Question

# 1. Consider a project with free cash flows in one year of \$132,824 in a weak...

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.

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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