1.A company is considering the following projects: Project A B C Construction co
ID: 1115656 • Letter: 1
Question
1.A company is considering the following projects:
Project
A
B
C
Construction cost 1000$
100
150
300
Annual Benefits 1000$/yr (prob)
30(0.2) 40(0.6) 45(0.2)
25(0.3) 35(0.6) 40(0.1)
45(0.1) 45(0.6) 50(0.3)
Life yrs
7
8
9
Their minimum acceptable B/C is 3.0. Which project should they select, if any at all? The rate is 4%. Clue: Select the project that maximizes the probability of B/C>3.
Project
A
B
C
Construction cost 1000$
100
150
300
Annual Benefits 1000$/yr (prob)
30(0.2) 40(0.6) 45(0.2)
25(0.3) 35(0.6) 40(0.1)
45(0.1) 45(0.6) 50(0.3)
Life yrs
7
8
9
Explanation / Answer
B/C is the ratio of sum of present value of all the benefits with present value of all costs
Present value = cash flow/(1+r)n, where r is rate of return and n is number of years
r = 4%
For project A, Construction cost = $100
Annual Benefit = $30 with probability of 0.2
Annual Benefit = $40 with probability of 0.6
Annual Benefit = $45 with probability of 0.2
Life = 7 years
If annual benefit is 30 then PV of benefit = 30/(1+0.04)1 + 30/(1.04)2 + ................................. + 30/(1.04)7 = 180.06
B/C = 180.06/100 = 1.80
If annual benefit is 40 then PV of benefit = 40/(1+0.04)1 + 40/(1.04)2 + ................................. + 40/(1.04)7 = 240.08
B/C = 240.08/100 = 2.40
If annual benefit is 45 then PV of benefit = 45/(1+0.04)1 + 45/(1.04)2 + ................................. + 45/(1.04)7 = 270.09
B/C = 270.09/100 = 2.70
B/C ratio for project A = 0.2*1.80 + 0.6*2.40 + 0.2*2.70 = 2.34
For project B, Construction cost = $150
Annual Benefit = $25 with probability of 0.3
Annual Benefit = $35 with probability of 0.6
Annual Benefit = $40 with probability of 0.1
Life = 8 years
If annual benefit is 25 then PV of benefit = 25/(1+0.04)1 + 25/(1.04)2 + ................................. + 25/(1.04)8 = 168.32
B/C = 168.32/150 = 1.12
If annual benefit is 35 then PV of benefit = 35/(1+0.04)1 + 35/(1.04)2 + ................................. + 35/(1.04)8 = 235.65
B/C = 235.65/150 = 1.57
If annual benefit is 40 then PV of benefit = 40/(1+0.04)1 + 40/(1.04)2 + ................................. + 40/(1.04)8 = 250.22
B/C = 250.22/150 = 1.67
B/C ratio for project B = 0.3*1.12 + 0.6*1.57 + 0.1*1.67 = 1.45
For project C, Construction cost = $300
Annual Benefit = $45 with probability of 0.1
Annual Benefit = $45 with probability of 0.6
Annual Benefit = $50 with probability of 0.3
Life = 9 years
If annual benefit is 45 then PV of benefit = 45/(1+0.04)1 + 45/(1.04)2 + ................................. + 45/(1.04)9 = 334.59
B/C = 334.59/300 = 1.12
If annual benefit is 50 then PV of benefit = 50/(1+0.04)1 + 50/(1.04)2 + ................................. + 50/(1.04)9 = 371.77
B/C = 371.77/300 = 2.48
B/C ratio for project B = 0.1*1.12 + 0.6*1.12 + 0.3*2.48 = 1.52
B/C for every project is less than 3 so no project shoul be selected
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