# Value of firm/market value of equity

Alpha Corporation and Beta Corporation are identical in every way

except their capital structures. Alpha Corporation, an all-equity firm, has 5,000 shares outstanding, currently worth $20 per share. Beta Corporation uses leverage in its capital structure. The market value of Betaâ??s debt is $25,000. The cost of his debt is 12 percent per annum. Each firm is expected to have earnings before interest of $350,000 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 12 percent per annum.

a. What is the value of Alpha Corporation?

b. What is the value of Beta Corporation?

c. What is the market value of Beta Corporationâ??s equity?

d. How much will it cost to purchase 20 percent of each firmâ??s equity?

e. Assuming each firm meets its earnings estimates, what will be the dollar

return to each position in part (d) over the next year?

f. Construct an investment strategy in which an investor purchases 20 percent of

Alphaâ??s equity and replicates both the cost and dollar return of purchasing 20

percent of Betaâ??s equity.

g. Is Alphaâ??s equity more or less risky than Betaâ??s equity? Explain.

#### Solution Preview

a. What is the value of Alpha Corporation?

Since Alpha is an all equity firm, its value is the market value of shares = 5,000 X $20 = $100,000

b. What is the value of Beta Corporation?

MM proposition 1 states that if there are no taxes, then the value of the levered firm would be the same as the value of unlevered firm. In this case there are no taxes and Beta is identical to Alpha

Value of Beta will be the same as the value of Alpha = $100,000

c. What is the market value of Beta Corporation's equity?

The total value of Beta is $100,000

Value of debt = $25,000

Value of equity = ...

#### Solution Summary

This posting assesses value of firm and market value of equity.