DuPont Analysis: Decomposing Return on Equity Into Its Drivers

A DuPont decomposition takes a return on equity apart into three things that produced it: what survives each sale, how much revenue each rupee of assets generates, and how much of the asset base the shareholders funded themselves. At Anjani Stationers, 21.1 per cent is 11.1 per cent, times 1.50, times 1.27. The decomposition always reconciles, so it proves nothing and locates everything.

The panel opens on what Anjani Stationers published, and here is that opening setting written out. Revenue Rs 2,70,00,000, profit before tax Rs 38,00,000, finance costs Rs 3,50,000, tax expense Rs 8,00,000, total assets Rs 1,80,00,000 and equity Rs 1,42,00,000. The six figures give profit after tax of Rs 30,00,000 and EBIT of Rs 41,50,000. The three factors are then 0.111111, 1.500000 and 1.267606, and the five are 0.789474, 0.915663, 0.153704, 1.500000 and 1.267606. Both chains multiply to 0.211268, a return on equity of 21.13 per cent, and both close because they are the same arithmetic written at two levels of detail. Round each factor to three places before multiplying and the three give 21.1122 per cent instead. The factors are therefore multiplied unrounded, and the product is rounded once at the end.

The DuPont decompositionA way of writing a return on equity as the product of separate ratios, each describing one part of how the return was produced. is not a discovery about a business. The decomposition is a rearrangement of one division into three, and it is true of every set of accounts ever prepared, including a set with a mistake in it. Performing it changes nothing about what is known of the business. The decomposition changes how many places there are to look, and how precisely the driver that moved can be named.

Return on equity was built for Anjani Stationers Private Limited at 21.1 per cent, being profit after tax of Rs 30,00,000 over equity of Rs 1,42,00,000. The margin ladder ran gross 45.0 per cent, then earnings before interest, tax, depreciation and amortisation (EBITDA) at 19.8, EBIT at 15.4 and net at 11.1 for the year just closed, and asset turnover of 1.50 times came out of the fixed asset work. A decomposition measures nothing new, and that fact sets a firm limit on what it is entitled to claim.

How to Perform DuPont Analysis, and why is step three not optional?

Five steps, in order, and none of them is a judgement. Step one, compute the return on equity that is to be taken apart. The target has to exist before any driver does. Step two, compute the three drivers from the statements: net marginProfit after tax divided by revenue. How many paise of every rupee of sales are left once every cost, every interest payment and every rupee of tax has been met., asset turnoverRevenue divided by total assets. How much revenue each rupee of assets produced during the year, and nothing about whether that revenue was profitable. and the equity multiplierTotal assets divided by equity. How many rupees of assets the business carries for every rupee the shareholders have in it, so it rises whenever the business is funded by anything other than equity.. Step three, multiply the three and check that the product equals the return from step one. Step four, compute the same three drivers for the prior year, from the prior year statements, on the same basis. Step five, compare driver against driver and name the one that moved.

Work all five on Anjani Stationers. Step one gives Rs 30,00,000 over Rs 1,42,00,000, or 0.211268. Step two gives 0.111111, 1.500000 and 1.267606. Step three multiplies them and lands on 0.211268 again. Steps four and five repeat step two on the prior year and set the two sets of drivers side by side.

Step three is not optional, and the reason is that a product which fails to close reports a misplaced input rather than anything about the business. Profit after tax from the consolidated statement with equity from the standalone one. Revenue for twelve months against a nine month balance sheet. Average assets in one driver and closing assets in the next. Each of those produces a product that misses the return, and each is a sourcing error that takes about a minute to find once looked for and is invisible otherwise. One practical trap sits beside it, and the panel above prints it live: rounding the drivers before multiplying makes the product miss the return by a little. The check runs unrounded, with the rounding done once at the end, or step three fails for a reason that has nothing to do with sourcing.

What does each of the three drivers actually describe?

