Question

10. 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 30 percent to 45 percent. The firm currently has $10 million worth of debt outstanding. The cost of this debt is 6.5 percent per year. The firm expects to have an EBIT of $3 million per year in perpetuity and pays no taxes.

a. What is the market value of the firm before and after the repurchase announcement? (0.75 point)

b. What is the expected return on the firm’s equity before the announcement of the stock repurchase plan? (0.75 point)

c. What is the expected return on the equity of an otherwise identical all-equity firm? (0.75 point)

d. What is the expected return on the firm’s equity after the announcement of the stock repurchase plan? (0.75 point)

Answer 1

(a).

Market value of the firm before repurchase announcement = $43333333.33 (Approx.)

Market value of the firm after repurchase announcement = $43333333.33 (Approx.)

Explanation;

Market value of the firm = value of debt + value of equity

Value of debt = $10000000

Debt equity ratio is given = 30%

So, now let’s calculate value of equity;

0.30 = $10000000 / Equity

Equity ($10000000 / 0.3) = $33333333.33

Thus market value of the firm before repurchase announcement ($10000000 + $33333333.33) = $43333333.33 (Approx.)

So, as per MM proposition value of the firm will be same before and after repurchase announcement in case of no taxes.

(b).

Expected return on the firm’s equity before the announcement of the stock repurchase plan = 7.05%

Explanation;

EBIT	$3000000
Less: Interest expense ($10000000 * 0.065)	($650000)
Earnings available for equity	$2350000
Value of equity	$33333333.33
Expected return on the firm’s equity ($2350000 / $33333333.33)	7.05%

(c).

Expected return on the equity of an otherwise identical all-equity firm = 6.92%

Explanation;

EBIT	$3000000
Value of firm	$43333333.33
Expected return on the firm’s equity ($3000000 / $43333333.33)	6.92%

(d).

Expected return on the firm’s equity after the announcement of the stock repurchase plan = 7.109% OR 7.11%

Explanation;

Formula of return on equity is as follow;

Return on equity = Return on equity with all equity + Debt-equity ratio * (Return on equity with all equity – Cost of debt)

Return on equity = 6.92% + 0.45 * (6.92% – 6.5%)

Return on equity = 6.92% + 0.189%

Return on equity = 7.109% OR 7.11%