51
Solutions to Chapter 12
Risk, Return, and Capital Budgeting
1.
a.
False.
Investors require higher expected rates of return on investments with high
market
risk, not high
total
risk.
Variability of returns is a measure of total risk.
b.
False.
If beta = 0, then the asset’s expected return should equal the riskfree rate, not
zero.
c.
False.
The portfolio is invested onethird in Treasury bills and twothirds in the market.
Its beta will be:
(1/3
×
0) + (2/3
×
1.0) = 2/3
d.
True.
e.
True.
6.
a.
The expected cash flows from the firm are in the form of a perpetuity.
The discount rate is:
r
f
+
β
(r
m
– r
f
) = 4% + 0.4
×
(11% – 4%) = 6.8%
Therefore, the value of the firm would be:
82
.
058
,
147
$
068
.
0
000
,
10
$
r
flow
Cash
P
0
=
=
=
b.
If the true beta is actually 0.6, the discount rate should be:
r
f
+
β
(r
m
– r
f
) = 4% + [0.6
×
(11% – 4%)] = 8.2%
Therefore, the value of the firm is:
22
.
951
,
121
$
082
.
0
000
,
10
$
r
flow
Cash
P
0
=
=
=
By underestimating beta, you would overvalue the firm by:
$147,058.82 – $121,951.22 = $25,107.60
13.
The appropriate discount rate for the project is:
r = r
f
+
β
(r
m
– r
f
) = 4% + 1.4
×
(12% – 4%) = 15.2%
Therefore:
NPV = –$100 + [$15
×
annuity factor(15.2%, 10 years)]
= –$100 + $15
29
.
25
$
(1.152)
0.152
1
0.152
1
10
−
=
×
−
×
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You should reject the project.
15.
From the CAPM, the appropriate discount rate is:
r = r
f
+
β
(r
m
– r
f
) = 4% + (0.75
×
7%) = 9.25%
r = 0.0925 =
⇒
+
=
+
50
50)

P
(
2
price
gain
capital
DIV
1
P
1
= $52.625
22.
r = r
f
+
β
(r
m
–
r
f
)
5 = r
f
+ 0.5(r
m
–
r
f
)
(stock A)
13 = r
f
+ 1.5(r
m
–
r
f
)
(stock B)
Solve these simultaneous equations to find that: r
f
= 1% and r
m
= 9%
Chapter 13
3.
×
+
×
+
−
×
×
=
equity
preferred
C
debt
r
V
E
r
V
P
)
T
1
(
r
V
D
WACC
= [0.3
×
7.50%
×
(1 – 0.35)] + [0.2
×
10%] + [0.5
×
12.0%] = 9.46%
5.
The total value of the firm is $80 million.
The weights for each security class are as
follows:
Debt:
D/V = 20/80 = 0.250
Preferred:
P/V = 10/80 = 0.125
Common:
E/V = 50/80 = 0.625
×
+
×
+
−
×
×
=
equity
preferred
C
debt
r
V
E
r
V
P
)
T
1
(
r
V
D
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 Spring '09
 LI
 Net Present Value, Weighted average cost of capital, rm – rf

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