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 (wc) = 1 - wd. Other things held constant, and based on the data below, if the firm increases the percentage of debt in its capital structure (wd) to 60.0%, by how much would the ROE change, i.e., what is ROENew - ROEOld?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the DuPont formula to calculate the return on equity (ROE) before and after the proposed capital structure change.

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

Given data:

Debt ratio (old) = 5.00%
Debt ratio (new) = 60.0%
Equity ratio (old) = 95.00% (1 - 0.05)
Equity ratio (new) = 40.00% (1 - 0.60)

We are not given any information on net income, sales or total assets so we will assume that they remain constant.

ROE (old) = (Net Income / Sales) x (Sales / Total Assets) x (Total Assets / Total Equity)
ROE (old) = (Constant / Constant) x [(Total Assets / Equity ratio (old))]  
ROE (old) = [(Total Assets / Equity) / Equity ratio (old)]
ROE (old) = (1 / 0.95) = 1.0526 or 10.526%

ROE (new) = (Net Income / Sales) x (Sales / Total Assets) x (Total Assets / Total Equity)
ROE (new) = (Constant / Constant) x [(Total Assets / Equity ratio (new))]  
ROE (new) = [(Total Assets / Equity) / Equity ratio (new)]
ROE (new) = (1 / 0.40) = 2.5000 or 25.000%

ROE change = ROE (new) - ROE (old)
ROE change = 25.000% - 10.526% = 14.474%

Therefore, if the firm increases the percentage of debt in its capital structure from 5.00% to 60.0%, the ROE would increase by 14.474%.

However, none of the answer choices match this result. The closest option is C) 7.46%, which may be the result of a calculation error or rounding.

Your Firm's Debt Ratio Is Only 5