The DuPont identity can be accurately defined as (assume values are all obtained on the same date):
a. Return on equity \times Total asset turnover \times Equity multiplier.
b. Equity multiplier \times Return on assets.
c. Profit margin \times Return on equity.
d. Total asset turnover \times Profit margin \times Debt-equity ratio.
e. Equity multiplier \times Return on assets \times Profit margin.
The Correct Answer and Explanation is :
The correct answer is e. Equity multiplier × Return on assets × Profit margin.
Explanation
The DuPont identity is a powerful financial formula used to analyze a company’s return on equity (ROE), which breaks down the elements that contribute to a company’s financial performance. This identity provides insight into how well a company uses its assets to generate earnings.
Return on Equity (ROE) is calculated using the formula:
[ \text{ROE} = \text{Net Income} / \text{Equity} ]
The DuPont identity expands this formula into three parts:
- Profit Margin (Net Profit Margin): This is calculated as Net Income divided by Sales. It shows how much profit a company generates for each dollar of sales.
- Total Asset Turnover: This is calculated as Sales divided by Total Assets. It indicates how efficiently a company uses its assets to generate sales.
- Equity Multiplier: This is calculated as Total Assets divided by Total Equity. It illustrates how much the company is leveraged with debt.
The DuPont Identity combines these elements as follows:
[ \text{ROE} = (\text{Net Profit Margin}) \times (\text{Total Asset Turnover}) \times (\text{Equity Multiplier}) ]
Thus, the identity can be expressed in a simplified form:
[ \text{ROE} = (\text{Profit Margin}) \times (\text{Return on Assets}) \times (\text{Equity Multiplier}) ]
Here, Return on Assets (ROA) is itself a product of Profit Margin and Total Asset Turnover:
[ \text{ROA} = (\text{Profit Margin}) \times (\text{Total Asset Turnover}) ]
When combined with the Equity Multiplier, it reflects the three parts of the DuPont Identity:
[ \text{ROE} = (\text{ROA}) \times (\text{Equity Multiplier}) ]
Conclusion: The DuPont formula allows investors and analysts to understand how a company is performing in terms of profitability, asset use efficiency, and financial leverage, which together drive the return on equity.
Let’s create an image that visually represents this formula to better understand the components and their relationship.
Here is a visual representation of the DuPont Identity, detailing its three main components: Profit Margin, Total Asset Turnover, and Equity Multiplier. Each section is illustrated with charts and mathematical connections to show how these components combine to determine Return on Equity (ROE). This illustration should help clarify how these financial metrics interact within the DuPont formula.
