Huang Industries is considering a proposed project whose estimated NPV is $12 million. this estimate assumes that exonomic 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 0.2.0 (14 million)
average 0.50 12 million
above average 0.20 24 million
boom 0.05 32 million
calculate the projects expected NPV, standard deviation, and coefficient of variation
Answer
expected NPV…sum all (probability of scenario * NPV if that scenario)
= 5.3 mil
Working notes for the above answer is as under
| Prbabelity | NPV | |
| (A) | (B) | (A*B) |
| 0.05 | -86 | -4.3 |
| 0.2 | -14 | -2.8 |
| 0.5 | 12 | 6 |
| 0.2 | 24 | 4.8 |
| 0.05 | 32 | 1.6 |
| 1 | 5.3 |
So NPV = 5.3 Million
(2)
std dev is sq rt of variance
variance = for each economic scenario…(NPV for that scenario – 5.3mil)^2 * probability of that scenario…then sum all
| Prbabelity | NPV | NPV of Project |
|||
| (A) | (B) | ( C) | D = (B-C) | Square of D |
D*A |
| 0.05 | -86 | 5.3 | -91.3 | 8335.69 | 416.7845 |
| 0.2 | -14 | 5.3 | -19.3 | 372.49 | 74.498 |
| 0.5 | 12 | 5.3 | 6.7 | 44.89 | 22.445 |
| 0.2 | 24 | 5.3 | 18.7 | 349.69 | 69.938 |
| 0.05 | 32 | 5.3 | 26.7 | 712.89 | 35.6445 |
| 619.31 |
= 619.31,… sq rt (std dev)
= 24.8859
3
coeff of variation
= std dev / expected value
= 24.8859 / 5.3
= 4.6395
CV =4.695
