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.

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