1. (20 points) A company is considering a project and estimates that there are t
ID: 1121127 • Letter: 1
Question
1. (20 points) A company is considering a project and estimates that there are three possible scenarios for the cash flows and costs. The outcomes and corresponding probabilities, cash flows and life estimated are as shown below. What is the expected value and variance of the net present worth of the project with a MARR of 12%? What is the probability that the present worth will be greater than 0? Scenario 1 Scenario 2 Scenario 3 Initial Investment $800,000 25 8 years $600,000 $400,000 Probability Project Life Annual Revenue Annual Cost Salvage Value $450,000 $200,000 $100,000 35 years 400,000 $180,000 $80,000 40 8 years $300,000 $150,000 60,000Explanation / Answer
Expected value of NPV is calculated as under:
Scenario 1 = Annual cash inflow is = Annual revenue - annual cost = 450000-200000 = 250000
hence NPV for Option 1 = Present value of cash inflows -net investment
Present value of cash inflow = 250000 PVIFA(12 %,8) + 100000 PVIF(12%,8) =250000 *4.976 +100000 *0.4039 =1244000+40390 = 1284390
Hence NPV for scenario 1 = present value of cash inflows - initial investment = 1284390-800000 =484390
Similarly for scenario 2 : Annuall cash inflows =Annual revenue -annual cost = 400000-180000 = 220000
Present value of annual cash inflows = 220000 PVIFA(12%,8) +80000 PVIF(12%,8) = 1094720 +32312= 1127032
NPV for option 2 = Present value of cash inflows - initial investment = 1127032- 600000 =527032
Similarly NPV for option 3 is calculated as :
Annual cash inflows for option 3 = Annual revenue - Annual Cost = 300000 - 150000 = 150000
Present value of cash inflow = 150000 PVIFA(12%,8) + 60000 PVIF( 12%,8) = 150000*4.9679 +60000*0.4039 = 745185 +24234 = 769419
NPV for option 3 = Present value of cash inflows - initial investment = 769419 - 400000 = 369419
Expected NPV = NPV of option 1 * prob +NPV of option 2* prob + NPV of option 3 * prob.
= 484390 *0.25 +527032 * 0.35 +369419 *0.40 = 121097.5 +184461.2 +147767.6 = 453326.3
Ans b ) The variance of the net worth is calculated as under:
= Scnario 1 (Expected NPV - Actual NPV )^2 * prob + Scnario 2 (Expected NPV -Actual NPV)^2 * Prob + Scenario 3 ( Expected NPV -Actual NPV )^2 * Prob = (453326.3 -484390)^2 *0.25 +(453326.3-527032)^2 *0.35 +(453326.3-369419)^2*0.40
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