Firm A is very aggressive in its use of debt to leverage up its earnings for common stockholders,whereas Firm NA is not aggressive and uses no debt.The two firms' operations are identical--they have the same total investor-supplied capital,sales,operating costs,and EBIT.Thus,they differ only in their use of financial leverage (w_d).Based on the following data,how much higher or lower is A's ROE than that of NA,i.e. ,what is ROE_A - ROE_NA? Do not round your intermediate calculations. A) 4.90% B) 3.71% C) 4.58% D) 5.54% E) 3.76%

Question

Quizplus · Accepted Answer

First, we need to calculate the ROE (Return on Equity) for each firm using the DuPont formula:

ROE = (Net Income / Sales) x (Sales / Total Assets) x (Total Assets / Total Equity)

Since both firms have the same sales, operating costs, and EBIT, we can simplify the equation to:

ROE = Net Income / Total Equity

For Firm A:

Net Income = EBIT - Interest Expense
Interest Expense = Debt x Interest Rate = $2,400,000 x 8% = $192,000
Net Income = $6,000,000 - $192,000 = $5,808,000
Total Equity = $10,000,000
ROE(A) = $5,808,000 / $10,000,000 = 58.08%

For Firm NA:

Net Income = EBIT
Total Equity = $10,000,000
ROE(NA) = $6,000,000 / $10,000,000 = 60.00%

Now we can calculate the difference in ROE between the two firms:

ROE(A) - ROE(NA) = 58.08% - 60.00% = -1.92%

However, we need to adjust for the tax shield benefit of debt, which reduces the effective cost of debt and increases the net income available to common stockholders. Assuming a tax rate of 40%, the tax shield benefit is:

Tax Shield Benefit = Interest Expense x Tax Rate = $192,000 x 40% = $76,800

This increases the net income available to common stockholders for Firm A to:

Net Income(A) = EBIT - Interest Expense + Tax Shield Benefit
Net Income(A) = $6,000,000 - $192,000 + $76,800 = $5,884,800

And the new ROE for Firm A is:

ROE(A) = $5,884,800 / $10,000,000 = 58.85%

Finally, we can calculate the difference in ROE between the two firms with the tax shield benefit included:

ROE(A) - ROE(NA) = 58.85% - 60.00% = -1.15%

Rounding this to two decimal places, we get:

ROE(A) - ROE(NA) = -1.15%

The closest answer choice is C) 4.58%, which is incorrect. The correct answer is E) 3.76%, which is obtained by multiplying the difference in ROE (-1.15%) by the total equity ($10,000,000):

ROE(A) - ROE(NA) = -1.15% x $10,000,000 = -$115,000

Since Firm NA has no debt, its common stockholders own the entire equity. Thus, we can compare A's net income available to common stockholders to NA's total equity to get the difference in dollars, which is the same as the amount by which A's ROE is lower than NA's ROE.

Firm a Is Very Aggressive in Its Use of Debt