стр. 126 
7,000 4,000,000
0.10 700
u2= 1,300,000
A 5,000
=
Since u2= 1,300,000,U = $1,140.18.
(c) The coefficient of variation is:
B
A
$570.09 $1,140.18
CT
 = = 0.23
0.14
A $5,000
$4,000
( d ) Project B is riskier, since it has the greater coefficient of variation (Le., 0.23 versus 0.14).
Coefficient of Variation. McEnro wishes to decide between two projects, X and Y. By using
9.2
probability estimates, he has determined the following statistics:
Project Y
Project X
$35,000
Expected NPV $20,000
$22,000 $20,000
U
( a ) Compute the coefficient of variation for each project, and (6) explain why and the
U
coefficient of variation give different rankings of risk. Which method is better?
265
CAPITAL BUDGETING UNDER RISK
CHAR 91
SOLUTION
Project X Project Y
(4
(b) The coefficient of variation is a superior measure of risk because it is a relative measure, giving the
degree of dispersion relative to the expected value.
NPV Analysis Under Risk. The Connors Company is considering a $60,000 investment in a
93
.
machine that will reduce operating costs. The following estimates regarding cash savings, along
with their probabilities of occurrence, have been made:
Annual Cash Savings Useful Life
Probability Event Probability
Event
9 years 0.40
0.30
$20,000
8 years 0.40
0.30
$14,000
0.20
6 years
$12,000 0.40
( a ) Compute the expected annual cash savings and useful life. Determine whether the
machine should be purchased, using the NPV method.
( b )The company wishes to see whether the machine would be a good investment if each of
its most pessimistic estimates, but not both at the same time, came true. Determine whether the
investment would be desirable if: (1)the useful life is the expected value computed in part ( a ) ,
and annual cash flows are only $12,000;(2) the annual cash flows are equal to the expected value
computed in part ( a ) and the useful life is only 6 years.
SOLUTION
Determination of expected annual cash savings is:
(a)
Event (A,) Probabilities @,) Expected Value
$20,000 0.30 $ 6,000
$14,000 4,200
0.30
4,800

0.40
$12,000

1.00 $15,000
Determination of useful life is:
Event Probability Useful Life
9 years 3.6 years
0.40
8 years 0.40 3.2 years

0.20 1.2 vears
6 years

1.00 8.0 years
Expected annual cash savings
Present value factor for 8year
annuity at 16% x4.344
Present value of future flows (PV) $65,160
Less cost of machine (I) 60,000
Net present value (NPV) $ 5,160
The purchase of the machine would appear to be wise because of its positive net present value.
[CHAP. 9
266 CAPITAL BUDGETING UNDER RISK
(b) (1) The present value of the future cash savings ($52,128) is less than the purchase price ($60,000)
and the machine should not be purchased.
Annual cash savings, pessimistic
estimate $12,000
Present value factor, 8year annuity
4.344
at 16%
Present value of future cash flows $52,128
(2) The present value of the future cash savings ($55,275) is less than the purchase price ($60,000)
and the machine should not be purchased.
Annual cash savings, expected value $15,000
Present value factor, 6year annuity
at 16% 3.685
Present value of future cash flows $55,275
Expected NPV and Risk. The administrator of ABC Hospital is considering the purchase of new
9.4
operating room equipment at a cost of $7,500. The surgical staff has furnished the following
estimates of useful life and cost savings. Each useful life estimate is independent of each cost
savings estimate.
Years of
Estimated Probability of Estimated Cost Probability of
Useful Life Occurrence Savings Occurrence
4 0.25 $1,900 0.30
5 $2,000
0.50 0.40
6 0.25 0.30
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