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	($30 million)
Below average	0.20	(18 million)
Average	0.50	12 million
Above average	0.20	14 million
Boom	0.05	36 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
σNPV:	million
CV:

Answer 1

State	Probability of State (P)	NPV (R)	P*R	P*R^2
Recession	5%	-30.00	-1.50	45.00
Below Average	20%	18.00	3.60	64.80
Average	50%	12.00	6.00	72.00
Above Average	20%	14.00	2.80	39.20
Boom	5%	36.00	1.80	64.80
		Sum	12.70	285.80

Expected return = sum of (probability of state * return of state)

= 12.70 million

E(X^2) =  sum of (probability of state * return of state^2)

= 285.80 million

variance = E(X^2) - (E(X))^2

= 285.8 - (12.7)^2

= 124.51

Standard deviation = sqrt(variance)

= sqrt(124.51)

= 11.16 million

CV = standard deviation/expected return

= 11.16/12.7

= 0.88