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