стр. 129 
Products Initial Investment ($) Cash M o w s ($) Probabilities
.oo
225,000
A 1
450,000 0.4
200,000 0.5
100,OOO 0.1
B .oo
80,000 1
320,000 0.2
100,000 0.6
150,000 0.2
( a ) Construct a decision tree to analyze the two products. (b) Which product would you
introduce? Comment on your decision.
270 CAPITAL BUDGETING UNDER RISK [CHAP. 9
SOLUTION
(4
PV of PV of
Initial
Cash Inflows
Investment Probability Cash Mows
(1) (2) x (3) = (4)
(3)
(2)
$450,000 $18O,OOO
$225,000 $200,000 100.000
$lOO,o00 10,Ooo
Product A p x p e c t e d PV of Cash Inflows $270,000
1
Choice
A or B
$ 64,000
Product B $320,000
 1$80,000 $100,000 60,000
$lSO,OoO 30,000
Expected PV of Cash Inflows $ 94,000
For product A:
= $45,000
expected PV  I  $225,000
Expected NPV = $270,000
=
For product B:
$94,000 $80,000 = $14,000
Expected NPV =
(b) Based on the expected NPV, choose product A over product B; however, this analysis fails to
recognize the risk factor in project analysis.
Dependent Cash Inflows and Expected NPV. The Newcome Corporation has determined that
9.9
its aftertax cash inflow (ATCI) distributions are not independent. Further, the company has
estimated that the year 1results (ATCI1) will affect the year 2 flows (ATC12) as follows:
If ATCIl = $40,000 with a 30 percent chance, the distribution for ATC12 is:
$20,000
0.2
0.6 $50,000
0.2 $80,000
If ATCIl = $60,000 with a 40 percent chance, the distribution for ATC12 is:
0.3 $70,000
0.4 $80,000
0.3 $90,000
If ATCIl = $80,000 with a 30 percent chance, the distribution for ATC12 is:
0.1 $80,000
$100,000
0.8
$120,000
0.1
Assume that the project's initial investment is $100,OOO.
( a ) Set up a decision tree to depict the above cash flow possibilities, and calculate an
expected NPV for each 2year possibility using a riskfree rate of 15 percent. ( b ) Determine
if the project should be accepted.
CAPITAL BUDGETING UNDER RISK 271
CHAP. 91
SOLUTION
(4
Expected
Joint
NPV
NPV at 10% Probability
The 2
"lme 1
llme 0
$50,080" $ 3,005
OMb
$ 20,000
$27,400 4,912
0.18
283
0.06
$ 4,720
$ 80,000
6 14
$ 5,120 0.12
$ 70,000
2,029
$12,680 0.16
2,428
0.12
$20,240
902
0.03
$ 80,000 $30,080
0.24 10,848
$45,200
 1.810
0.03
0.1\ $120,000 $60,320
1.oo

7
$40,000 $20,000
 (1 + 0.15)2 $100,000
"NPV = PV  I =
+
(1+ 0.15)

= $40,000(PVIF15%,1)+ $20,oOO(PVIF1,%,2) $100,000
$34,800 + $15,120  $loO,oOr, = $50,080
= $40,000(0.87)+ $20,000(0.756)  $lOO,OOO
Joint probability of the first path = (0.3)(0.2) = 0.06
The expected NPV is $10,431.
(b) Accept the project, since the expected NPV is positive.
стр. 129 