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# NPV/Black-Scholes

A company is considering a project with the following data:
Initial Cost = \$500,000
Cost of Capital = 12%
Risk Free Rate = 5%
Cash Flows occur for 3 years according to the following:
Demand Probability Annual Cash Flow
High .30 \$270,000
Average .50 \$180,000
Low .20 \$90,000

a. Compute the NPV of the project.

b. If the company were to wait one year, then the firm would gain additional information regarding demand. The company would be able to not implement the project if demand were low. If the company were to wait, the up front cost and cash flow would remain the same, except they would be shifted ahead by one year. Compute the expected NPV if the company were to wait.

#### Solution Preview

The formula for NPV is:
NPV = initial cost + CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3
here CFn = Cash Flow in year n, r = interest rate or cost of capital or risk free rate.

(a) First of all, we have the same CF for all the 3 years. To compute it, we need to use Bayes' theorem (conditional probability). That gives us:
CF = 0.30*270,000 + ...

#### Solution Summary

This solution uses the NPV equation to calculate the net present value of the company according to the data and also if the company were to wait a year to gain additional information on demand. All formulas and workings are shown.

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