DuPont Decomposition (3-Way)

Builds onReturn on Equity · Net Profit Margin — if this page feels steep, start there.

ROE = \underbrace{\frac{NI}{Rev}}_{\text{margin}} \times \underbrace{\frac{Rev}{Assets}}_{\text{turnover}} \times \underbrace{\frac{Assets}{Equity}}_{\text{leverage}}

$\frac{NI}{Rev}$: net profit margin: cents of profit per dollar of sales — the pricing/cost lever
$\frac{Rev}{Assets}$: asset turnover: dollars of sales per dollar of assets — the efficiency lever
$\frac{Assets}{Equity}$: the equity multiplier: assets per dollar of owners' money — the leverage lever (1 = no debt)
$ROE$: the product of the three — margin × turnover × leverage, exactly

Why it must be true

Two companies post identical 18% ROEs. One earns fat margins on slow-turning assets (a luxury house); the other earns razor margins on furiously turning assets (a discount grocer); a third fakes the whole thing with borrowed money. ROE alone cannot tell them apart — DuPont can.

The trick is beautiful bookkeeping: multiply ROE by Revenue/Revenue and Assets/Assets (both equal 1, changing nothing) and it falls apart into three separate levers — how much profit per sale (margin), how many sales per dollar of assets (turnover), and how many assets per dollar of owners' money (leverage). Same number, but now it has a story: where the return comes from, and which lever moved when it changes.

The derivation

Start from ROE and insert two harmless factors of one:

ROE = \frac{NI}{E} = \frac{NI}{E} \times \frac{Rev}{Rev} \times \frac{A}{A}

Regroup the fractions:

ROE = \frac{NI}{Rev} \times \frac{Rev}{A} \times \frac{A}{E}

Each factor is a ratio an analyst already tracks: net margin, total asset turnover, and the equity multiplier. Revenue and Assets each cancel across neighboring terms, so the product collapses back to NI/E exactly — the decomposition is an identity, not an approximation.

When to reach for it

Explaining WHERE an ROE comes from, comparing companies with similar ROEs but different models, or tracing which lever moved an ROE year over year.

Listen for

“decompose return on equity”“margin, turnover and leverage”“equity multiplier”“is the ROE driven by operations or debt”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

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Multiply the easy pair first: turnover × multiplier is usually a clean small number; then one multiplication by the margin finishes it.
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The equity multiplier is a debt gauge in disguise: A/E = 2 means half the assets are financed by liabilities. An ROE story with multiplier > 3 is a leverage story.
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Cross-check: margin × turnover alone is ROA. If the given ROA and multiplier are consistent, ROA × multiplier must equal the ROE.

Traps in applying it

✗Adding the three components instead of multiplying — it is a product of ratios, not a sum of contributions.
✗Mixing period and point-in-time bases (income-statement flows vs balance-sheet snapshots) inconsistently across the three ratios.
✗Reading a rising ROE as improvement without checking WHICH factor rose — a margin gain and a leverage gain are opposite stories.

Limits & criticisms

The decomposition is an accounting identity, so it inherits every accounting distortion: book equity shrunk by buybacks inflates the multiplier, and one-off items pollute the margin. The 3-way version also buries taxes and interest inside net margin — the 5-way variant separates them precisely because a "margin improvement" can secretly be a tax change. It explains an ROE; it does not judge whether the ROE is sustainable.

Where it came from

Donaldson Brown, an electrical-engineer-turned-financier at DuPont, built this decomposition around 1919 to compare the wildly different businesses DuPont owned; when DuPont bought into General Motors, Brown took it there and it became the management system of the century's biggest company. The "DuPont system" is now the standard first move on any ROE: equity analysts use it to see whether returns are operational or borrowed, and credit analysts read the third factor as a warning light.

One identity, 1 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

ROE from its three levers

ROE = \text{margin} \times \text{turnover} \times \text{leverage}

The assembly face: given the three levers, the ROE is forced — and each lever names a different way to improve (or fake) it.

Drill this face →

On the BA II Plus

Worked example: An analyst decomposes a company's profitability: margin 11%, turnover 0.4×, leverage (assets/equity) 1.75×. What ROE do the three levers assemble into?

1.0.11 [×] 0.4 [×] 1.75 [=]margin × turnover × leverage (decimal ROE)

→ 7.7%

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