A corporation must decide between two mutually exclusive projects. Bo(h projects
ID: 1189976 • Letter: A
Question
A corporation must decide between two mutually exclusive projects. Bo(h projects require an initial outlay of 100 million euro, and (hey generate cash flows that are independent of the growth of the economy. Project A bas an equal probability of four gross payoffs: 80 million euro, 100 million euro. 120 million euro or 140 million euro. Project B has a 50:50 chance of paying either 90 million euro or 130 million euro. Assuming that shareholders are ail risk averse, show that they unanimously prefer Project B to Project A.Explanation / Answer
The coefficient of variance (CV) should be calculated for both these projects. The project of lower CV should be chosen, since it indicates lower risk.
Project A
X
P
PX
(X – E)
(X – E)^2
P(X – E)^2
80
0.25
20
-30
900
225
100
0.25
25
-10
100
25
120
0.25
30
10
100
25
140
0.25
35
30
900
225
1
110 = E
500 = V
CV = (v) / E = 500 / 110 = 0.20
Project B
X
P
PX
(X – E)
(X – E)^2
P(X – E)^2
90
0.5
45
-20
400
200
130
0.5
65
20
400
200
1
110 = E
400 = V
CV = (v) / E = 400 / 110 = 0.18
Since project B has lower CV, it should be chosen before A
X
P
PX
(X – E)
(X – E)^2
P(X – E)^2
80
0.25
20
-30
900
225
100
0.25
25
-10
100
25
120
0.25
30
10
100
25
140
0.25
35
30
900
225
1
110 = E
500 = V
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