Your firm's debt ratio is only 5.00%,but the new CFO thinks that more debt should be employed.She wants to sell bonds and use the proceeds to buy back and retire common shares so the percentage of common equity in the capital structure (w_c) = 1 − w_d.Other things held constant,and based on the data below,if the firm increases the percentage of debt in its capital structure (w_d) to 60.0%,by how much would the ROE change,i.e.,what is ROE_New − ROE_Old?

Question

Quizplus · Accepted Answer

The formula to calculate the new ROE is:

ROE_new = ROE_old + (ROE_old - (1-tax rate) * R_D) * (D/E)

Where

ROE_old = net income / equity 
tax rate = 40%
R_D = interest rate on debt 
D/E = debt-to-equity ratio

Plugging in the numbers, we get:

ROE_old = 14.00% (given)
tax rate = 40%
R_D = 9.00% (given)
D/E = 60%/40% = 1.50

ROE_new = 14.00% + (14.00% - (1-0.40)*0.09) * 1.50 = 21.46%

Therefore, the change in ROE is:

ROE_new - ROE_old = 21.46% - 14.00% = 7.46%

Hence, the answer is C) 7.46%.

Your Firm's Debt Ratio Is Only 5