A firm faces a 30 percent tax rate and has $200m in assets, currently financed entirely with equity. Equity is worth $10 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 $10m. The firm is considering switching to a 25 percent debt capital structure, and has determined that they would have to pay a 10 percent yield on perpetual debt. What will be the firm's new ROE if they switch to the proposed capital structure?

Question

Quizplus · Accepted Answer

First, let's calculate the initial ROE with the all equity financing:

ROE = Net income / Equity
ROE = EBIT x (1 - tax rate) / Equity
ROE = $10m x (1-0.3) / $200m
ROE = 0.07 or 7.0%

Now, let's calculate the new ROE with the proposed capital structure:

1. Calculate the new debt-to-equity ratio:
Debt-to-equity ratio = 25% / (1 - 25%) = 1/3

2. Calculate the new equity and debt values:
Equity value = $200m x 2/3 = $133.33m
Debt value = $200m x 1/3 = $66.67m

3. Calculate the interest expense:
Interest expense = Debt value x Yield
Interest expense = $66.67m x 10% = $6.67m

4. Calculate the new net income:
Net income = EBIT x (1 - tax rate) - Interest expense
Net income = $10m x (1 - 0.3) - $6.67m
Net income = $1.33m

5. Calculate the new ROE:
ROE = Net income / Equity
ROE = $1.33m / $133.33m
ROE = 0.01 or 1.33%

Therefore, the new ROE after switching to the proposed capital structure is 1.33%, which is lower than the initial ROE of 7.0%. None of the options matches with this result, but the closest one is A) 2.33 percent.

A Firm Faces a 30 Percent Tax Rate and Has