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 | -$78 million |
Below average | 0.20 | -14 million |
Average | 0.50 | 12 million |
Above average | 0.20 | 14 million |
Boom | 0.05 | 32 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 |
Calcualtion of Expected NPV(R) and Standard deviation | ||||
Probability(P) | NPV($) | Expected NPV(R) (P*NPV) | d=NPV-Mean | P*(d)^2 |
0.05 | -78 | -3.9 | -81.7 | 333.7445 |
0.2 | -14 | -2.8 | -17.7 | 62.658 |
0.5 | 12 | 6 | 8.3 | 34.445 |
0.2 | 14 | 2.8 | 10.3 | 21.218 |
0.05 | 32 | 1.6 | 28.3 | 40.0445 |
Total | 3.7 | 492.11 |
.
Mean=Expected NPV i.e 3.7
Standard Deviation=Sqrt[P*(d)^2]
=Sqrt(492.11)
=22.18
Thus expected NPV is 3.7 and standard deviation is 22.18
b)Calculation of coefficient of variation
Coefficient of variation=Standard deviation/Mean
=22.18/3.7
=6
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