpolate to get a more precise answer, see the bookвЂ™s home page at www.
W
aw.com/gitman
253
CHAPTER 6 Interest Rates and Bond Valuation

Table Use
B0 \$50 (PVIFA6%,20periods) \$1,000 (PVIF6%,20periods)
\$50 (11.470) \$1,000 (0.312) \$885.50
Input Function
20 N
I
6
Calculator Use In using a calculator to find bond value when interest is paid
50 PMT semiannually, we must double the number of periods and divide both the
FV required stated annual return and the annual interest by 2. For the Mills Com-
1000

pany bond, we would use 20 periods (2 10 years), a required return of 6%
CPT
(12% 2), and an interest payment of \$50 (\$100 2). Using these inputs, you
PV
should find the bond value with semiannual interest to be \$885.30, as shown at
Solution
the left. Note that this value is more precise than the value calculated using the
885.30
rounded financial-table factors.

Comparing this result with the \$887.00 value found earlier for annual com-
pounding (see Table 6.6), we can see that the bondвЂ™s value is lower when semian-
nual interest is paid. This will always occur when the bond sells at a discount. For
bonds selling at a premium, the opposite will occur: The value with semiannual
interest will be greater than with annual interest.

Review Questions

6вЂ“16 What basic procedure is used to value a bond that pays annual interest?
Semiannual interest?
6вЂ“17 What relationship between the required return and the coupon interest
rate will cause a bond to sell at a discount? At a premium? At its par
value?
6вЂ“18 If the required return on a bond differs from its coupon interest rate,
describe the behavior of the bond value over time as the bond moves
toward maturity.
6вЂ“19 As a risk-averse investor, would you prefer bonds with short or long peri-
ods until maturity? Why?
6вЂ“20 What is a bondвЂ™s yield to maturity (YTM)? Briefly describe both the trial-
and-error approach and the use of a financial calculator for finding YTM.

SUMMARY
FOCUS ON VALUE
Interest rates and required returns embody the real cost of money, inflationary expecta-
tions, and issuer and issue risk. They reflect the level of return required by market partici-
pants as compensation for the risk perceived in a specific security or asset investment.
Because these returns are affected by economic expectations, they vary as a function of
254 PART 2 Important Financial Concepts

time, typically rising for longer-term maturities or transactions. The yield curve reflects such
market expectations at any point in time.
The value of an asset can be found by calculating the present value of its expected cash
flows, using the required return as the discount rate. Bonds are the easiest financial assets to
value, because both the amounts and the timing of their cash flows are known with certainty.
The financial manager needs to understand how to apply valuation techniques to bonds in
order to make decisions that are consistent with the firmвЂ™s share price maximization goal.

