Question

Scenario Analysis

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	-$82 million
Below average	0.20	-24 million
Average	0.50	12 million
Above average	0.20	20 million
Boom	0.05	34 million

What are the project's expected NPV, standard deviation, and coefficient of variation? Enter your answers for the NPV and standard deviation in millions. For example, an answer of $1.24 million should be entered as 1.24, not 1,240,000. Do not round intermediate calculations. Round your answers to two decimal places.

E(NPV)	$   million
σNPV	$   million
CVNPV

Answer 1

Expected NPV = 0.05 * (-82) + 0.20 * (-24) + 0.50 * 12 + 0.20 * 20 + 0.05 * 34
Expected NPV = 2.80

So, Expected NPV is $2.80 million

Variance = 0.05 * (-82 - 2.80)^2 + 0.20 * (-24 - 2.80)^2 + 0.50 * (12 - 2.80)^2 + 0.20 * (20 - 2.80)^2 + 0.05 * (34 - 2.80)^2
Variance = 653.36

Standard Deviation = (653.36)^(1/2)
Standard Deviation = 25.56

Standard Deviation in NPV = $25.56 million

Coefficient of Variation = Standard Deviation in NPV / Expected NPV
Coefficient of Variation = $25.56 million / $2.80 million
Coefficient of Variation = 9.13