Final answer:
The question asks to calculate the firm's profit margin given its growth rate, retention ratio, and asset turnover. Using the sustainable growth rate formula, the profit margin can be determined by rearranging the formula of ROE, which is the product of profit margin and asset turnover. However, there seems to be an inaccuracy in the information provided as the calculated profit margin does not match any of the options given.
Step-by-step explanation:
The student's question is about determining the firm's profit margin given certain financial metrics, specifically the internal growth rate, retention ratio, and total asset turnover. To find the profit margin, we can use the sustainable growth rate formula, which is: Sustainable Growth Rate (SGR) = Retention Ratio (b) × Return on Equity (ROE).
In this case, we know the internal growth rate is essentially the SGR, which is 15%, and the retention ratio is 60% or 0.6. The equation becomes: 15% = 0.6 × ROE. Solving for ROE gives us 25%. Knowing that ROE is also the product of profit margin and asset turnover, we can rearrange the formula to find the profit margin: ROE = Profit Margin × Total Asset Turnover. Substituting the given turnover rate of 25%, we arrive at 25% = Profit Margin × 0.25, leading to a profit margin of 1 or 100%.
However, a profit margin of 100% does not match any of the answer choices provided. This is because the turnover rate should be interpreted as 1/0.25, or 4, not 25%. This discrepancy suggests a typo or error in the data provided. Considering the correct turnover rate (which is 4 times the assets), the calculation should be: ROE = Profit Margin × 4. Substituting 25% for ROE, we get 25% = Profit Margin × 4, which gives us a profit margin of 6.25%. This answer is still not found in the options provided, which likely indicates an error in the phrasing or choices presented in the student's question.