Wealth and Health Company is financed entirely by common stock that is priced to offer a 15 percent expected return. The common stock price is $40/share. The earnings per share (EPS)is expected to be $6. If the company repurchases 25 percent of the common stock and substitutes an equal value of debt yielding 6 percent, what is the expected value of earnings per share after refinancing? (Ignore taxes.)
A)$6.00
B)$7.52
C)$7.20
D)$6.90

Question

Quizplus · Accepted Answer

First, calculate the current expected dividend per share (DPS):
DPS = EPS * payout ratio = $6 * 1 = $6

Next, calculate the current expected return on equity (ROE):
ROE = DPS/Stock Price + g = $6/$40 + 0 = 0.15 or 15%

Since the company repurchases 25% of its common stock, the new number of shares outstanding is 0.75 times the original amount. The amount of debt issued to fund the stock repurchase is equal in value to the repurchased shares, or 0.25 times the original market value of the equity.

The new cost of equity can be calculated using the capital asset pricing model (CAPM):
cost of equity = risk-free rate + beta * (market rate of return - risk-free rate) = 6% + 1.0 * (10% - 6%) = 10%

The new cost of debt is 6%.

Next, calculate the new weighted average cost of capital (WACC):
WACC = (E/V * cost of equity) + (D/V * cost of debt) * (1 - tax rate)
where:
E = market value of equity
D = market value of debt
V = total value of the firm (E + D)
tax rate = 0 (since taxes are ignored)

Since the debt issued is equal in value to 0.25 times the market value of the equity, we can express the market value of debt as:
D = 0.25 * E

Substituting in the values:
WACC = (E/E+D * 10%) + (D/E+D * 6%) = (0.75 * 10%) + (0.25 * 6%) = 8.4%

Finally, calculate the expected EPS after refinancing using the Gordon growth model:
EPS = (DPS * (1 + g)) / (WACC - g)
where:
g = expected growth rate

Assuming a constant growth rate of 5% in perpetuity:
EPS = ($6 * (1 + 5%)) / (8.4% - 5%) = $7.20

Wealth and Health Company Is Financed Entirely by Common Stock