Chapter 13: Risk, Return, and Capital Budgeting
13.1
The discount rate for the project is equal to the expected return for the security,
R
S
, since the project
has the same risk as the firm as a whole.
Apply the CAPM to express the firm’s required return,
R
S
,
in terms of the firm’s beta,
β
, the risk–free rate,
R
F
, and the expected market return,
R
M
.
R
S
=
R
F
+
β
×
(
R
M
–
R
F
)
= 0.05 + 1.6 (0.09)
= 0.194
Subtract the initial investment at year 0.
To calculate the PV of the cash inflows, apply the annuity
formula, discounted at 0.194.
NPV
= C
0
+ C
1
A
T
r
= –$1,450,000 + $510,000 A
5
0.194
=
$
277.402.65
Undertake the project since the NPV is positive.
13.2
Apply the CAPM to express the firm’s cost of equity capital,
R
S
, in terms of the firm’s beta,
, the
risk–free rate,
R
F
, and the expected market return,
R
M
.
R
S
=
R
F
+
β
×
(
R
M
–
R
F
)
= 0.045 + 1.3 (0.12–0.045)
= 0.1425
13.3
Calculate the square root of the stock’s variance and the market’s variance to find the standard
deviation,
σ
, of each.
σ
C
= (
σ
2
C
)
1/2
= (0.005112)
1/2
= 0.07149825
σ
M
= (
σ
2
M
)
1/2
= (0.001668)
1/2
= 0.0408412
Use the formula for beta:
β
C
= [Corr (
R
C
,
R
M
)
×
σ
C
] /
σ
M
= [(0.910) (0.07149825)] / (0.0408412)
= 1.593
The beta of Ceramics Craftsman is 1.593.
13.4
a.
To compute the beta of Mercantile’s stock, divide the covariance of the stock’s
return with the market’s return by the market variance.
Since those two values are provided
in the problem, the 13 quarterly returns of Mercantile’s stock and the market are not needed
for the calculation.
Answers to End–of–Chapter Problems
B–
186
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D
= Cov (
R
D
,
R
M
) /
σ
2
M
= (0.038711) / (0.038588)
= 1.0032
The beta of Mercantile Banking Corporation is 1.0032.
b.
The beta of the average stock is one.
Since Mercantile’s beta is close to one, its stock has
approximately the same risk as the overall market.
13.5
You are assuming that the new project’s risk is the same as the risk of the firm as a whole, and that
the firm is financed entirely with equity.
13.6
a.
Lang Cosmetics should use its stock beta in the evaluation of the project only if
the risk of the perfume project is the same as the risk of Lang Cosmetics as a whole.
b.
If the risk of the project is the same as the risk of the firm, use the firm’s stock beta.
Otherwise, Lang should use the beta of an all–equity firm that has similar risks as the
perfume project.
An effective way to estimate the beta of the perfume project is to average
the betas of several all–equity, perfume–producing firms.
13.7
First, calculate the expected return on Compton’s stock.
R
S
=
Σ
[
R
S
×
Prob(
R
S
)]
= (0.04) (0.15) + (0.09) (0.25) + (0.19) (0.3) + (0.16) (0.3)
= 0.1335
Calculate the expected return on Compton’s debt.
R
B
=
Σ
[
R
B
×
Prob(
R
B
)]
= (0.07) (0.15) + (0.07) (0.25) + (0.09) (0.3) + (0.11) (0.3)
= 0.088
Calculate the expected return on the market.
R
M
=
Σ
[
R
M
×
Prob(
R
M
)]
= (0.06) (0.15) + (0.09) (0.25) + (0.15) (0.3) + (0.19) (0.3)
= 0.1335
Calculate the covariance of the stock’s return with the market’s return.
Cov (
R
S
,
R
M
) =
Σ
[(
R
S
–
R
S
)
×
(
R
M
–
R
M
)
×
Prob]
= (0.04 – 0.1335) (0.06 – 0.1335) (0.15) + (0.09– 0.1335) (0.09 – 0.1335) (0.25)
+ (0.19 – 0.1335) (0.15 – 0.1335) (0.3) + (0.16 – 0.1335) (0.19 – 0.1335) (0.3)
= 0.00223275
Calculate the covariance of the debt’s return with the market’s return.
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 Summer '10
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 Weighted average cost of capital, YTM, Zerocoupon bond, End–of–Chapter Problems

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