Return on Capital: ROE, ROCE and ROIC Compared

Three measures ask the same question of different pools of money. Return on equity asks what the shareholders earned on what the shareholders put in. Return on capital employed asks what the business earned on every long-term rupee it uses, borrowed or contributed. Return on invested capital asks that second question after tax. Anjani Stationers returns 21.1, 27.3 and 21.5 per cent, and the spread is not disagreement; each answers its own question.

Here is what sits underneath that. No new accounting is needed. Every figure used below has already been printed somewhere in Anjani Stationers Private Limited's statements: the operating profit and the profit after tax off the statement of profit and loss, the equity and the capital employed off the balance sheet. A return measure adds no information at all. A return measure takes two amounts already in hand and puts one over the other, and the entire skill lies in choosing which two. So a return measure can be wrong while every number feeding it is right. Pairing is where the difficulty lives, not arithmetic.

All of it is already in hand. The margin ladder is published, so Anjani Stationers is known to have earned an operating profit of Rs 41,50,000 on revenue of Rs 2,70,00,000 in year two and a profit after tax of Rs 30,00,000. The balance sheet is published, so equity stands at Rs 1,42,00,000 and capital employed at Rs 1,52,00,000 on both routes to it. The three returns are built from those figures, the two mismatched versions are computed as errors, and the after-tax measure is reconciled to the tax actually charged.

What does a return measure actually divide, and who has to match whom?

Start with something that can be settled at a kitchen table before any accounting arrives. A household puts Rs 4,00,000 of its own savings into a small tuition centre and borrows another Rs 2,00,000 from a relative at a fixed monthly amount. The centre takes in Rs 90,000 over the year after paying its rent, its electricity and the person who sweeps it. Ask what the household earned on its savings, and the relative must first be handed the fixed monthly amount the relative is due. That part of the Rs 90,000 was never the household's to keep. Ask instead what the centre earned on the whole Rs 6,00,000 put to work in it, and the relative must be handed nothing. The relative's money is sitting inside the Rs 6,00,000 that forms the denominator. Two honest questions. Two different top lines. Nobody is disagreeing about the Rs 90,000.

A return measure divides what a pool of money earned by the size of that pool, so the figure on top must belong to exactly the providers counted in the figure underneath, and every mismatch worked out below is a failure of that one rule. The numeratorThe figure on top of a fraction, the amount being divided. In a return measure it is a profit figure covering some period. is a flow: profit earned over a year. The denominatorThe figure underneath a fraction, the amount being divided by. In a return measure it is a capital figure standing on the balance sheet on one date. is a stock: capital standing on a date. The link between them is the list of people whose money is in the pool. Walk down the statement of profit and loss and watch that list shrink. At the operating profit line nobody outside the business has been paid yet, so the whole of it is available to the long-term lenders and the shareholders together. Below the finance cost the lenders have been paid, so what remains is available to the tax authority and the shareholders. Below the tax line the tax authority has been paid too, and what remains belongs to the shareholders alone.

Three profit figures, three different lists of people. The pairing rule is the whole of it. Given a profit figure, the rule fixes which capital figure it has to sit above; given a capital figure, the rule fixes which profit figure has to sit on top of it. Once that rule is held, any of the three measures can be derived from the question actually being asked, so the measures build themselves and no formula needs memorising.

What did the shareholders of Anjani Stationers earn on what they put in?

Return on equityProfit after tax divided by equity. It measures what the shareholders earned on the money they contributed and left in the business. takes the profit after tax and divides it by equity, and the reason it uses that particular profit figure is that both of the other claimants have already been settled above it. Anjani Stationers earned an operating profit of Rs 41,50,000 in year two. The lenders took Rs 3,50,000 as a finance cost, leaving Rs 38,00,000 of profit before tax. The tax authority took Rs 8,00,000, leaving Rs 30,00,000. Not one rupee of that Rs 30,00,000 is owed to anybody outside the shareholder register.

Anjani Stationers' return on equity is Rs 30,00,000 over Rs 1,42,00,000, or 21.1 per cent, and it is the only one of the three measures whose numerator has had both the lenders and the tax authority removed from it. Read that as a rate rather than a ratio and it becomes concrete: for every Rs 100 of shareholder money standing in Anjani Stationers at the year end, the year produced Rs 21.10 that the shareholders may keep in the business or take out of it. The published earnings per share of Rs 7.50 across 4,00,000 shares says the same thing per share instead of per rupee of equity. The two figures therefore always move together.

