 # Conditional Probability Question

An analyst has been hired to evaluate a venture capital opportunity by a syndicate of interested potential investors. The analyst estimates the probability that the project will fail in the first year as well as the conditional probability of failure in each of the ramaining four years of the project as follows: Year 1: .25 Year 2: .20 Year 3: .20 Year 4: .15 Year 5: .10 The syndicate has told the analyst that he will have to put up \$2 million initially and believe that he will reap a windfall payoff of \$20 million at the end of the fifth year when he plans on taking the new venture public through an initial public offering. Because of its high risk, the requireed rate of return on the invested equity is 25%. Based on this information, the expected NPV of the project is closest to: A. \$406,480 B. \$1,265,600 C. \$1,672,080 D. \$2,553,600 Sorry about the length of the problem…

I get C

A

The correct answer is A, but i can’t figure how they arrived at this conclusion

Probability of succeeding: .75*.8*.8*.85*.9 = .3672 NPV = 4,553,600 * .3672 = 1,672,081.92 If fails = -2,000,000 * (1-.3672) = -1,265,600 1,672,081.92 - 1,265,600 = 406,481.92 A

right on Dsylexic, can you show how you worked out the problem?

expected pay off = 20 million *prob of success discounted back at 25% and subtracted from 2 million initial investment = 2 million - 20 m *(1-.25)(1-.2)(1-.2) (1-.15)(1-.1)/1.25^5

Probabilty that it will survive till the end = (1 - 0.25)* (1- 0.20 )* (1- 0.20)*(1- 0.15)*(1- 0.10) = 0.3672 Probabilty that it will not = (1 - 0.3672) = 0.6328 NPV(if successful) = 4.5536 NPV(if failure) = -2 expected NPV of the project = NPV(if successful) *P(success) + NPV(if failure)*P(failure) = 4.5536*0.3672 + (-2) *0.6328 = 1.67206 - 1.265 = 0.40706M = A ?? - Dinesh S

Another way is, .3672 * 20M / ((1.25) ^ 5) - 2M.

I see my mistake. I think I’ve even done one like this before and gotten it correct… disheartening…

A is correct