Question

Huang Industries is considering a proposed project whose estimated NPV is $12 million. This estimate assumes that economic conditions will be "average." However the CFO realizes that conditions could be better or worse, so she performed a scenario analysis and obtained these results:

Economic Scenario	Probability of Outcome	NPV
Recession	0.05	- $54 million
Below average	0.20	- $14 million
Average	0.50	12 million
Above average	0.20	20 million
Boom	0.05	28 million

Calculate the project's expected NPV, standard deviation, and coefficient of variation. Enter your answers for the project's expected NPV and standard deviation in millions. For example, an answer of $13,000,000 should be entered as 13. Do not round intermediate calculations. Round your answers to two decimal places.

E(NPV): $    million
σ_NPV: $    million
CV:

Answer 1

1)The project's expected NPV is the sum of the product of probability and respective NPV of all the economic scenarios:

Economic scenario	Probability of outcome(P)	NPV	P * NPV
Recession	0.05	-54	-2.7
Below average	0.2	-14	-2.8
Average	0.5	12	6
Above average	0.2	20	4
Boom	0.05	28	1.4
		Total	5.9

Hence, E(NPV): $ 5.9 million

2)

Economic scenario	Probability of outcome(P)	NPV	P * NPV	X=(NPV - Expected NPV)	X^2	P * (X^2)
Recession	0.05	-54	-2.7	-59.9	3588.01	179.4005
Below average	0.2	-14	-2.8	-19.9	396.01	79.202
Average	0.5	12	6	6.1	37.21	18.605
Above average	0.2	20	4	14.1	198.81	39.762
Boom	0.05	28	1.4	22.1	488.41	24.4205
		Expected NPV	5.9		Variance	341.39

Standard deviation = sqrt (variance) = sqrt (341.39) =18.48

σNPV: $ 18.48 million

3)

coefficient of variation = Standard dev / mean

= 18.48/ 5.9

= 3.13

CV= 3.13