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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
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View Full Document 12.3
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
= (0.004225)
1/2
= 0.065
σ
M
= (
σ
2
M
)
1/2
= (0.001467)
1/2
= 0.0383
Use the formula for beta:
β
C
= [Corr (
R
C
,
R
M
)
×
σ
C
] /
σ
M
= [(0.675) (0.065)] / (0.0383)
=
1.146
The beta of Ceramics Craftsman is 1.146.
12.4
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.
12.5
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This note was uploaded on 06/26/2008 for the course ECON 134a taught by Professor Lim during the Spring '08 term at UCSB.
 Spring '08
 Lim

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