The three drivers are three questions that could be put to a shopkeeper on any street, asked instead of a set of accounts. How much does the shopkeeper keep out of every hundred rupees taken at the counter? Net margin answers that. How many times a year does the shop sell everything it is worth? Asset turnover answers that. How much of what is in the shop did the shopkeeper pay for, and how much did somebody else fund? The equity multiplier answers that. All three answered describe the whole of the return. Only the first answered describes a fraction of it.

Note what asset turnover refuses to say. Profitability is the first driver's job entirely, and asset turnover is silent on whether the revenue was profitable. And note where the equity multiplier's extra 27 paise came from. The business carries Rs 1.27 of assets for every rupee of equity, and that gap is the Rs 38,00,000 of liabilities sitting between total assets of Rs 1,80,00,000 and equity of Rs 1,42,00,000.

The equity multiplier is a leverage measure wearing a different name, and it is the only one of the three that rises simply because a business borrowed, so a return on equity that improved only through the third driver has not improved anything about how the business operates. Hold Anjani Stationers' net margin at 11.1 per cent and its asset turnover at 1.50, and let the equity multiplier rise from 1.27 to 1.60. The return on equity goes from 21.13 to 26.67 per cent. No customer paid more, no machine ran faster, no rupee of cost came out. The shareholders' slice of an unchanged profit stream simply got measured against a smaller base.

Why can a DuPont decomposition never fail to reconcile?

A reader who takes the reconciliation as evidence has learned something false. Written out as fractions, the drivers are profit after tax over revenue, times revenue over total assets, times total assets over equity. Revenue cancels between the first two and total assets cancels between the second and third, and what is left is profit after tax over equity, the return the working started from.

The decomposition is an identityA statement true for every possible set of values, because both sides are the same expression written differently.. An identity holds for every set of numbers anybody could put into it, and reconciling is therefore a check on the arithmetic and never evidence about the business. Try to make it fail. A business with a negative margin still closes. The same wrong revenue cancels against itself, so a business whose accounts are wrong in every line still closes. An identity cannot distinguish a true set of accounts from a false one, and anyone who says a decomposition confirms the numbers has said something the arithmetic cannot support.

So why perform it at all? Because locating is worth a great deal even when it proves nothing. A single return that fell gives no direction beyond looking at everything. Three drivers say which of three doors to open first. Locating is the entire honest claim, and it is a good one: the decomposition converts one undifferentiated question into three specific ones, each pointing at a different part of the business and a different set of people to ask.

What do the extra two drivers in the five-step version separate?

The three-step version puts everything between EBIT and profit after tax inside one driver. The five-step version pulls that driver into three, so the chain becomes tax burdenProfit after tax divided by profit before tax. A figure of 0.79 means about seventy-nine paise of every pre-tax rupee got through the tax charge., then interest burdenProfit before tax divided by EBIT. A figure of 0.92 means about eight per cent of operating profit went to lenders., then operating margin, then asset turnover, then equity multiplier. On Anjani Stationers those five multiply to 0.211268, the identical return.

Read the first two carefully. Their names invite a misreading. Tax burden of 0.789474 is profit after tax of Rs 30,00,000 over profit before tax of Rs 38,00,000, the share of pre-tax profit that survived the Rs 8,00,000 tax charge. Interest burden of 0.915663 is that same profit before tax over EBIT of Rs 41,50,000, the share of operating profit that survived the Rs 3,50,000 finance cost. In both, a higher figure means more survived. The word burden points at the cost while the ratio measures the survival, and readers who forget that read both drivers backwards.

The three-step version buries financing and tax inside net margin and reports two quite different situations as one number, so the extra two matter precisely when businesses financed differently or taxed differently are being compared. Two businesses can show identical net margins of 11.1 per cent while one earns a thin operating margin and pays almost nothing to lenders or the tax authority, and the other earns a fat operating margin and hands most of it over. On a three-step decomposition they look like the same business. On a five-step one they do not, and the difference shows in the first two drivers, before operations are reached.

How to Benchmark a Company Against Peers Using Ratios: what has to be true before the comparison means anything?

