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	($86 million)
Below average	0.20	(28 million)
Average	0.50	12 million
Above average	0.20	14 million
Boom	0.05	34 million

Calculate the project's expected NPV, standard deviation, and coefficient of variation. Round your answers to two decimal places. 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.

E(NPV)	= $  million?
σNPV	= $  million ?
CV	=?

Answer 1

Project's expected NPV - E(NPV)

E(NPV) = Sum[NPV x Probability of Outcome]

= Sum[(-$86 x 0.05) + (-$28 x 0.20) + ($12 x 0.50) + ($14 x 0.20) + ($34 x 0.05)]

= -$4.30 - $5.60 + $6.00 + $2.80 + $1.70

= $0.60 Million

“E(NPV) = $0.60 Million”

Projects Standard Deviation - σNPV

σNPV = √[{0.05(-86 – 0.60)²} + {0.20(-28 – 0.60)²} + {0.50(12 – 0.60)²} + {0.20(14 – 0.60)²} + {0.05(34 – 0.60)²}]

= √[ 374.98 + 163.59 + 64.98 + 35.91 + 55.78]

= √695.24

= $26.37 Million

“σNPV = $26.37 Million”

Coefficient of Variation - CV

CV = σNPV / E(NPV)

= $0.60 Million / $26.37 Million

= 43.95

“CV = 43.95”