стр. 128 
0.079
==$70
A $890
CAPITAL BUDGETING UNDER RISK
268 [CHAP. 9
For project B:
+ $800(0.3) + $1,000(0.3) + $1,400(0,2)
A = $550(0.2)
= $110 + $240 + $300 + $280 = $930
Q = d($550  $930)*(0.2)+ ($800 $930)*(0.3) + ($1,000  $930)2(0.3) + ($1,400  $930)2(0.2)
+ $5,070 + $1,470 + $44,180 = = $282.13
= v$28,880
 o.30
= $282.13
A $930
(b) Project A is relatively less risky than project B. Therefore, project AвЂ™s expected cash inflow is
discounted at 14 percent, while project BвЂ™s expected cash inflow is discounted at 16 percent.
For project A:
Expected NPV = PV  I  $4,500
= $89O(PVIFA14%.lo) $4,500 = $890(5.216)

 $4,500
= $4,642.24 = $142.24
For project B:
  $4,500
Expected NPV = $930(PVIFA16%,lo)$4,500 = $930(4.833)
 $4,500 = $5.31
= $4,494.69
Because project A has a positive NPV, project A should be chosen.
The company should also consider the potential diversification effect associated with these projects.
(c)
If the projectвЂ™s cash inflow patterns are negatively correlated with those of the company, the overall
risk of the company may be significantly reduced.
RiskAdjusted NPV.Kyoto Laboratories, Inc., is contemplating a capital investment project with
9.6
an expected useful life of 10 years that requires an initial cash outlay of $225,000. The company
estimates the following data:
Annual Cash Mows ($) Probabilities
0.10
0
50,000 0.20
65,000 0.40
70,000 0.20
90,000 0.10
( a )Assuming a riskadjusted required rate of return of 25 percent is appropriate for projects
of this level of risk, calculate the riskadjusted NPV of the project. (b) Should the project be
accepted? I
SOLUTION
n
2A,Pi + $50,000(0.2) + $65,000(0,4) + $70,000(0.2) + $90,000(0.1)
A
(4 = $0(0.10)
=
i=l
+ $26,000 + $14,000 + $9,000 = $59,000
= $0 + $10,000
PV  I
Expected NPV =
= $59,000 (PVIFAzs%,Io) $225,000 = $210,689  $225,000 = $14,311

(6) Reject the project, since the expected NPV is negative.
269
CAPITAL BUDGETING UNDER RISK
CHAP. 91
Certainty Equivalent NPV. Rush Corporation is considering the purchase of a new machine that
9.7
will last 5 years and require a cash outlay of $300,000. The firm has a 12 percent cost of capital
rate and its aftertax riskfree rate is 9 percent. The company has expected cash inflows and
certainty equivalents for these cash inflows, as follows:
AftepTax Cash M o w s ($)
Year Certainty Equivalent
1.00
1 100,OOO
2 100,OOO 0.95
3 100,OOO 0.90
4 100,OOO 0.80
5 100,000 0.70
Calculate ( a ) the unadjusted NPV, and (b) the certainty equivalent NPV. (c) Determine if
the machine should be purchased.
SOLUTION
NPV = PV  I = $lOO,OOO(PVIFA12%5) $300,000
(4
= $100,000(3.605)  $300,000 = $360,500 $300,000 = $60,500
(6)
AfteFTax Certainty Certain
Cash M o w s ($) Cash Mows ($) PV at 9%
Equivalents pv ($1
Year
.oo 100,OoO 0.917 91,700
100,OoO 1
1
79,990
0.95 95,000 0.842
1 0O O
0, O
2
69,480
1 0O O
0, O %OoO 0.772
3 0.90
80,000 0.708 56,640
100,OOO
4 0.80
0.70 70,000 0.650 45,500
100,OOO
5
343,310
Certainty equivalent NPV = $343,310  $300,000= $43,310
Because of a positive NPV, the machine should be purchased.
(c)
Decision "ree. The Summerall Corporation wishes to introduce one of two products to the
9.8
market this year. The probabilities and present values of projected cash inflows are given
below.
стр. 128 