Question

Consider a project with free cash flows in one year of $133,605 in a weak market or $196,786 in a strong​ market, with each outcome being equally likely. The initial investment required for the project is $65,000​, and the​ project's unlevered cost of capital is 24%. The​ risk-free interest rate is 9%. ​(Assume no taxes or distress​ costs.)

a. What is the NPV of this​ project?

The NPV is ​$ _____?

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 way—that ​is, what is the initial market value of the unlevered​ equity?

   The initial market value of the unlevered equity is ​$ ___?

c. Suppose the initial $65,000 is instead raised by borrowing at the​ risk-free interest rate. What are the cash flows of the levered equity in a weak market and a strong market at the end of year​ 1, and what is its initial market value of the levered equity according to​ MM?  

Assume that the​ risk-free rate remains at its current level and ignore any arbitrage opportunity.

	Date 0	Date 1
	Initial Value	Cash Flow Strong Economy	Cash Flow Weak Economy
Debt	$65,000	​$	​$
Levered Equity	​$	​$	​$

Answer 1

Project
a. What is the NPV of this​ project?
EC = (0.5 x 133605 ) + ( 0.5 x 196786 ) = $165195.50
NPV = 165195.50 / 1.24 - 65000 = $68222.18
b.What is the initial market value of the unlevered​ equity?
Equity Value = PV ( C ) = 165195.50 / 1.25 = $133222.2
c.what is its initial market value of the levered equity according to​ MM?
Debt payments = 65,000 x 1.09 = 70,850
Equity receives 133,605 – 70,850 = 62,755
or 196,786 – 70,850.5 = 125,935.5.
Initial value, by MM, is 133,222.22 – 65,000 = $68,222.18