Question

Consider a project with free cash flows in one year of ​$142,000 or ​$180,000​, with each outcome being equally likely. The initial investment required for the project is

​$90,700​, and the​ project's cost of capital is 17%.  The​ risk-free interest rate is 10%.

                            

a. What is the NPV of this​ project?

b. Suppose that to raise the funds for the initial​ investment, the project is sold to investors as an​ all-equity firm. The equity holders will receive the cash flows of the project in one ear. How much money can be raised in this waylong—that ​is, what is the initial market value of the unlevered​ equity? 

c. Suppose the initial ​$90,700 is instead raised by borrowing at the​ risk-free interest rate. What are the cash flows of the levered​ equity, what is its initial value and what is the initial equity according to​ MM?

Answer 1

a) NPV of the project is present value of the future cash flow subtracted from the initial investment.

So, The present value of the future cash flow will be

142,000(0.5) + 180,000(0.5) ---- multiplying by 0.5 as both have equal probability of happening. So taking 50% of both outcomes

So total is 161,000

Now present value of 161,000 is

161,000/(1.17) ---- don't use risk free rate for discounting. Always use cost of capital

= 137,606

So the NPV of the project is 137,606 - 90,700

46,906. So it is a positive NPV project and should be accepted.