 # Question about NPV of Project

Could someone please explain this answer? An investor works for a venture capital firm and is considering investing \$4.5 million in a specific project. Based on his caluclations, he expects the project to pay \$10.3 million after 6 years. Realizing that the project may not survive until then, he estimates a 45% probability of survival through the sixth year. The net present value (NPV) of the project is \$2.8 million. Should he recommend investing in the project? A) No, because the NPV of \$2.8 million is less than the \$4.5 million invested. B) Yes, because the NPV is positive. The answer is B but I thought it would be B… My question is: don’t we need to factor in the probability of the failure???

Since NPV is positive – and NPV has figured in the probability of success of the project – go ahead and choose B. In most of these venture capital problems there are two ways to solve them 1. On the success path P(Success) * (Final Outflow / (1+r)^n - Initial Investment) 2. On the failure path - P(Failure) * Initial Investment and NPV = 1 + 2 But if you simplify the sum it is equal to -Initial Investment + P(Success) * Final Outflow / (1+r)^n because p(Success) + P(Failure) = 1 This is a simplification that you might be able to do, with ease. Check it out on a couple of problems. CP

I thought when the project is failed, you get nothing. NPV = -Initial Investment + P(Success) * Final Outflow / (1+r)^n + P(failure)*0

You do. Which is what cpk123 said. >But if you simplify the sum >it is equal to >-Initial Investment + P(Success) * Final Outflow / (1+r)^n