Question

Locomotive Corporation is planning to repurchase part of its common stock by issuing corporate debt. As a result, the firm’s debt–equity ratio is expected to rise from 35% to 50%. The firm currently has $3.1 million worth of debt outstanding. The cost of this debt is 6.7% per year. Locomotive expects to earn $1.075 million per year in perpetuity. Locomotive pays no taxes.
a. What is the market value of Locomotive Corporation before and after the repurchase announcement?
b. What is the expected return on the firm’s equity before the announcement of the stock repurchase plan?
c. What is the expected return on the equity of an otherwise identical all-equity firm?
d. What is the expected return on the firm’s equity after the announcement of the stock repurchase plan?

Answer 1

a). Debt-equity ratio = B / S

0.35 = $3,100,000 / S

S = $8,857,142.86

Vl = B + S

Vl = $3,100,000 + $8,857,142.86 = $11,957,142.86

According to MM Proposition I without taxes, changes in a firm's capital structure have no effect on the overall value of the firm. Therefore, the value of the firm will not change after the announcement of the stock repurchase plan.

b). The expected return on a firm's equity is the ratio of annual earnings to the market value of the firm's equity or return on equity. Before the restructuring, the company was expected to pay interest:

Interest payment = 0.067($3,100,000) = $207,700

The return on equity, which is equal to Rs, will be:

ROE = Rs = ($1,075,000 - $207,700) / $8,857,142.86 = 0.0979 or 9.79%

c). Ro = Earnings before interest / Vu

According to Modigliani-Miller Proposition I, in a world with no taxes, the value of a levered firm equals the value of an otherwise-identical unlevered firm. Since the value of the company as a levered firm is calculated in part a as $11,957,142.86 and since the firm pays no taxes, the value of the company as an unlevered firm will be also $11,957,142.86

So,

Ro = $1,075,000 / $11,957,142.86 = 0.0899 or 8.99%

d). Use the Modigliani-Miller Proposition II with no taxes again to find the cost of equity for the firm with the new leverage ratio. The cost of equity under the stock repurchase plan will be:

Rs = R0+ (B/S)(R0 - Rb)

= 0.0899 + (0.50)(0.0899 - 0.067)

= 0.0899 + 0.0115 = 0.1014 or 10.14%