Chapter 12: Risk, Cost of Capital, and Capital Budgeting
12.1
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 riskfree rate,
R
F
, and the expected market return,
R
M
.
R
S
=
R
F
+
β
×
(
R
M
–
R
F
)
= 0.05 + 0.95 (0.09)
= 0.1355
Subtract the initial investment at year 0.
To calculate the PV of the cash inflows, apply the annuity
formula, discounted at 0.1355.
NPV
= C
0
+ C
1
A
T
r
= $1,200,000 + $340,000 A
5
0.1355
=
$20,016.52
Do not undertake the project since the NPV is negative.
12.2
a.
Calculate the average return for Douglas stock and the market.
R
D
= (Sum of Yearly Returns) / (Number of Years)
= (0.05 + 0.05 + 0.08 + 0.15 + 0.10) / (5)
=
0.066
R
M
= (0.12 + 0.01 + 0.06 + 0.10 + 0.05) / (5)
=
0.020
To calculate the beta of Douglas stock, calculate the variance of the market, (
R
M

R
M
)
2
,
and the covariance of Douglas stock’s return with the market’s return, (
R
D

R
D
)
×
(
R
M

R
M
).
The beta of Douglas stock is equal to the covariance of Douglas stock’s return and
the market’s return divided by the variance of the market.
Remember to divide both the
covariance of Douglas stock’s return and the market’s return and the variance of the market
by 4.
Because the data are historical, the appropriate denominator in the calculation of the
variance is 4 (=
T
– 1).
R
D

R
D
R
M

R
M
(R
M

R
M
)
2
(R
D

R
D
) (R
M

R
M
)
0.116
0.14
0.0196
0.01624
0.016
0.01
0.0001
0.00016
0.014
0.04
0.0016
0.00056
0.084
0.08
0.0064
0.00672
0.034
0.03
0.0009
0.00102
0.0286
0.02470
β
D
= [Cov (
R
D
,
R
M
) / (T1)] / [Var (
R
M
) / (T1)]
= (0.02470 / 4) / (0.0286 / 4)
=
0.864
The beta of Douglas stock is 0.864.
B236