ñòð. 133 
A 4 2
B 2 6 12
10 15 20
C
50
8
D 25
Assume that the riskfree rate of return is 6 percent and the market rate of return is 12
percent. Which projects should be selected?
SOLUTlON
Use the CAPM equation to compute:
r = rj+ b(rm rj)
Projects
r A = 6% + (0.5)(12%  6%) = 3%
A
r˜ = 6% + (O.8)(12Yo  6%) = 10.8%
B
rc = 6â€™Xo + (1.2)(12%  6%) = 13.2%
C
rD = 6% + (2.0)(12%  6%) = 18%
D
Average rates of return are:
Projects
4(0.4) + 2(0.5) + 5(0.1) = 3.1%
A
2(0.4) + 6(0.5) + 12(0.1) = 5%
B
lO(0.4) + 15(0.5) + 20(0.1) = 13.5%
C
8(0.4) + 25(0.5) + 50(0.1) = 14.3%
D
278 CAPITAL BUDGETING UNDER RISK [CHAP. 9
Projects A and C should be selected, since their average rates of return exceed the required rates of
return provided by the CAYM equation.
Beta and NPV Analysis. The riskfree rate is 5 percent and the expected return on the market
9.16
portfolio is 13 percent. On the basis of the CAPM, answer the following questions: ( a ) What is
the risk premium on the market? (b) What is the required rate of return on an investment with
a beta equal to 1.2? (c) If an investment with a beta of 0.6 offers an expected return of 8.5 percent,
does it have a positive NPV? (d) If the market expects a return of 12.5percent from stock A, what
is its beta?
SOLUTION
Risk premium = (rn, r f ) = 13%  5% = 8%
(4
The answer is no.
(c)
+ 0.6(13%  5%) = 9.8%
rj = 5%
Since the required rate of return is 9.8 percent and the expected return from the investment is
only 8.5 percent, the project produces a negative NPV.
rj = rf + b(rnl r f )
12.5% = 5% 4 b(13Yo  5%)
b = 0.9375
9 1 Beta and NPV Analysis. A project has the following forecasted cash flows (in thousands of
.7
dollars):
Year 1
Year0 Year2 Year3
$90
$50
$30
($100)
The estimated project beta is 2.0. The market return is 13percent, and the neasury bill yield
is 6 percent. Compute ( a ) the projectâ€™s cost of capital and (6) the projectâ€™s NPV.
SOLUTION
of capital is:
( a ) The projectâ€™s cost
rf + b(rnl r f )
r =
+ 14% = 20%
= 6% + 2.0(13%  6%) = 6%
(b) The projectâ€™s NPV is:
pv 6)
Cash Flow ($)
Year PV at 20%
(100)
0 (100)
1.WO
30 0.833 25
1
0.694 35
50
2

3 90 0.579 52
N P V = 12

279
CHAP. 91 CAPITAL BUDGETING UNDER RISK
Calculationof Beta Using RegressionAnalysis.You are given the following data for stock A and
9.18
the market portfolio:
Historic Rates of Return
r, (Yo) r,,, (%)
Year
19x0 2
1
3 7
19x1
19x2 14 .20
19x3 18 30
Assuming that the riskfree rate is 4 percent, compute ( a ) the beta coefficient and (b) the
required rate of return to be used for capital budgeting decisions in 19x4 when the market
rate of return is expected to be 18percent?
SOLUTION
(4
Excess Excess
Market RiskFkee
Stock Cross
Market Return Product
Return, Return, Rate, Stock Return
Mz
( 9  f,) = K MK
(r,rm) = M
9
r
l
m
Year fJ
0.02 0.04 0.0018
0.06 0.0036
ñòð. 133 