ROA vs ROE
ROA is net income over assets. ROE is net income over equity. On $45,000 of profit, $800,000 of assets and $300,000 of equity they read 5.625 percent and 15 percent. The 2.67 equity multiplier is the conversion.
| Return on assets | Return on equity | |
|---|---|---|
| Denominator | Total book assets. | Book equity. |
| First DuPont sheet | $45,000 / $800,000 = 5.625 percent. | $45,000 / $300,000 = 15 percent. |
| The conversion | Margin 9 percent times turnover 0.625. | That 5.625 percent times the 2.67 multiplier. |
| Less borrowed sheet | $60,000 / $800,000 = 7.5 percent. | $60,000 / $600,000 = 10 percent. Higher ROA, lower ROE, because the multiplier is 1.33. |
| Fast turnover sheet | $80,000 / $500,000 = 16 percent. | $80,000 / $400,000 = 20 percent. Multiplier 1.25. |
| When you would pick it | What the whole sheet earned after interest. | What the residual claim earned after interest. |
On this page
The multiplier is the whole gap
On the first sheet ROA is 5.625 percent and ROE is 15 percent. . How return on assets works is the 5.625 percent. How ROE works is the 15 percent. DuPont analysis is the identity. How the equity multiplier works is the 2.67.
They are not two names for one rate. Mixing them in a table without the multiplier is how a 15 percent looks three times a 5.625 percent as if two firms were being compared.
A higher ROA can sit under a lower ROE
The second sheet earns 7.5 percent on assets and 10 percent on equity. ROA rose. ROE fell. The multiplier halved. That is the point of reading both. This is educational material, not financial advice.
Worked examples
5.625 percent against 15 percent
Net income $45,000, sales $500,000, assets $800,000, equity $300,000. ROA and ROE?
- ROA 5.625 percent. Margin 9 percent, turnover 0.625.
- ROE 15 percent. Multiplier 2.67.
ROA is 5.625 percent. ROE is 15 percent. Margin 9 percent, turnover 0.625, multiplier 2.67.
7.5 percent against 10 percent
Net income $60,000, sales $400,000, assets $800,000, equity $600,000. ROA and ROE?
- ROA 7.5 percent. Turnover 0.5. Margin 15 percent.
- ROE 10 percent. Multiplier 1.33.
ROA is 7.5 percent. ROE is 10 percent. Higher ROA, lower ROE than the first sheet.
16 percent against 20 percent
Net income $80,000, sales $1,000,000, assets $500,000, equity $400,000. ROA and ROE?
- ROA 16 percent. Turnover 2. Margin 8 percent.
- ROE 20 percent. Multiplier 1.25.
ROA is 16 percent. ROE is 20 percent. Margin 8 percent, turnover 2, multiplier 1.25.
Common questions
Is a higher ROE a better firm?
Not by itself. The first sheet's 15 percent is a 5.625 percent ROA times 2.67. Check the multiplier before treating the rate as operating.
Why is neither of these ROIC?
Both use net income, which is after interest. ROIC uses NOPAT and invested capital.
Are 5.625 percent and 15 percent two firms?
No. They are one $45,000 profit on one sheet. This is educational material, not financial advice.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.