CHAPTER 14
CAPITAL BUDGETING UNDER UNCERTAINTY
141
(a)
R
A
= (900)(0.50) + (500)(0.30) + (350)(0.20) = $670
R
B
= (700)(0.50) + (700)(0.30) + (550)(0.20) = $670
σ
A
= [(900  670)
2
(0.50) + (500  670)
2
(0.30) + (350  670)
2
(0.20)]
1/2
= $236
σ
B
= [(700 670)
2
(0.50) + (700  670)
2
(0.30) + (550  670)
2
(0.20)]
1/2
= $60
CV
A
= 236 ÷ 670 = 0.35
CV
B
= 60 ÷ 670 = 0.09
(b)
The two projects have the same expected value, but Project B has a smaller degree
of risk as measured by the standard deviation and the coefficient of variation.
Hence, Project B is better than Project A.
142
(a)
R = 1,000(0.20) + 2,000(0.10) + 3,000(0.30) +
4,000(0.40) = $2,900
(b)
or by financial calculator:
Hit CF; key in 2800 for CFo, then +/, then hit enter and scroll down; key 2900 for
CO1, hit enter, scroll down; key in 3 for F01, hit enter; hit NPV, key in 10 for I and
hit enter; scroll down to NPV screen and hit compute = NPV = $4411.87
(c)
σ
=
[(1,000  2,900)
2
(0.20) + (2,000  2,900)
2
(0.10) +
3,000  2,900)
2
(0.30) + (4,000  2,900)
2
(0.40)]
1/2
=
$1,136
143
(a)
Standard
Net Present
Coefficient of
Project
Deviation
Value
Variation
Rank
A$1,400
$7,000
0.20
5
B
6,300
70,000 0.09
1
C
2,800
21,000 0.13
3
D
4,900
35,000 0.14
4
E
2,100
21,000
0.10
2
(b)
Project C and E have an equal net present value of $21,000, but Project E has the
smaller standard deviation than Project C. This leads us to conclude that Project E is
better than Project C. Thus, to choose between Projects C and E only, we do not
need to use the coefficient of variation.
14.4 (a)NPV
=
$8000/(1.12)
1
+
$9000/(1.12)
2
+
$10000/(1.12)
3
+
$11000/(1.12)
4

$15000
=
$13433