How this calculation works
Return on equity can change through profit margin, asset use or the relationship between assets and equity. The three-factor DuPont identity separates those arithmetic components instead of treating one ROE number as a complete explanation. This page reconciles the factor product with income divided directly by average equity. It is a financial-statement scenario, not an automatic business-quality score.
ROE = (net income/sales) × (sales/average assets) × (average assets/average equity)A worked example
With net income ten, sales one hundred, average assets two hundred and average equity fifty, margin is ten percent, turnover 0.5 and equity multiplier four. Their product is 0.1 times 0.5 times four, or twenty percent ROE. Direct income divided by average equity gives the same twenty percent.
Good to know
Accounting classifications and reported values are entered without normalization or audit. Extraordinary items, differing consolidation boundaries and inconsistent periods can make comparisons misleading. No industry benchmark, valuation estimate or investment recommendation is supplied. The decomposition helps inspect a stated ratio; it does not establish solvency, earnings quality or future performance.
Reference: OpenStax — DuPont profitability factors (opens in a new tab) ↗
What this calculation answers
Return on equity can change through profit margin, asset use or the relationship between assets and equity. The three-factor DuPont identity separates those arithmetic components instead of treating one ROE number as a complete explanation.
This page reconciles the factor product with income divided directly by average equity. It is a financial-statement scenario, not an automatic business-quality score.
The ROI calculator measures a general return ratio. DuPont additionally decomposes the entered equity return into margin, asset turnover and equity multiplier.
Use the right input conventions
Use income and sales from the same period and assets and equity averaged consistently over that period. Point-in-time balances can produce a different ratio from period-average balances.
Income may be negative, but this implementation requires positive sales, average assets and average equity. A negative or near-zero equity denominator needs a different interpretation and is outside the supported comparison.
Interpret the result
Margin is income divided by sales; asset turnover is sales divided by average assets; the equity multiplier is average assets divided by average equity. Intermediate sales and assets cancel algebraically.
That cancellation verifies the identity but does not show which management action caused a change. Raising leverage can increase the multiplier while also changing financing risk and future income, neither of which the identity predicts.
Work through the example
With net income ten, sales one hundred, average assets two hundred and average equity fifty, margin is ten percent, turnover 0.5 and equity multiplier four.
Their product is 0.1 times 0.5 times four, or twenty percent ROE. Direct income divided by average equity gives the same twenty percent.
Where the model stops
Accounting classifications and reported values are entered without normalization or audit. Extraordinary items, differing consolidation boundaries and inconsistent periods can make comparisons misleading.
No industry benchmark, valuation estimate or investment recommendation is supplied. The decomposition helps inspect a stated ratio; it does not establish solvency, earnings quality or future performance.
A few questions, answered
Why use average assets and equity?
Income and sales cover a period, so a consistently averaged capital denominator better matches that period than an unrelated snapshot.
What changes in the comparison?
Keep capital and sales unchanged but introduce a period loss.