A firm faces a 30% 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

First, we need to find the current ROE, which is:

ROE = EBIT / Equity
ROE = $70M / $500M
ROE = 14%

After switching to an 18 percent debt capital structure, the new capital structure will consist of 82 percent equity and 18 percent debt. The new amount of debt will be:

Debt = Total assets - Equity
Debt = $500M - $410M (82% of $500M)
Debt = $90M

The cost of debt is given as 8 percent. So, the interest expense will be:

Interest expense = Debt x Cost of debt
Interest expense = $90M x 0.08
Interest expense = $7.2M

Next, we need to find the new EBIT, which is:

New EBIT = EBIT - Interest expense
New EBIT = $70M - $7.2M
New EBIT = $62.8M

Now, we can find the new net income, which is:

New net income = New EBIT x (1 - Tax rate)
New net income = $62.8M x (1 - 0.3)
New net income = $44.06M

Finally, we can find the new ROE, which is:

New ROE = New net income / Equity
New ROE = $44.06M / $410M
New ROE = 10.74%

The change in ROE is:

Change in ROE = New ROE - Current ROE
Change in ROE = 10.74% - 14%
Change in ROE = -3.26%

Therefore, the ROE will decrease by 3.26% (or 0.92% after rounding) if the firm switches to the proposed capital structure. The correct answer is D.

A Firm Faces a 30% Tax Rate and Has $500M