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# Free Cash Flows and Unlevered Equity

1. Consider a project with free cash flows in one year of \$90,000 in a weak economy or \$117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is \$80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%. What is the NPV?

2. Consider a project with free cash flows in one year of \$90,000 in a weak economy or \$117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is \$80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%. 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. What is the market value of the unlevered equity?

3. Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity firm, with 1 million shares outstanding that trade for a price of \$24 per share. With has 2 million shares outstanding and \$12 million dollars in debt at an interest rate of 5%. According to MM Proposition 1, what is the stock price?

4. Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity firm, with 1 million shares outstanding that trade for a price of \$24 per share. With has 2 million shares outstanding and \$12 million dollars in debt at an interest rate of 5%. Assume that MM's perfect capital markets conditions are met and that you can borrow and lend at the same 5% rate as with. You have \$5000 of your own money to invest and you plan on buying Without stock. Using homemade leverage, how much do you need to borrow in your margin account so that the payoff of your margined purchase of Without stock will be the same as a \$5000 investment in With stock?

#### Solution Preview

Question 1
(90000 x 0.5 + 117000 x 0.5) = 103,500
Present value factor of 15% in year 1 = 1/(1+.15)^1 = 0.8696
103,500 x ...

#### Solution Summary

This response determines NPV, market values, and stock prices.

\$2.19