REVIEW OF LEARNING GOALS
cial press, provide information on bonds, including
Describe interest rate fundamentals, the term
LG2
current price data and statistics on recent price be-
structure of interest rates, and risk premiums.
havior. Bond ratings by independent agencies indi-
The flow of funds between savers (suppliers) and
cate the risk of a bond issue. Various types of tradi-
investors (demanders) is regulated by the interest
tional and contemporary bonds are available.
rate or required return. In a perfect, inflation-free,
Eurobonds and foreign bonds enable established
certain world there would be one cost of moneyвЂ”
creditworthy companies and governments to bor-
the real rate of interest. For any class of similar-risk
row large amounts internationally.
securities, the term structure of interest rates reflects
the relationship between the interest rate, or rate of
Understand the key inputs and basic model
return, and the time to maturity. Yield curves can
LG4
used in the valuation process. Key inputs to the
be downward-sloping (inverted), upward-sloping
valuation process include cash flows (returns), tim-
(normal), or flat. Three theoriesвЂ”expectations the-
ing, and risk and the required return. The value of
ory, liquidity preference theory, and market seg-
any asset is equal to the present value of all future
mentation theoryвЂ”are cited to explain the general
cash flows it is expected to provide over the relevant
shape of the yield curve. Risk premiums for non-
time period. The basic valuation formula for any
Treasury debt issues result from interest rate risk,
asset is summarized in Table 6.7.
liquidity risk, tax risk, default risk, maturity risk,
and contractual provision risk.
Apply the basic valuation model to bonds and
LG5
describe the impact of required return and time
Review the legal aspects of bond financing and
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to maturity on bond values. The value of a bond is
bond cost. Corporate bonds are long-term debt
the present value of its interest payments plus the
instruments indicating that a corporation has bor-
present value of its par value. The basic valuation
rowed an amount that it promises to repay in the
model for a bond is summarized in Table 6.7. The
future under clearly defined terms. Most bonds are
discount rate used to determine bond value is the re-
issued with maturities of 10 to 30 years and a par
quired return, which may differ from the bondвЂ™s
value of \$1,000. The bond indenture, enforced by a
coupon interest rate. A bond can sell at a discount, at
trustee, states all conditions of the bond issue. It
par, or at a premium, depending on whether the re-
contains both standard debt provisions and restric-
quired return is greater than, equal to, or less than its
tive covenants, which may include a sinking-fund
coupon interest rate. The amount of time to maturity
requirement and/or a security interest. The cost of
affects bond values. Even if the required return re-
bonds to an issuer depends on its maturity, offering
mains constant, the value of a bond will approach its
size, and issuer risk and on the basic cost of money.
par value as the bond moves closer to maturity. The
chance that interest rates will change and thereby
Discuss the general features, quotations, ratings,
LG3
change the required return and bond value is called
popular types, and international issues of corpo-
interest rate risk. The shorter the amount of time un-
rate bonds. A bond issue may include a conversion
til a bondвЂ™s maturity, the less responsive is its market
feature, a call feature, or stock purchase warrants.
value to a given change in the required return.
Bond quotations, published regularly in the finan-
255
CHAPTER 6 Interest Rates and Bond Valuation

TABLE 6.7 Summary of Key Valuation Definitions
and Formulas for Any Asset and for Bonds

Definitions of variables

B0 bond value
CFt cash flow expected at the end of year t
I annual interest on a bond
k appropriate required return (discount rate)
kd required return on a bond
M par, or face, value of a bond
n relevant time period, or number of years to maturity
V0 value of the asset at time zero

Valuation formulas

Value of any asset:
CF1 CF2 CFn
...
V0 [Eq. 6.1]
(1 k)1 (1 k)2 (1 k)n
...
[CF1 (PVIFk,1)] [CF2 (PVIFk,2)] [CFn (PVIFk,n )] [Eq. 6.2]

Bond value:
n
1 1
B0 I M [Eq. 6.3]
kd)t kd)n
(1 (1
t1

I (PVIFAkd ,n) M (PVIFkd ,n) [Eq. 6.3a]

nually are valued by using the same procedure used
Explain yield to maturity (YTM), its calcula-
LG6
to value bonds paying annual interest, except that
tion, and the procedure used to value bonds
the interest payments are one-half of the annual in-
that pay interest semiannually. Yield to maturity
terest payments, the number of periods is twice the
(YTM) is the rate of return investors earn if they
number of years to maturity, and the required re-
buy a bond at a specific price and hold it until ma-
turn is one-half of the stated annual required return
turity. YTM can be calculated by trial and error or
on similar-risk bonds.
financial calculator. Bonds that pay interest semian-

SELF-TEST PROBLEMS (Solutions in Appendix B)
ST 6вЂ“1 Bond valuation Lahey Industries has outstanding a \$1,000 par-value bond
LG5 LG6
with an 8% coupon interest rate. The bond has 12 years remaining to its matu-
rity date.
a. If interest is paid annually, find the value of the bond when the required
return is (1) 7%, (2) 8%, and (3) 10%?
b. Indicate for each case in part a whether the bond is selling at a discount, at a
premium, or at its par value.
c. Using the 10% required return, find the bondвЂ™s value when interest is paid
semiannually.
256 PART 2 Important Financial Concepts

ST 6вЂ“2 Yield to maturity Elliot EnterprisesвЂ™ bonds currently sell for \$1,150, have an
LG6
11% coupon interest rate and a \$1,000 par value, pay interest annually, and
have 18 years to maturity.
a. Calculate the bondsвЂ™ yield to maturity (YTM).
b. Compare the YTM calculated in part a to the bondsвЂ™ coupon interest rate,
and use a comparison of the bondsвЂ™ current price and their par value to
explain this difference.