Everything so far has compared Anjani Stationers to Anjani Stationers. The other use of a ratio is comparing one business to a peer groupA set of other businesses chosen as the comparison for the one being analysed, on the basis that they do close enough to the same thing for a shared measure to mean something., and that use carries a procedure of its own. Six steps, almost entirely about making the comparison legitimate before making it at all.

Step one, choose the peers by what the businesses actually do, not by the classification code sitting in a database. A code will happily place a notebook maker beside a printer of packaging film, on the ground that both consume paper. Step two, put every business on the same accounting basis, standalone against standalone or consolidated against consolidated, never one of each. Step three, use the same period ends, or say clearly that this was not possible. A business with a seasonal year end and one without are describing different moments. Step four, compute every ratio directly from the statements. Two published figures called the same thing are routinely built from different inclusions. Step five, decompose rather than compare headline numbers. Two businesses at the same return on equity may be there for opposite reasons. Step six, write down every item that could not be made comparable, and keep that list beside the comparison.

An unrecorded incomparability quietly becomes a finding, so step six is both the step people skip and the step that decides whether the whole comparison meant anything. A lease that one business capitalised and another did not moves total assets, and therefore moves asset turnover and the equity multiplier at once. A revaluation against historic cost does the same. If that sits in a recorded footnote, the reader treats the difference with the caution it deserves. If it sits nowhere, the reader treats a difference in accounting policy as a difference in performance.

A peer comparison is worth no more than the filings behind it, and a comparator whose figures came from nowhere is worse than no comparator at all. A competitor with an asset turnover nobody ever filed leaves a reader with an impression of what is normal for a notebook maker in India, and that impression rests on nothing. A real comparison is built from real filings, one statement at a time, through the six steps.

Financial Ratio Analysis: What Ratios Can and Cannot Do, so which side is which?

A ratio is arithmetic performed on figures that were already printed in the accounts, so it adds no information whatever to what a reader already had. Nothing is discovered by dividing. The entire value of a ratio is that it makes a pattern visible which was sitting in plain figures and was hard to see, and every honest claim about ratio analysis is a claim about visibility rather than about knowledge.

Four things it can do, and the figure below sets them beside their limits: locate where something changed, compare a business to its own past on a consistent basis, raise a question precise enough to be worth somebody's time answering, and put businesses of very different sizes on one axis. Five things it can never do, and each of them is attempted daily: explain why anything changed, establish causation, detect a well-executed misstatement, say whether a level is good, or speak to prospects. One of those five is worth naming plainly, and it is the one people assume the arithmetic covers. A misstatement that is internally consistent produces perfectly ordinary ratios, and no ratio will catch it.

Liquidity Ratios Explained: What They Reveal Beyond the Formula, so what is each one counting?

Anjani Stationers shows a current ratio of 4.25, a quick ratio of 3.25 and a cash ratio of 0.18. One business, one balance sheet date, one set of figures. The same business looks extremely liquid on the first measure and extremely thin on the last, and the entire difference is what each measure is willing to count. Current liabilities of Rs 28,00,000 are the denominator of all three, and the numerator moves from Rs 1,19,00,000 of current assets, to Rs 91,00,000 once inventory is dropped, to the Rs 5,00,000 of cash alone. Nothing about the business changed between those three lines. Only the definition did.

The household version has the same shape. A person with Rs 5,000 in a bank account, Rs 86,000 that a relative has promised to repay and Rs 28,000 of gold in a locker, facing a Rs 28,000 bill this month, is comfortable on one arithmetic and short on another. All three are assets and all three are real. Only one of them settles the bill this week without somebody else's cooperation.

The quality of what is being counted lies beyond the formula. Rs 86,00,000 of the Rs 1,19,00,000 of current assets is money customers have not paid yet, and the gross receivables behind that net figure carry a collection period of about 128 days, published alongside the working capital cycle of 143.1 days. A rupee that arrives in four months and a rupee sitting in the bank are treated as identical by a current ratio, and are not remotely identical to somebody with a payment due on Friday. The formula cannot see the other side either: a current ratio treats an amount due next week and an amount due in eleven months as the same denominator.

