A firm wishes to maintain a growth rate of 10% per year and a debt-to-equity ratio of 1/2. The dividend payout is.2, and the ratio of total assets to sales is constant at 1.2. What must the profit margin be?
A) 10.00%
B) 9.09%
C) 11.11%
D) 8.00%

Question

Quizplus · Accepted Answer

The profit margin can be found using the sustainable growth rate formula, which is: Sustainable Growth Rate = ROE * (1 - dividend payout ratio). Given a growth rate of 10% and a dividend payout of 0.2, we need to find the ROE that would result in a 10% growth rate. The debt-to-equity ratio is 1/2, meaning for every $2 of equity, there is $1 of debt, so the equity multiplier is 1 + 1/2 = 1.5. ROE can be decomposed into profit margin (PM), asset turnover (AT), and equity multiplier (EM) in the DuPont Identity: ROE = PM * AT * EM. Given AT as sales/total assets = 1/1.2 = 0.833 and EM = 1.5, we solve for PM in the equation 10% = PM * 0.833 * 1.5, resulting in a profit margin of approximately 9.09%.

A Firm Wishes to Maintain a Growth Rate of 10