One caution belongs here rather than later. The Rs 1,42,00,000 of equity is a closing figure standing on the last day of the year. The Rs 30,00,000 was earned across all of it. Anjani Stationers began the year with equity of Rs 1,12,00,000, so the money that produced the profit was smaller for most of the period than the money the return is measured against. Some readers therefore divide by an average of the opening and closing equity instead. Averaging is a defensible choice and it produces a different, higher answer. The convention used has to be stated. Two people using two conventions will get two figures, and neither of them has made an error.

What did Anjani Stationers earn on every long-term rupee it uses?

Return on capital employedOperating profit divided by capital employed. It measures what a business earned on all its long-term funding, before any question of who supplied that funding. answers the question the shareholders' measure cannot: how well does this business use money, leaving aside entirely who happened to supply it. Its numerator is the operating profit of Rs 41,50,000, taken at the point where nobody outside the business has been paid. The money in the denominator was supplied by both the long-term lenders and the shareholders, so the return has to cover both of them.

The denominator needs care because it can be assembled two ways, and the check that they close is worth doing every time. Capital employedThe long-term funding a business has at work: total assets less current liabilities, which is the same thing as equity plus non-current liabilities. is either total assets less current liabilities, or equity plus non-current liabilities. Take the first route on Anjani Stationers: total assets of Rs 1,80,00,000 less current liabilities of Rs 28,00,000 is Rs 1,52,00,000. Take the second: equity of Rs 1,42,00,000 plus non-current liabilities of Rs 10,00,000 is Rs 1,52,00,000. The two routes agree because they are the same subtraction read from opposite sides of a balance sheet that already balances, and if they ever fail to agree on a real set of accounts, something has been classified inconsistently between the two workings rather than discovered about the business.

Anjani Stationers' return on capital employed is Rs 41,50,000 over Rs 1,52,00,000, or 27.3 per cent, and it is higher than the return on equity for the plain reason that its numerator still contains money the shareholders never received. Look at the parts the denominator is made of and the whole measure becomes readable. Of the Rs 1,52,00,000, the shareholders supplied Rs 1,42,00,000, or 93.4 per cent, and long-term lenders supplied Rs 10,00,000, or 6.6 per cent. Current liabilities of Rs 28,00,000, the trade payables and the accruals and the rest, are deliberately excluded. Short-term funding of that kind turns over inside the year and is not capital anybody set out to employ.

What is left of that return once the tax authority has been paid?

Return on invested capitalOperating profit after a notional tax charge, divided by the capital invested in the business. It measures the same pool as the pre-tax measure, with tax removed from the numerator. asks the identical question about the identical pool of money, and then takes tax off the top. Its providers are the same long-term lenders and shareholders, and Anjani Stationers' denominator stays at the same Rs 1,52,00,000. Only the numerator moves. The operating profit of Rs 41,50,000 is reduced by the tax that operating profit would carry, at the effective tax rateTotal tax expense divided by profit before tax, worked out from the accounts rather than looked up in the law. the business actually bore: Rs 8,00,000 of tax over Rs 38,00,000 of profit before tax, or 21.1 per cent.

Multiply by one less the rate rather than by the rate. Rs 41,50,000 times 0.789 is Rs 32,74,350, and over Rs 1,52,00,000 that is 21.5 per cent. Because the denominator never moved, the relationship between the two measures is exact: 27.3 per cent times 0.789 is 21.5 per cent, and the 5.8 points separating them are the tax and nothing else.

One precision has to be stated out loud, or the notional tax below will look like a contradiction of the tax the accounts report. The notional tax of Rs 8,75,650 used in this numerator is larger than the Rs 8,00,000 of tax Anjani Stationers was actually charged, and that is by construction rather than by error. The reported charge was levied on profit before tax of Rs 38,00,000, a figure that already has the finance cost taken out of it. The whole point is to measure what the operations produced before any question of how they were funded, so the rate is deliberately applied to the bigger operating profit of Rs 41,50,000. The difference is Rs 75,650, and it splits exactly two ways: Rs 73,850 is the rate applied to the Rs 3,50,000 of finance cost that sits between operating profit and profit before tax, and Rs 1,800 is the effect of using the rate rounded to 21.1 per cent rather than the raw Rs 8,00,000 over Rs 38,00,000. Neither figure is a mistake in either place. One is the tax the accounts report; the other is the tax the operations would have carried had there been no borrowing.

What happens to the answer when the numerator and denominator do not match?

Naming the pairing rule is not enough to make it stick, so here it is broken in both directions on Anjani Stationers' own figures, with the size of each error worked out. Neither mistake is exotic. Both appear in spreadsheets built by careful people working at speed. Both look like ordinary return measures, and neither produces an answer absurd enough to be queried on sight.

