Shao Industries is considering a proposed project for its capital budget. The co

Question

Shao Industries is considering a proposed project for its capital budget. The company estimates the project's NPV is $12 million. This estimate assumes that the economy and market conditions will be average over the next few years. The company's CFO, however, forecasts there is only a 50% chance that the economy will be average. Recognizing this uncertainty, she has also performed the following scenario analysis: Economic Scenario Probability of Outcome NPV Recession 0.05 -$56 million Below average 0.20 -28 million Average 0.50 12 million Above average 0.20 18 million Boom 0.05 36 million What is the project's expected NPV, its standard deviation, and its coefficient of variation? Enter your answers for the NPV and standard deviation in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answers to two decimal places.

E(NPV) $ ? million

NPV $ ? million

CVNPV ?

Explanation / Answer

Probability NPV

0.05 -56

0.2 -28

0.5 12

0.2 18

0.05 36

Mean or Expected NPV=0.05*-56+0.2*-28+0.5*12+0.2*18+0.05*36=$3 million

Variance=0.05*(-56-3)^2+0.2*(-28-3)^2+0.5*(12-3)^2+0.2*(18-3)^2+0.05*(36-3)^2=506.20 million^2

So, standard deviation=square root of variance=22.50 million

Coefficient of Variation=Standard Deviation/Mean=22.50/3=7.50

Standard Deviation

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