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	-$40 million
Below average	0.20	-24 million
Average	0.50	12 million
Above average	0.20	22 million
Boom	0.05	38 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)	$
σNPV	$
CVNPV

Answer 1

Calcualtion of Expected NPV(R) and Standard deviation

Probability(P)	NPV($)	Expected NPV(R) (P*NPV)	d=NPV-Mean	P*(d)^2
.05	-40	-2	-45.5	103.5125
.20	-24	-4.8	-29.5	174.05
.50	12	6	6.5	21.125
.20	22	4.4	16.5	54.45
.05	38	1.9	32.5	52.8125
Total	5.5		405.95

Mean=Expected NPV i.e 5.5

Standard Deviation=Sqrt[P*(d)^2]

=Sqrt(405.95)

=20.15

Thus expected NPV is 5.5 and standard deviation is 20.15

b)Calculation of coefficient of variation

coefficient of variation=Standard deviation/Mean

=20.15/5.5

=3.66