The first mismatch puts profit after tax over capital employed. Rs 30,00,000 over Rs 1,52,00,000 is 19.7 per cent. The damage shows in both halves of the fraction. The numerator has had the lenders paid out of it and the tax authority paid out of it, so it is a shareholders-only figure. The denominator still counts the long-term lenders' Rs 10,00,000. A smaller top is being measured against a bigger bottom, and the answer is too low in both directions at once. Against the correctly paired 27.3 per cent, the mismatched 19.7 per cent understates the return by 7.6 percentage points, more than a quarter of the true figure.

The second mismatch runs the other way and puts operating profit over equity. Rs 41,50,000 over Rs 1,42,00,000 is 29.2 per cent. Here the numerator still contains the lenders' interest and the tax authority's share, neither of which the shareholders will ever see. The denominator counts only the shareholders. A bigger top over a smaller bottom. Against the correctly paired 21.1 per cent, the mismatched 29.2 per cent overstates the return by 8.1 percentage points, nearly two fifths of the true figure. Notice that both wrong answers land in the neighbourhood of the two right ones, between 19 and 30 per cent, and landing there is exactly why neither gets caught.

How do the three measures move when Anjani Stationers borrows?

The three measures now stop being three ways of saying one thing and start doing work no single measure could do. Borrowing does something asymmetric to them, and the asymmetry is the point.

Take the household with the tuition centre again. Suppose the household puts in Rs 2,00,000 of its own instead of Rs 4,00,000 and borrows Rs 4,00,000 from the relative rather than Rs 2,00,000. The centre is identical: same rooms, same students, same Rs 90,000 earned before the relative is paid. Nothing about the centre changed, so what the centre earns on the Rs 6,00,000 put to work in it has not changed by a single rupee. The household's own return on its Rs 2,00,000 has changed a great deal. The household now pays the relative more and divides what is left by half as much of its own money.

Borrowed money enters the denominator while the assets it funds enter the numerator, so borrowing leaves the return on capital employed almost exactly where it was. Borrowing moves the return on equity sharply instead, because interest reduces the profit after tax at the same moment the shareholders' capital shrinks. Work it on Anjani Stationers with the total capital employed held at Rs 1,52,00,000 and the operating profit held at Rs 41,50,000. Only the funding mix moves. Replace Rs 50,00,000 of the shareholders' money with borrowing, taking debt inside capital employed from Rs 10,00,000 to Rs 60,00,000 and equity down from Rs 1,42,00,000 to Rs 92,00,000. At an assumed 9.5 per cent on the additional borrowing, an invented rate used only for this illustration, the finance cost rises from Rs 3,50,000 to Rs 8,25,000 and the profit after tax falls from Rs 30,00,000 to Rs 26,25,225. Return on equity rises from 21.1 to 28.5 per cent. Return on capital employed does not move at all: Rs 41,50,000 over Rs 1,52,00,000 is 27.3 per cent before and after.

Hold on to what that means. Nothing else these three measures do together is as useful. A business whose return on equity is climbing while its return on capital employed is flat has not become better at anything. The business has changed who supplied its money. The operations produced the same Rs 41,50,000 on the same Rs 1,52,00,000 in both versions of Anjani Stationers. Everything that moved, moved on the funding side. And the direction does not hold automatically either: borrowing lifts the return on equity only while the money costs less than the capital it replaced was earning before tax. Push the borrowing rate up to about 26.8 per cent on Anjani Stationers' figures and the return on equity stops moving altogether whatever the debt level; push it beyond that and more borrowing pulls the return on equity down.

A panel is lost to a reader working from a printout, so the settings that matter are set down in words. At the default, debt of Rs 10,00,000 against equity of Rs 1,42,00,000 gives a finance cost of Rs 3,50,000, a profit after tax of Rs 30,00,000 and the published trio of 21.1, 27.3 and 21.5 per cent. Push the debt to Rs 60,00,000 at 9.5 per cent and the return on equity reaches 28.5 per cent while the other two do not move. Push it to Rs 1,10,00,000 and the return on equity reaches 53.6 per cent, still with no movement in the other two. Along the way it crosses the return on invested capital at debt of about Rs 14,00,000 and the return on capital employed at about Rs 54,00,000. Now change the rate to 26.8 per cent and drag the slider from one end to the other: the return on equity sits at 21.1 per cent and refuses to move. At that rate every borrowed rupee costs the shareholders exactly what the shareholders' rupee it replaced was earning before tax. At 35 per cent the line runs the other way and the return on equity falls as the borrowing rises.

Why did Anjani Stationers' return on capital employed fall from 44.9 to 27.3 per cent?

