Question

Herman Co. is considering a four-year project that will require an initial investment of $7,000. The base-case cash flows for this project are projected to be $12,000 per year. The best-case cash flows are projected to be $19,000 per year, and the worst-case cash flows are projected to be –$3,000 per year. The company’s analysts have estimated that there is a 50% probability that the project will generate the base-case cash flows. The analysts also think that there is a 25% probability of the project generating the best-case cash flows and a 25% probability of the project generating the worst-case cash flows.
What would be the expected net present value (NPV) of this project if the project's cost of capital is 12%?

Answer 1

Answer:

Net Present Value    $ 23,373.49

Explanation:

First, we solve for the expected return:

$\left[\begin{array}{cccc}State&Return&Probability&Weight\\best-case&19,000&0.25&4,750\\base-case&12,000&0.5&6,000\\worst-case&-3,000&0.25&-750\\Total&&1&10,000\\\end{array}\right]$

Now, we solve for the present value of this vaue over the four-year period:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 10,000.00

time 4

rate 0.12

$10000 \times \frac{1-(1+0.12)^{-4} }{0.12} = PV$

PV $30,373.4935

Last we subtract the investment cosT:

30,373.49 - 7,000 = 23,373.49