DuPont Decomposition (5-Way)

Builds onDuPont Decomposition (3-Way) — if this page feels steep, start there.

ROE = \underbrace{\frac{NI}{EBT}}_{\text{tax burden}} \times \underbrace{\frac{EBT}{EBIT}}_{\text{interest burden}} \times \underbrace{\frac{EBIT}{Rev}}_{\text{operating margin}} \times \underbrace{\frac{Rev}{Assets}}_{\text{turnover}} \times \underbrace{\frac{Assets}{Equity}}_{\text{leverage}}

$\frac{NI}{EBT}$: tax burden: the fraction of pretax income kept after taxes (lower = higher tax rate)
$\frac{EBT}{EBIT}$: interest burden: the fraction of operating income kept after paying lenders
$\frac{EBIT}{Rev}$: operating margin: operating profit per dollar of sales, before financing and taxes
$\frac{Rev}{Assets}$: asset turnover: the same efficiency lever as the 3-way version
$\frac{Assets}{Equity}$: the equity multiplier: the same leverage lever as the 3-way version

Why it must be true

The 3-way decomposition calls its first factor "net margin" and moves on — but net margin itself is really THREE separate stories mashed together: how much operating profit the business earns before financing (operating margin), how much of that operating profit survives paying lenders (interest burden), and how much of what's left survives the tax authority (tax burden). A margin change could be any of the three, and they mean completely different things.

Split them apart and a "declining margin" stops being one vague finding and becomes a specific one: did operations get worse, did debt get more expensive, or did the tax rate change? The 5-way version exists so a tax-law change never gets mistaken for a deteriorating business.

The derivation

Start exactly where the 3-way version does, then split its margin term further. Insert two more harmless ratios of one — EBT/EBT and EBIT/EBIT — inside the net margin factor:

\frac{NI}{Rev} = \frac{NI}{Rev} \times \frac{EBT}{EBT} \times \frac{EBIT}{EBIT} = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{Rev}

Each new factor isolates one financing/tax step: tax burden (what tax takes), interest burden (what lenders take), and operating margin (what's left from the operating business itself). Recombining with turnover and leverage, exactly as in the 3-way case, gives the full identity:

ROE = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{Rev} \times \frac{Rev}{Assets} \times \frac{Assets}{Equity}

Every intermediate term (EBT, EBIT, Rev, Assets) cancels in sequence, so — like the 3-way version — this is an exact identity, not an approximation.

When to reach for it

Tracing an ROE change to its precise source when the 3-way decomposition's margin term isn't specific enough — separating operating performance from tax-rate or interest-cost effects.

Listen for

“5-way DuPont / extended DuPont decomposition”“tax burden and interest burden”“isolate the effect of a tax change / financing cost on ROE”“operating margin distinct from net margin”

Back-of-the-envelope

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

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Tax burden × interest burden × operating margin must multiply back to the same net margin used in the 3-way version — a fast internal consistency check.
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Both burden ratios are ≤ 1 by construction (each strips something away) — a computed burden above 1 signals a sign or ratio-direction error.
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A tax burden that jumped between two years with an unchanged interest burden and operating margin points straight at a tax-rate story, not an operating one.

Traps in applying it

✗Adding the five factors instead of multiplying — like the 3-way version, this is a product, not a sum.
✗Confusing operating margin (EBIT/Revenue) with net margin (NI/Revenue) — the 5-way version deliberately keeps them separate.
✗Mixing up which burden is which: tax burden uses EBT and NI; interest burden uses EBIT and EBT.

Limits & criticisms

Splitting the ratio further doesn't fix what the 3-way version already can't fix — it's still a book-value, single-period accounting identity, vulnerable to the same buyback-inflated leverage and one-off items. The extra precision helps diagnose WHERE a change came from, but the decomposition still says nothing about whether any of the five levers is sustainable going forward.

Where it came from

The 5-way extension is a later refinement of Donaldson Brown's original 1919 DuPont system, developed as equity and credit analysts needed to separate operating performance from financing and tax effects with more precision than the 3-way version allows — particularly useful after major tax reforms (e.g. the US Tax Cuts and Jobs Act of 2017), when a jump in ROE driven purely by a lower tax rate could otherwise be mistaken for genuinely improved operations. It remains the standard deeper dive whenever the 3-way version's margin term needs unpacking.

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 all five levers

ROE = \text{tax burden} \times \text{interest burden} \times \text{operating margin} \times \text{turnover} \times \text{leverage}

The full diagnostic face: every accounting and financing step between revenue and the owners' return, isolated one at a time.

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On the BA II Plus

Worked example: An analyst runs the extended DuPont breakdown: tax burden 76%, interest burden 64%, operating margin 16%, asset turnover 1.25×, equity multiplier 2.25×. What ROE do the five levers assemble into?

1.0.76 [×] 0.64 [×] 0.16 [×] 1.25 [×] 2.25 [=]tax burden × interest burden × operating margin × turnover × leverage

→ 21.89%

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