A single year of a single business compares to nothing at all, and its own past is the only comparison available. Put the two published years side by side. In year one Anjani Stationers earned an operating profit of Rs 53,00,000 on capital employed of Rs 1,18,00,000, a return of 44.9 per cent. In year two it earned Rs 41,50,000 on Rs 1,52,00,000, a return of 27.3 per cent. The return on equity moved the same way, from 33.9 to 21.1 per cent. Profit after tax fell from Rs 38,00,000 to Rs 30,00,000 while equity rose from Rs 1,12,00,000 to Rs 1,42,00,000.

Anjani Stationers' return on capital employed fell 17.6 percentage points across a year in which revenue rose 12.5 per cent, and the arithmetic locates that fall precisely without saying a word about whether it is bad. Two things moved in opposite directions. The operating profit fell Rs 11,50,000 in money, from Rs 53,00,000 to Rs 41,50,000, even though revenue rose Rs 30,00,000, so the operating margin fell from 22.1 to 15.4 per cent. At the same time the capital employed grew 28.8 per cent, from Rs 1,18,00,000 to Rs 1,52,00,000, and total assets grew 35.3 per cent, from Rs 1,33,00,000 to Rs 1,80,00,000. A smaller numerator over a larger denominator, and the ratio has nowhere to go but down.

The measure has pointed at two questions, and that is the entire extent of its usefulness. Why did the operating profit fall while revenue grew? Why did the asset base grow at nearly three times the rate of revenue? Neither question is answered by any return measure, and neither can be. The answers live in the published detail: the movement in receivables and inventory, the provision charged against doubtful debts, the additions to the fixed asset base and the year they will start earning. A return measure is a very good pointer and a very poor explanation, and confusing the two is how a diagnostic becomes a verdict.

Which of the three to use, and for what?

None of the three is more correct than the others, and the question is never which one is right but which one answers what was actually asked. The return on capital employed answers how well a business uses money, regardless of who supplied it. Of the three it is the least disturbed by the funding mix, and therefore the one that says most about the operations. The return on equity answers what the shareholders got, a genuinely different question and the only one of the three that a shareholder is entitled to care about directly. The return on invested capital is the only one of the three that has already removed tax from the numerator, so it serves when two businesses whose tax positions differ are set side by side.

The three answers on Anjani Stationers alone span 21.1 to 27.3 per cent on identical, correctly assembled figures, so quoting one of the three without saying which one is meant is a common source of confusion and the easiest of all to avoid. Somebody who says the business returns 27 per cent and somebody who says it returns 21 per cent may both be exactly right and describing exactly the same year, and the only thing separating them is a definition neither of them stated. The remedy is the full name of the measure, the name of the denominator used, and a statement of whether the closing figure or an average was taken.

Which documents govern where each of these inputs sits?

Everything above is arithmetic, and arithmetic is the same wherever it is read. The printed statement the inputs are lifted from is local, and it belongs in one clearly marked place rather than scattered through the working.

Who reads these three returns, and what do they do with them?

Leave the mechanism for a moment. Four different people can open Anjani Stationers' accounts in the same week, and none of them wants the same one of these three figures.

A lender reads the return on capital employed against what its own money costs, an equity analyst reads the return on equity beside the return on capital employed to see whether an improvement is operational or financial, and Vaidehi Rao reads all three because she is the one who will be asked to explain the gap between them. Watch each of them work. The lender's money sits inside the Rs 1,52,00,000 alongside the shareholders' money, so the figure that describes what the whole pool produced is the one that matters: Rs 41,50,000 of operating profit is what stands available to pay interest before anybody else is paid, and the return on equity of 21.1 per cent describes a claim that ranks behind the lender's own. A lender who reads only the return on equity has read the wrong pool.

The equity analyst's use is the comparison itself. A return on equity of 21.1 per cent tells that analyst almost nothing until it is set beside a return on capital employed of 27.3 per cent. The pair is what separates a business that improved from a business that borrowed. Run the two across the two published years and the pattern is unmistakable: both fell together, 44.9 to 27.3 and 33.9 to 21.1. Falling together is the signature of something happening in the operations rather than in the financing. Had the return on equity risen while the return on capital employed sat still, the reading would have been the opposite one.

A household running a small business reads the same pair without ever naming it. The question is whether the shop is worth the trouble compared with what the money could do sitting still, and that is the return on capital employed question. Whether taking a loan made the household better off is the return on equity question. And Vaidehi Rao, as finance controller of Anjani Stationers, has the most immediate job of all: when a bank asks why the return fell from 44.9 to 27.3 per cent, the answer is not a ratio. The answer is Rs 11,50,000 less of operating profit and Rs 34,00,000 more of capital employed, and she is expected to say which line each of those came from.

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