Question

1. Consider a project with free cash flows in one year of
$132,824 in a weak market or $171,945 in a strong market, with
each outcome being equally likely. The initial investment required
for the project is $90,000, and the project's unlevered cost of
capital is 10%. The risk-free interest rate is 12%. (Assume no
taxes or distress costs.)

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

c. Suppose the initial $90,000 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.

Answer #1

**a. NPV of the project**

Expected cash flow of project in one year = 1/2*132824 + 1/2*171945 = 152385

Present Value = (Cash Flow / (1+r)^t) - Initial Investment

where,

Cash Flow = 152385

r = required rate of return = 10%

t = Number of time periods = 1

Initial Investment = 90000

So, Present Value = (152385 / (1+ 10%)^1) - 90000 = 48531.82

Thus, NPV of this project is $ 48531.82.

**b. Initial market value of the unlevered
equity**

= 152385 / 1.10 = 138531.82

**c. Cash Flows**

Date 0 | Cost | Date 1 | ||

Initial Value | Cash flow strong economy | Cash flow weak economy | ||

Debt | $90000 | $10800 | $71145 | $32084 |

Leveraged Equity | $48531.82 | $4853.18 | $118560 | $79439 |

Initial market value of levered equity according to MM is $ 48531.82.

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