PROBLEMS
6вЂ“1 Yield curve A firm wishing to evaluate interest rate behavior has gathered yield
LG2
data on five U.S. Treasury securities, each having a different maturity and all
measured at the same point in time. The summarized data follow.

U.S. Treasury security Time to maturity Yield

A 1 year 12.6%
B 10 years 11.2
C 6 months 13.0
D 20 years 11.0
E 5 years 11.4

a. Draw the yield curve associated with these data.
b. Describe the resulting yield curve in part a, and explain the general expecta-
tions embodied in it.

6вЂ“2 Term structure of interest rates The following yield data for a number of high-
LG2
est quality corporate bonds existed at each of the three points in time noted.

Yield
Time to maturity (years) 5 years ago 2 years ago Today

1 9.1% 14.6% 9.3%
3 9.2 12.8 9.8
5 9.3 12.2 10.9
10 9.5 10.9 12.6
15 9.4 10.7 12.7
20 9.3 10.5 12.9
30 9.4 10.5 13.5

a. On the same set of axes, draw the yield curve at each of the three given times.
b. Label each curve in part a with its general shape (downward-sloping,
upward-sloping, flat).
c. Describe the general inflationary and interest rate expectation existing at
each of the three times.

6вЂ“3 Risk-free rate and risk premiums The real rate of interest is currently 3%; the
LG2
inflation expectation and risk premiums for a number of securities follow.
257
CHAPTER 6 Interest Rates and Bond Valuation

Inflation expectation

A 6% 3%
B 9 2
C 8 2
D 5 4
E 11 1

a. Find the risk-free rate of interest, RF , that is applicable to each security.
b. Although not noted, what factor must be the cause of the differing risk-free
rates found in part a?
c. Find the actual rate of interest for each security.

6вЂ“4 Risk premiums Eleanor Burns is attempting to find the actual rate of interest
LG2
for each of two securitiesвЂ”A and BвЂ”issued by different firms at the same point
in time. She has gathered the following data:

Characteristic Security A Security B

Time to maturity 3 years 15 years
Liquidity risk 1.0% 1.0%
Default risk 1.0% 2.0%
Maturity risk 0.5% 1.5%
Other risk 0.5% 1.5%

a. If the real rate of interest is currently 2%, find the risk-free rate of interest
applicable to each security.
b. Find the total risk premium attributable to each securityвЂ™s issuer and issue
characteristics.
c. Calculate the actual rate of interest for each security. Compare and discuss

6вЂ“5 Bond interest payments before and after taxes Charter Corp. has issued 2,500
LG2
debentures with a total principal value of \$2,500,000. The bonds have a coupon
interest rate of 7%.
a. What dollar amount of interest per bond can an investor expect to receive
each year from Charter Corp.?
b. What is CharterвЂ™s total interest expense per year associated with this bond
issue?
c. Assuming that Charter is in a 35% corporate tax bracket, what is the com-
panyвЂ™s net after-tax interest cost associated with this bond issue?

