Chapter 13: Risk, Return, and Capital Budgeting
13.2
Apply the CAPM to express the firm’s cost of equity capital,
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
)
= 0.045 + 1.3 (0.12–0.045)
= 0.1425
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.
β
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.
13.6
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.
13.8
The pretax cost of debt is the YTM of the company’s bonds, so:
P
0
= $1,050 = $40
+ $1,000 / (1+r)
24
24
r
Α
r = 3.683%
YTM = 2 × 3.683% = 7.37%
And the aftertax cost of debt is:
r
B
= .0737(1 – .35) = .0479 or 4.79%
13.10
The book value of debt is the total par value of all outstanding debt, so:
B = $20M + 80M = $100M
To find the market value of debt, we find the price of the bonds and multiply by the number of
bonds. Alternatively, we can multiply the price quote of the bond times the par value of the
bonds. Doing so, we find:
Answers to End–of–Chapter Problems
B–
186