1. A firm is considering two projects, A and B, with the following probability d
ID: 2536449 • Letter: 1
Question
1. A firm is considering two projects, A and B, with the following probability distributions for profit Profit ($1,000s) $ 20 40 60 80 100 Project A Probability (96) 10 15 50 15 10 Project B Probability (%) 10 15 25 40 10 a. Compute the expected value of project A (in $1,000s). b. Compute the variance of project A (in $1000s). c. Compute the expected value of project B (in $1000s). d. Which project would be selected if an analysis of variance rule were applied? e. Which project would a risk-neutral manager select? f. Report the coefficients of variation (v's)for projects A and B.Explanation / Answer
(a) Expected value of project A = Summation of X * Px where X is profit and Px is the probability of achieving that X profit.
= 20*0.1 + 40*0.15 + 60*0.50 + 80*0.15 + 100*0.1 = 2+6+30+12+10 = $60
(b) Variance of Project A = Summation of X^2 * Px - 60^2 = 20^2*0.1 + 40^2*0.15 + 60^2*0.50 + 80^2*0.15 + 100^2*0.1 = 40+240+1800+960+1000 - 3600 = 4040 - 3600 = 440
(c)
Expected value of project B = Summation of X * Px where X is profit and Px is the probability of achieving that X profit.
= 20*0.1 + 40*0.15 + 60*0.25 + 80*0.40 + 100*0.1 = 2+6+15+32+10 = $65
(d) Variance of Project B = Summation of X^2 * Px - 65^2 = 20^2*0.1 + 40^2*0.15 + 60^2*0.25 + 80^2*0.40 + 100^2*0.1 = 40+240+900+2560+1000 - 3600 = 4740 - 4225 = 515
Variance measures the level of risk in a project. Since, the variance of Project B is higher than project A, so project A will be selected.
(e) If the manager is risk neutral, then the project with higher expected value will be selected. Expected value of project B ($65) is higher than expected value of project A ($60). So, project B will be selected.
(f) Coefficient of variation = Standard deviation / Expected value where Standard deviation = Variance ^ (0.5)
Project A = 440^0.5 / 60 = 34.96%
Project B = 515^0.5 / 65 = 34.91%
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