6вЂ“6 Bond quotation Assume that the following quote for the Financial Manage-
LG3
ment CorporationвЂ™s \$1,000-par-value bond was found in the Wednesday,
November 8, issue of the Wall Street Journal.
Fin Mgmt 8.75 05 8.7 558 100.25 0.63
258 PART 2 Important Financial Concepts

Given this information, answer the following questions.
a. On what day did the trading activity occur?
b. At what price did the bond close at the end of the day on November 7?
c. In what year does the bond mature?
d. How many bonds were traded on the day quoted?
e. What is the bondвЂ™s coupon interest rate?
f. What is the bondвЂ™s current yield? Explain how this value was calculated.
g. How much of a change, if any, in the bondвЂ™s closing price took place between
the day quoted and the day before? At what price did the bond close on the
day before?

6вЂ“7 Valuation fundamentals Imagine that you are trying to evaluate the economics
LG4
of purchasing an automobile. You expect the car to provide annual after-tax
cash benefits of \$1,200 at the end of each year, and assume that you can sell the
car for after-tax proceeds of \$5,000 at the end of the planned 5-year ownership
period. All funds for purchasing the car will be drawn from your savings, which
are currently earning 6% after taxes.
a. Identify the cash flows, their timing, and the required return applicable to
valuing the car.
b. What is the maximum price you would be willing to pay to acquire the car?
Explain.

6вЂ“8 Valuation of assets Using the information provided in the following table, find
LG4
the value of each asset.

Cash flow
Asset End of year Amount Appropriate required return

A 1 \$ 5,000 18%
2 5,000
3 5,000

1 through в€ћ
B \$ 300 15%

C 1 \$ 0 16%
2 0
3 0
4 0
5 35,000

D 1 through 5 \$ 1,500 12%
6 8,500

E 1 \$ 2,000 14%
2 3,000
3 5,000
4 7,000
5 4,000
6 1,000
259
CHAPTER 6 Interest Rates and Bond Valuation

6вЂ“9 Asset valuation and risk Laura Drake wishes to estimate the value of an
LG4
asset expected to provide cash inflows of \$3,000 per year at the end of years 1
through 4 and \$15,000 at the end of year 5. Her research indicates that she
must earn 10% on low-risk assets, 15% on average-risk assets, and 22% on
high-risk assets.
a. Determine what is the most Laura should pay for the asset if it is classified as
(1) low-risk, (2) average-risk, and (3) high-risk.
b. Say Laura is unable to assess the risk of the asset and wants to be certain
sheвЂ™s making a good deal. On the basis of your findings in part a, what is the
most she should pay? Why?
c. All else being the same, what effect does increasing risk have on the value of
an asset? Explain in light of your findings in part a.

6вЂ“10 Basic bond valuation Complex Systems has an outstanding issue of \$1,000-
LG5
par-value bonds with a 12% coupon interest rate. The issue pays interest annu-
ally and has 16 years remaining to its maturity date.
a. If bonds of similar risk are currently earning a 10% rate of return, how much
should the Complex Systems bond sell for today?
b. Describe the two possible reasons why similar-risk bonds are currently earn-
ing a return below the coupon interest rate on the Complex Systems bond.
c. If the required return were at 12% instead of 10%, what would the current
value of Complex SystemsвЂ™ bond be? Contrast this finding with your findings
in part a and discuss.

6вЂ“11 Bond valuationвЂ”Annual interest Calculate the value of each of the bonds
LG5
shown in the following table, all of which pay interest annually.

Bond Par value Coupon interest rate Years to maturity Required return

A \$1,000 14% 20 12%
B 1,000 8 16 8
C 100 10 8 13
D 500 16 13 18
E 1,000 12 10 10

6вЂ“12 Bond value and changing required returns Midland Utilities has outstanding a
LG5
bond issue that will mature to its \$1,000 par value in 12 years. The bond has a
coupon interest rate of 11% and pays interest annually.
a. Find the value of the bond if the required return is (1) 11%, (2) 15%, and
(3) 8%.
b. Plot your findings in part a on a set of вЂњrequired return (x axis)вЂ“market value
of bond (y axis)вЂќ axes.
c. Use your findings in parts a and b to discuss the relationship between the
coupon interest rate on a bond and the required return and the market value
of the bond relative to its par value.
d. What two possible reasons could cause the required return to differ from the
coupon interest rate?
260 PART 2 Important Financial Concepts

