Consider a project with free cash flows in one year of $131,704 or $169,027, wit

Question

Consider a project with free cash flows in one year of

$131,704 or $169,027, with each outcome being equally likely. The initial investment required for the project is $108,058 and the project's cost of capital is 18 % The risk-free interest rate is 6%.

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 year. How much money can be raised in this waylong dash—that is, what is the initial market value of the unlevered equity?

c. Suppose the initial

$108,058 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?

Explanation / Answer

a)

Expected cashflow = 0.5*131704 + 0.5*169027 = 150365.5

NPV = -108058 + 150365.5 / (1+18%) = 19370.39

b)

Equity value = PV of cashflow = 150365.5 / (1+18%) = 127428.39

c)

Interest payments = 6%*108058 = 6483.48

Repayment = 108058

Levered equity cashflows = 131704 - 108058 - 6483.48 = 17162.52

Levered equity cashflows = 169027 - 108058 - 6483.48 = 54485.52

Intial value = 127428.39 - 108058 = 19370.39

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