Health and Wealth Company is financed entirely by common stock that is priced to offer a
15% expected return. If the company repurchases 25% of the common stock and substitutes an equal value of debt yielding 6%, what is the expected return on the common stock after refinancing? (Ignore taxes.)
A) 18%
B) 21%
C) 15%
D) None of the above

Question

Quizplus · Accepted Answer

The expected return on common stock is 15%. When the company repurchases 25% of the common stock with debt yielding 6%, the overall expected return on equity should increase due to the reduction in shares outstanding. However, we need to calculate the new expected return:

Current cost of equity = 15%
Current cost of debt = 6%
Debt-to-equity ratio after repurchase = 0.25/0.75 = 1/3

Using the Weighted Average Cost of Capital (WACC) formula:
WACC = (Cost of Equity x Equity Proportion) + (Cost of Debt x Debt Proportion)
WACC = (15% x 2/3) + (6% x 1/3)
WACC = 12%

The WACC represents the expected return on the entire firm, including debt and equity. To find the expected return on the remaining common stock, we need to adjust for the repurchase:

Expected return on remaining common stock = WACC + (WACC - Cost of Debt) x (Debt Proportion / Equity Proportion)
Expected return on remaining common stock = 12% + (12% - 6%) x (1/3 / 2/3)
Expected return on remaining common stock = 18%

Therefore, the expected return on the common stock after refinancing is 18%, which is higher than the original 15%. Option A is the correct answer.

Health and Wealth Company Is Financed Entirely by Common Stock