6вЂ“13 Bond value and timeвЂ”Constant required returns Pecos Manufacturing has just
LG5
issued a 15-year, 12% coupon interest rate, \$1,000-par bond that pays interest
annually. The required return is currently 14%, and the company is certain it
will remain at 14% until the bond matures in 15 years.
a. Assuming that the required return does remain at 14% until maturity, find
the value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years,
(5) 3 years, and (6) 1 year to maturity.
b. Plot your findings on a set of вЂњtime to maturity (x axis)вЂ“market value of
bond (y axis)вЂќ axes constructed similarly to Figure 6.6.
c. All else remaining the same, when the required return differs from the coupon
interest rate and is assumed to be constant to maturity, what happens to the
bond value as time moves toward maturity? Explain in light of the graph in
part b.

6вЂ“14 Bond value and timeвЂ”Changing required returns Lynn Parsons is considering
LG5
investing in either of two outstanding bonds. The bonds both have \$1,000 par
values and 11% coupon interest rates and pay annual interest. Bond A has
exactly 5 years to maturity, and bond B has 15 years to maturity.
a. Calculate the value of bond A if the required return is (1) 8%, (2) 11%, and
(3) 14%.
b. Calculate the value of bond B if the required return is (1) 8%, (2) 11%, and
(3) 14%.
c. From your findings in parts a and b, complete the following table, and dis-
cuss the relationship between time to maturity and changing required returns.

Required return Value of bond A Value of bond B

8% ? ?
11 ? ?
14 ? ?

d. If Lynn wanted to minimize interest rate risk, which bond should she pur-
chase? Why?

6вЂ“15 Yield to maturity The relationship between a bondвЂ™s yield to maturity and
LG6
coupon interest rate can be used to predict its pricing level. For each of the
bonds listed, state whether the price of the bond will be at a premium to par, at
par, or at a discount to par.

Bond Coupon interest rate Yield to maturity Price

A 6% 10%
B 8 8
C 9 7
D 7 9
E 12 10
261
CHAPTER 6 Interest Rates and Bond Valuation

6вЂ“16 Yield to maturity The Salem Company bond currently sells for \$955, has a
LG6
12% coupon interest rate and a \$1,000 par value, pays interest annually, and
has 15 years to maturity.
a. Calculate the yield to maturity (YTM) on this bond.
b. Explain the relationship that exists between the coupon interest rate
and yield to maturity and the par value and market value of a
bond.

6вЂ“17 Yield to maturity Each of the bonds shown in the following table pays interest
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annually.

Bond Par value Coupon interest rate Years to maturity Current value

A \$1,000 9% 8 \$ 820
B 1,000 12 16 1,000
C 500 12 12 560
D 1,000 15 10 1,120
E 1,000 5 3 900

a. Calculate the yield to maturity (YTM) for each bond.
b. What relationship exists between the coupon interest rate and yield to
maturity and the par value and market value of a bond? Explain.

6вЂ“18 Bond valuationвЂ”Semiannual interest Find the value of a bond maturing in 6
LG6
years, with a \$1,000 par value and a coupon interest rate of 10% (5% paid
semiannually) if the required return on similar-risk bonds is 14% annual interest
(7% paid semiannually).

6вЂ“19 Bond valuationвЂ”Semiannual interest Calculate the value of each of the bonds
LG6
shown in the following table, all of which pay interest semiannually.

