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P6-16 Bond valuation: Annual interest (LG 5; Basic)
Bond Years to
Maturity
(n)
Required
Return (r) Coupon (C) Par Value (M) Bond
Value
A 20 12% 0.11
$1,000
$110
$1,000 $925.31
$70
P6-17 Bond value and changing required returns (LG 5; Intermediate)
a. Required
Return (r) Years to
Maturity
(n) Coupon (C) Par Value (M) Bond
Value
11% 12 0.11 $1,000
$110
$1,000 $1,000.00
b.
c. When the coupon rate exceeds required return, market value exceeds par value (i.e., the bond
value equals par.
d. The required return on the bond could differ from the coupon rate because of changes in the: (i)
risk-free rate (perhaps because of changes in macroeconomic conditions), or (ii) risk of the
issuing firm.
P6-18 Bond value and time: Constant required returns (LG 5; Intermediate)
a. Using the PV function in Excel with the syntax:
=pv(required return, years to maturity, coupon, par value)
Required
Return (r) Years to
Maturity (n) Coupon (C) ParValue
(M) Bond
Value
14% 1 0.12 $1,000
$120
$1,000 $982.46
14% 3 $120 $1,000 $953.57
b.
c. As can be seen in part (b), other things equal, when required return differs from the coupon rate
and remains constant to maturity, bond value will approach par value as time to maturity
declines.
P6-19 Personal finance: Bond value and time—Changing required returns (LG 5; Challenge)
a. and b.
Bond Years to
Maturity
(n)
Required
Return (r) Coupon (C) Par
Value (M) Bond
Value
5 8% 0.11
$1,000
$110
$1,000
$1,119.78
c.
Value
Required Return Bond A Bond B
8% $1,119.78 $1,256.75
The longer the time to maturity, the more responsive bond price is to changes in required
return.
d. Lynn could minimize interest-rate risk by choosing Bond A with the shorter maturity. The price
P6-20 Yield to maturity (LG 6; Basic)
Bond A will sell at a discount to par; Bond B will sell at par value; Bond C will sell at a premium to
par; Bond D will sell at a discount to par, Bond E will sell at a premium to par.
P6-21 Yield to maturity (LG 6; Intermediate)
a. Yield to maturity (YTM) may be found in Excel using the RATE function with the following
syntax:
b. Note in part (a), the bond sells at a discount ($867.59) from par ($1,000), and YTM (7.5%)
exceeds the coupon rate (6%). Required return has risen since the bond was issued. For this
P6-22 Yield to maturity (LG 6; Intermediate)
a. In Excel, the RATE function will generate a bond’s yield to maturity (YTM). For example, for
where periods (n) is number of periods to maturity, payment (C) is coupon payment, present
b. If YTM exceeds coupon rate, the bond sells at a discount, and if the coupon rate exceeds YTM,
the bond sells at a premium. When YTM equals the coupon rate, the bond sells at par value.
P6-23 Personal finance: Bond valuation and yield to maturity (LG 2, LG 5, and LG 6; Challenge)
a. Value of the Crabbe Waste bond may be found in Excel using the PV function and n 5,
Value of the Malfoy bond may be found in Excel using the PV function and n 5,
b. The number of Crabbe Waste bonds $20,000 $952.42 21, and the number of Malfoy
bonds $20,000 $1052.60 19.
c. Annual interest income on Crabbe Waste bonds 21 bonds$63.24 per year $1,328.04, and
d. By purchasing the Crabbe Waste bonds, Mark will receive $1,328.04 in interest at the end of
years
where r is the required rate of return, n is years interest will be earned, and CF is total interest
reinvested interest may be found using the FV function in Excel with the following syntax:
e. The opportunity to reinvest coupon payments at 10% is attractive because both bonds offer
yield to maturities of only 7.5%. Although both bonds offer the same YTM, Malfoy has the
6-24 Bond valuation—Semiannual interest (LG 6; Intermediate)
To adjust the bond-valuation framework for semiannual interest, let n be the number of semiannual
P6-25 Bond valuation—Semiannual interest (LG 6; Challenge)
P6-26 Bond valuation—quarterly interest (LG 6; Challenge)
To adjust the bond-valuation framework for quarterly interest, let n be the number of quarterly
periods
P6-27 Ethics problem (LG 1; Intermediate)
This is a good question for class discussion. On the one hand, bundling ratings with other services
could reduce welfare by: (i) giving ratings agencies some market power and (ii) tempting agencies
to “tweak” ratings based on issuer willingness to buy other services. The counterargument
Case: “Evaluating Annie’s Proposed Investment in
Atilier Industries Bonds”
Case studies are available on www.pearson.com/mylab/finance.
a. Annie should convert the bonds. The value of the stock if the bond is converted is 50 shares$30 per
b. Current value of bond under different required returns:
c.
Under all three required returns for both annual and semiannual interest payments, the relationship
between required return (relative to coupon rate) and bond price (relative to par value) is the same. When
d. If expected inflation increases by 1%, required return will increase from 8% to 9%, and bond price will
e. If the ratings downgrade raises expected return from 8% to 8.75%, bond price will fall to $924.81 (i.e.,
f. In three years, the bond will be worth $1,110.61 (i.e., with n 22, r 7%, C $80, and M $1,000,
g. In ten years, the bond will be worth $1,091.08 (i.e., with n 15, r 7%, C $80, and M $1,000,
price $1,091.08)—the present value of remaining interest and principal payments. If Annie
h. Yield to maturity, given n 25, r 7%, C $80, and a bond price (V0) $983.80, is 8.154%.
i. Annie should probably not invest in the Atilier bond because:
The potential for a rating downgrade means significant risk of capital loss from a rise in the default
premium.
Spreadsheet Exercise
Answers to Chapter 6’s CSM Corporation spreadsheet problem are available on
www.pearson.com/mylab/finance.
Group Exercise
Group exercises are available on www.pearson.com/mylab/finance .
This chapter’s exercise focuses on debt. Each group will conduct Internet research to identify debt recently
issued by its shadow firm—specifically the issue’s rating and interest rate. Then, armed with this
information, each group will compare that interest rate with the rate on Treasuries with similar maturities to
infer the risk premium on the shadow firm’s debt. An important lesson from this exercise is the lack of
