Question

A project's base case or most likely NPV is $44,000, and assume its probability of occurrence is 50%. Assume the best case scenario NPV is 85% higher than the base case and assume the worst scenario NPV is 35% lower than the base case. Both the best case scenario and the worst case scenario have a 25% probability of occurrence. Find the project's coefficient of variation.

Answer 1

Base Case:

Probability of Occurrence = 50%
NPV = $44,000

Best Case:

Probability of Occurrence = 25%

NPV = $44,000 + 85% * $44,000
NPV = $81,400

Worst Case:

Probability of Occurrence = 25%

NPV = $44,000 - 35% * $44,000
NPV = $28,600

Expected NPV = 0.50 * $44,000 + 0.25 * $81,400 + 0.25 * $28,600
Expected NPV = $49,500

Variance = 0.50 * (44,000 - 49,500)^2 + 0.25 * (81,400 - 49,500)^2 + 0.25 * (28,600 - 49,500)^2
Variance = 378,730,000

Standard Deviation = (378,730,000)^(1/2)
Standard Deviation = $19,460.99

Coefficient of Variation = Standard Deviation / Expected NPV
Coefficient of Variation = $19,460.99 / $49,500
Coefficient of Variation = 0.393