A firm faces a 30 percent tax rate and has $500m in assets, currently financed entirely with equity. Equity is worth $100 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected EBIT is $70m. The firm is considering switching to an 18 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt. How much will ROE change if they switch to the proposed capital structure?

Question

Quizplus · Accepted Answer

ROE (Return on Equity) is calculated as:
ROE = Net Income / Book Value of Equity

Before the proposed capital structure:
Book Value of Equity = Market Value of Equity = $500m / $100 per share = 5m shares
Net Income = EBIT - Taxes
Taxes = 0.3 * EBIT = 0.3 * $70m = $21m
Net Income = $70m - $21m = $49m

ROE = $49m / (5m shares * $100 per share) = 9.8%

After the proposed capital structure:
The firm will have $500m * 0.18 = $90m in debt
Interest expense = $90m * 0.08 = $7.2m
EBIT - Interest expense = $70m - $7.2m = $62.8m
Taxes = 0.3 * $62.8m = $18.84m
Net Income = $62.8m - $18.84m = $43.96m

Book Value of Equity = Market Value of Equity = $43.96m / (5m shares + ($90m / $100 per share)) = $32.72 per share
ROE = $43.96m / (5m shares * $32.72 per share) = 26.8%

The change in ROE is:
26.8% - 9.8% = 17%
However, we need to adjust for the tax shield benefit of debt:
Tax Shield Benefit = Interest expense * Tax rate = $7.2m * 0.3 = $2.16m
Adjusted Change in ROE = (Net Income + Tax Shield Benefit) / Book Value of Equity - ROE before the change
Adjusted Change in ROE = ($43.96m + $2.16m) / ($32.72 per share * 5m shares) - 9.8%
Adjusted Change in ROE = 0.928 or 0.92%

Therefore, the correct answer is D, the ROE will increase by 0.92 percent.

A Firm Faces a 30 Percent Tax Rate and Has