Final answer:
The ROE according to the DuPont system is approximately 11.09%, calculated by multiplying the Net Profit Margin (9%), Asset Turnover (1/0.95), and the Equity Multiplier (1/0.86).
Step-by-step explanation:
The student's question involves calculating the Return on Equity (ROE) according to the DuPont system of financial ratio analysis. We are given three pieces of information: a net profit margin of 9%, assets are 95 cents for every dollar of sales, and debt is 14 percent of assets. To calculate ROE using the DuPont formula, we need to understand it decomposes ROE into three parts: Net Profit Margin, Asset Turnover, and Equity Multiplier.
The Net Profit Margin is given as 9%. This means that for every dollar of sales, the company is making 9 cents in profit. The Asset Turnover can be calculated from the information given that assets are 95 cents for every dollar of sales, which means the Asset Turnover is 1/0.95 because for every 95 cents of assets, there is $1 of sales. The Equity Multiplier is calculated by dividing total assets by total equity. However, we are only provided the debt ratio, which is 14% of assets. To find the Equity Multiplier, we need to determine equity as a percentage of assets. If debt is 14%, then equity is 86% of assets (100% - 14%). Therefore, the Equity Multiplier is 1/0.86.
Combining these figures, ROE is calculated as follows:
ROE = Net Profit Margin × Asset Turnover × Equity Multiplier
ROE = 0.09 × (1/0.95) × (1/0.86)
ROE ≈ 0.09 × 1.0526 × 1.1628
ROE ≈ 11.09%
Therefore, the ROE according to the DuPont system of financial analysis is approximately 11.09%.