стр. 130 
Decision 'Ikee Analysis. The Drysdale Corporation is contemplating the development of a new
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product. The initial investment required to purchase the necessary equipment is $200,000.There
is a 60 percent chance that demand will be high in year 1.If it is high, there is an 80 percent chance
that it will continue high indefinitely. If demand is low in year 1,there is a 60 percent chance that
it will continue to be low indefinitely. If demand is high, forecasted cash inflow (before taxes) is
$90,000 a year; if demand is low, forecasted cash inflow is $30,000 a year.
The corporate income tax rate is 40 percent. The company uses straightline depreciation and
will depreciate the equipment over 10 years with no salvage value.
( a ) Determine the aftertax cash inflows. ( b )Set up a decision tree representing all possible
outcomes, and compute the expected NPV using a 10 percent riskfree rate of return.
SOLUTION
first, compute the annual depreciation.
(a)
$200,000
 $20,00O/year
Depreciation = pricehseful life = =
10 years
Aftertax cash inflow = aftertax net profits + depreciation
Therefore, when demand is high:
Aftertax cash inflow = ($90,000  $20,000)(1  0.4) + $20,000 = $62,000
When demand is low:
Aftertax cash inflow = ($30,000  $20,000)(1  0.4) + $20,000 = $26,000
CAPITAL BUDGETING UNDER RISK
272 [CHAP. 9
Times Expected
Joint
NPV NPV
TTme 1 210 Probability
Time 0 at 10%
$180,990" 0.48b $ 86,875
7,506 0.12
$ 901
$200,000
$148,266 0.16 23,723
$ 40,230 0.24
 9,655

1 $100,042
.OO


UNPV = PV  I =  $62000 + . . . +
$62,000 +
(1+ 0.1) (1+ 0.1)2
+   $200,000
= $62,(KK)(PVIFlo%ql)$62,OOO(PVIFAlo%,˜o PVIFA˜OX,˜)
= $62,000(0.909) + $62,000(6.145  0.909)  $200,00O
= $56,358+ $324,632  $200,000 = $180,990
hJoint probability = (0.6)(0.8) = 0.48
The expected NPV is $100,042.
Decision lkee Analysis and Expected IRR. The NFL Systems, Inc., is considering the purchase
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of a minicomputer using the following decision tree:
The2
Tlme 1
nme 0
0.4
( a ) Complete the decision tree by computing IRR, joint probability, and the expected IRR
(round to the nearest whole percent of IRR). (6) Should this computer be purchased? (Assume
the company's cost of capital is 16 percent.)
273
CAPITAL BUDGETING UNDER RISK
CHAP. 91
SOLUTION
(4
Expected
Joint
IRR
e2 Probability IRR
h
"lme 0
"lme l 1.0
$10,000 0.4'
9%" 3.6
$17,500 $12,500 25% 0.30 7.5
$13,500 9.0
0.30
30%' 
1.oo 20.1%

"By definition, at IRR,1 = PV.
Thus,
$17,500 = $lO,OOO( PVIFA,2)
From Appendix D this value is close to 9 percent.
bJoint probability = (0.4)(в‚¬.0)= 0.4
"I = PV($17,500) = $12,50O(PVIF,,1) + $13,50O(PVIF,,2)
By trial and error, IRR is approximately 30 percent. In other words, at t = 30 percent:
I = PV
= $12,500(0.769)+ $13,500(0.592)= $9,613 + $7,992 = $17,605
(b) The expected IRR is 20.1 percent, which exceeds the cost of capital of 16 percent. Therefore, the
computer should be purchased.
Normal Distribution and NPV Analysis. The probability distribution of possible NPVs for
91
.2
project A has an expected cash inflow of $30,000 and a standard deviation of $15,000. Assuming
a normal distribution, compute the probability that: ( a ) the NPV will be zero or less; (6) the NPV
will be greater than $45,000; and (c) the NPV will be less than $7,500.
стр. 130 