A firm faces a 30 percent tax rate and has $700m 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 $100m. The firm is considering switching to a 45 percent debt capital structure, and has determined that they would have to pay a 10 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) = net income / equity

Before the capital structure change, the equity is $700m, and there is no debt, so net income = EBIT - taxes = $100m - 0.3($100m) = $70m

ROE = $70m / $700m = 10%

After the capital structure change, the firm will have $385m in debt (because 0.45 debt-to-capital ratio * $1.085bn total capital), and $315m in equity.

Interest expense = $385m * 0.10 = $38.5m

EBIT - interest = $100m - $38.5m = $61.5m

Taxes = 0.3($61.5m) = $18.45m

Net income = $61.5m - $18.45m = $43.05m

ROE = $43.05m / $315m = 13.67%

Therefore, the ROE will increase by 13.67% - 10% = 2.67%, or 2.45% rounded to two decimal places. So the answer is C.

A Firm Faces a 30 Percent Tax Rate and Has