How DuPont analysis works

Return on equity is net income over equity. DuPont writes the same rate as three pieces that have to multiply back to it:

$$ROE = \frac{NI}{Sales} \times \frac{Sales}{Assets} \times \frac{Assets}{Equity}$$

On $45,000 of net income, $500,000 of sales, $800,000 of assets and $300,000 of equity: net margin is 9 percent, asset turnover is 0.625, the equity multiplier is 2.67. Product: $0.09 \times 0.625 \times 8/3 = 0.15$, 15 percent. Directly: $45000 / 300000 = 0.15$.

ROA is the first two steps: $0.09 \times 0.625 = 0.05625$, 5.625 percent. Times 2.67 is 15 percent. Financial leverage sits in the third piece.

The DuPont calculator on this page is that product. How ROE works is the one division that does not split the sheet. ROA against ROE is the first two steps against all three.

Net income $60,000, sales $400,000, assets still $800,000, equity now $600,000. Margin 15 percent. Turnover 0.5. Multiplier 1.33. ROA 7.5 percent. ROE 10 percent.

Margin rose from 9 percent to 15 percent. Turnover fell. The multiplier halved, from $8/3$ to $4/3$, because this sheet owes $200{,}000$ rather than $500,000. ROE fell from 15 percent to 10 percent even though ROA rose. A single ROE would have hidden which piece moved.

Net income $80,000, sales $1,000,000, assets $500,000, equity $400,000. Margin 8 percent. Turnover 2. Multiplier 1.25. ROA 16 percent. ROE 20 percent.

The margin is narrower than the first sheet's 9 percent. Turnover is much faster than 0.625. Ranking on ROE puts this sheet first. Ranking on margin puts it last. Both rankings are the same four inputs, weighted differently.

Write the product with the four numbers in place and sales cancel, then assets cancel, and what remains is net income over equity. That is why the identity cannot disagree with the one-division ROE when the four inputs are one period and one consolidation.

Mixing a year of sales with a quarter of profit, or mixing market cap in as equity, breaks the cancel. Book equity and book assets, same stretch of time.

It does not know whether 15 percent clears the cost of equity. It does not take the coupon out the way ROIC does. Net income is after interest. A heavier coupon lowers the margin and lowers ROE even if EBIT did not move.

Five-step DuPont splits the margin further into tax and interest burdens. This page is the three-step teaching identity.

It is not ROIC, not a five-step tax split, and not a target of 15 percent. The three sheets are 9 percent times 0.625 times 2.67 (ROE 15 percent, ROA 5.625 percent), 15 percent times 0.5 times 1.33 (ROE 10 percent, ROA 7.5 percent), and 8 percent times 2 times 1.25 (ROE 20 percent, ROA 16 percent). This is educational material, not financial advice.