What does the two-year decomposition locate at Anjani Stationers?

Now put both years side by side. Return on equity fell from 33.9 per cent to 21.1 per cent, a fall of 12.8 percentage points, and a single number falling by that much gives no direction beyond looking at everything. The decomposition narrows the search.

Both products close before anything is read into them. The prior year gives 0.158333 times 1.804511 times 1.187500, or 0.339286. Profit after tax of Rs 38,00,000 over equity of Rs 1,12,00,000 is the same 0.339286. Only now is the comparison worth making.

Two drivers fell and the third rose against them. The fall is located in what survives a sale and in what the assets produced, and the funding shift pushed the other way without coming close to covering them. Substituting one driver at a time from the prior year to the year just closed, net margin accounts for a fall of about 10.1 points, asset turnover for about 4.0 more, and the equity multiplier gives back about 1.3, which nets to the 12.8 points observed. One caveat: those attributions depend on the order of substitution. Taken in a different order, net margin's share ranges from about 8.4 to about 10.8 points. The total never moves, the ranking of the two falling drivers never moves, and the precise split is an artefact of the method rather than a fact about the business.

The decomposition may now say the fall is located in margin and turnover, that the equity multiplier rose because assets grew 35.3 per cent while equity grew 26.8 per cent, and that anyone wanting the reason should read the cost lines and the asset additions. The decomposition may not say whether 21.1 per cent is a good return, whether the fall matters, or what Anjani Stationers should do about it. The decomposition pointed at two doors. Walking through them is somebody else's work with different evidence.

Here are the four driver sets the panel draws, each of which lands on the published 21.1 per cent, and each stated to the precision shown while the arithmetic behind it runs unrounded. Net margin 11.1 per cent, asset turnover 1.500 and an equity multiplier of 1.268, the set Anjani Stationers reported. Net margin 5.6 per cent with asset turnover 3.000 on the same multiplier, a business selling twice as hard on half the margin. Net margin 16.7 per cent with asset turnover 1.000, the trade in the other direction. And net margin 8.9 per cent with asset turnover 1.500 and an equity multiplier of 1.585, a fifth off the margin funded by a quarter more leverage. Four businesses that could hardly be less alike, one identical return on equity, and no reader could tell them apart from that number alone.

Who actually reaches for a decomposition, and what do they do with it?

Three people open the same set of accounts in the same week, and none of them decomposes the return for the same reason.

A lender decomposes to find out whether a rising return came from trading or from borrowing, an analyst decomposes to know which question to ask on a call, and Vaidehi Rao decomposes so that she is not surprised by a question she could have answered first. The lender's use is the sharpest. A lender assessing Anjani Stationers wants to know how much of the return came from the third driver. A return built on an equity multiplier will hurt on the way down as reliably as it helped on the way up. The margin and the turnover are evidence about the business; the multiplier is evidence about the lender's own risk, and the decomposition separates the two in one line of arithmetic.

The analyst's use is narrower. On a results call an analyst gets one question, and a single return on equity supports only a vague one. Three drivers support a specific one, and specific questions are the ones that get answered. Why did returns fall invites a paragraph about market conditions. Why did asset turnover fall from 1.80 to 1.50 while revenue grew invites a number.

Vaidehi Rao, as finance controller of Anjani Stationers, uses it defensively. She knows before anyone asks that assets grew 35.3 per cent while revenue grew 12.5 per cent, that the gap is the whole of the turnover fall, and that the answer to the question she will be asked lies in the asset additions during the year. Being able to name the driver that moved, with the underlying detail ready, is the difference between a two minute exchange and a follow-up letter.

Anjani Stationers Private Limited, Chitra Binding Works and Vaidehi Rao are invented.
Educational material. Not advice on any investment, tax, budget or market position.