Coupon Years to Required stated
Bond Par value interest rate maturity annual return

A \$1,000 10% 12 8%
B 1,000 12 20 12
C 500 12 5 14
D 1,000 14 10 10
E 100 6 4 14

6вЂ“20 Bond valuationвЂ”Quarterly interest Calculate the value of a \$5,000-par-value
LG6
bond paying quarterly interest at an annual coupon interest rate of 10% and
having 10 years until maturity if the required return on similar-risk bonds is cur-
rently a 12% annual rate paid quarterly.
262 PART 2 Important Financial Concepts

CHAPTER 6 CASE Evaluating Annie HeggвЂ™s Proposed Investment
in Atilier Industries Bonds

A nnie Hegg has been considering investing in the bonds of Atilier Industries.
The bonds were issued 5 years ago at their \$1,000 par value and have
exactly 25 years remaining until they mature. They have an 8% coupon interest
rate, are convertible into 50 shares of common stock, and can be called any time
at \$1,080. The bond is rated Aa by MoodyвЂ™s. Atilier Industries, a manufacturer
of sporting goods, recently acquired a small athletic-wear company that was in
financial distress. As a result of the acquisition, MoodyвЂ™s and other rating agen-
cies are considering a rating change for Atilier bonds. Recent economic data
suggest that inflation, currently at 5% annually, is likely to increase to a 6%
annual rate.
Annie remains interested in the Atilier bond but is concerned about infla-
tion, a potential rating change, and maturity risk. In order to get a feel for the
potential impact of these factors on the bond value, she decided to apply the val-
uation techniques she learned in her finance course.

Required
a. If the price of the common stock into which the bond is convertible rises to
\$30 per share after 5 years and the issuer calls the bonds at \$1,080, should
Annie let the bond be called away from her or should she convert it into com-
mon stock?
b. For each of the following required returns, calculate the bondвЂ™s value, assum-
ing annual interest. Indicate whether the bond will sell at a discount, at a pre-
mium, or at par value.
(1) Required return is 6%.
(2) Required return is 8%.
(3) Required return is 10%.
c. Repeat the calculations in part b, assuming that interest is paid semiannually
and that the semiannual required returns are one-half of those shown. Com-
pare and discuss differences between the bond values for each required return
calculated here and in part b under the annual versus semiannual payment
assumptions.
d. If Annie strongly believes that inflation will rise by 1% during the next 6
months, what is the most she should pay for the bond, assuming annual
interest?
e. If the Atilier bonds are downrated by MoodyвЂ™s from Aa to A, and if such a
rating change will result in an increase in the required return from 8% to
8.75%, what impact will this have on the bond value, assuming annual
interest?
f. If Annie buys the bond today at its \$1,000 par value and holds it for exactly
3 years, at which time the required return is 7%, how much of a gain or loss
will she experience in the value of the bond (ignoring interest already received
and assuming annual interest)?
g. Rework part f, assuming that Annie holds the bond for 10 years and sells it
when the required return is 7%. Compare your finding to that in part f, and
comment on the bondвЂ™s maturity risk.
263
CHAPTER 6 Interest Rates and Bond Valuation

h. Assume that Annie buys the bond at its current closing price of 98.38 and
holds it until maturity. What will her yield to maturity (YTM) be, assuming
annual interest?
i. After evaluating all of the issues raised above, what recommendation would
you give Annie with regard to her proposed investment in the Atilier Indus-
tries bonds?

WEB EXERCISE Go to the Web site www.smartmoney.com. Click on Economy & Bonds. Then
WW click on Bond Calculator, which is located down the page under the column
W
Bond Tools. Read the instructions on how to use the bond calculator. Using the
bond calculator:

1. Calculate the yield to maturity (YTM) for a bond whose coupon rate is
7.5% with maturity date of July 31, 2030, which you bought for 95.
2. What is the YTM of the above bond if you bought it for 105? For 100?
3. Change the yield % box to 8.5. What would be the price of this bond?
4. Change the yield % box to 9.5. What is this bondвЂ™s price?
5. Change the maturity date to 2006 and reset yield % to 6.5. What is the price
of this bond?
6. Why is the price of the bond in Question 5 higher than the price of the bond
in Question 4?
7. Explore the other bond-related resources at the site. Using Bond Market
Update, comment on current interest rate levels and the yield curve.

Remember to check the bookвЂ™s Web site at
www.aw.com/gitman