Question content area top

Part $1$

Consider a project with free cash flows in one year of

$ $145$ comma $648$$$145,648$

in a weak market or

$ $181$ comma $472$$$181,472$

in a strong$$ market, with each outcome being equally likely. The initial investment required for the project is

$ $85$ comma $000$$$85,000,$

and the$$ project's unlevered cost of capital is

$24\%24\%.$

The$$ risk$-$free interest rate is

$12\%12\%.$

$($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

waylong dash$$that

$$is$,$ what is the initial market value of the unlevered$$ equity?$$

c$.$ Suppose the initial

$ $85$ comma $000$$$85,000$

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.

As debt has a lower cost of capital than$$ equity, higher leverage lowers a$$ firm's WACC.

B$.$

With no$$ debt, the WACC is equal to the unlevered equity cost of capital.

C$.$

As the firm borrows at the low cost of capital for$$ debt, its equity cost of capital$$ rises, but the net effect is that the$$ firm's WACC is unchanged.

D$.$

With perfect capital$$ markets, a$$ firm's WACC is dependent on its capital structure and is equal to its equity cost of capital only if the firm is unlevered.

$$firm$,$ with $1$ million shares outstanding that trade for a price of$$ $$24$ per share. Firm X has $2$ million shares outstanding and$$ $$12$ million in debt at an interest rate of$5\%.$

According to MM Proposition$$ I, the stock price for Firm X is closest to$\_\_\_\_\_\_\_\_.$