Return on Invested Capital: Computing the After-Tax Return

Return on invested capital divides operating profit after tax by the capital invested in the business. The numerator, net operating profit after tax (NOPAT), is operating profit multiplied by one less the effective tax rate. The denominator is the capital tied up in the business over the long term. Because this numerator is after tax and the pre-tax measure's is not, the two returns differ by exactly the tax.

Here is the shape of the work. Two amounts are read off the accounts and one rate is read out of a note, and then there is a multiplication followed by a division. The operating profit comes off the statement of profit and loss. The effective tax rateTotal tax expense divided by profit before tax, expressed as a percentage. The rate is computed from the accounts rather than looked up in the law. comes from the tax computation done on that same statement. The capital figure comes off the balance sheet. The first multiplied by one less the rate, then divided by the third, gives the ratio. None of that is difficult arithmetic. A return quoted without its sources cannot be checked by anybody who was not present when it was computed. The care goes into locating all three amounts correctly and then recording where each one was located.

The worked figures belong to Anjani Stationers Private Limited, an invented stationery business, and its year two return lands below the 27.3 per cent return on capital employed already published for the same business and the same year. The tax step alone accounts for the distance.

What does this ratio answer?

The ratio answers a single question: for every rupee of capital tied up in the business, how much operating profit did the year produce once tax had been taken off. There is nothing more to it. Think of a neighbour who has put Rs 8,00,000 into a small tuition centre, counting the deposit on the premises, the desks and the money she keeps in the drawer for the month's running costs. At the end of the year she has Rs 1,20,000 of profit left after the tax on it. Fifteen paise came back for every rupee she had tied up. She did not need the phrase return on invested capital to work that out, and the ratio is doing nothing more sophisticated than what she just did.

Every return ratio is a flow divided by a stock, and the discipline of the computation is making sure the flow and the stock actually belong to each other. The flow here is a year of operating profit, measured after tax. The stock is the capital that was standing there to produce it. Notice what that pairing rules out. A profit figure that has had interest taken off it does not belong on top of a capital figure that includes the borrowing behind the interest. The cost of the money would be removed from the top while the money itself stayed at the bottom. Operating profit sits above the finance cost on the statement, and that position is exactly why this ratio starts from it.

What is NOPAT, and where do its two inputs come from?

NOPAT is the operating profit with tax taken off it and nothing else changed. Its two inputs live on the same statement, one line and one note apart. The operating profit is printed on the face of the statementThe printed statement proper, as distinct from the numbered explanations filed after it that take one of its lines apart. of profit and loss, above the finance cost and captioned operating profit or earnings before interest and tax. For Anjani Stationers' year two it is Rs 41,50,000. The effective tax rate is not printed anywhere as a rate. The rate is computed from that same statement as the total tax expense of Rs 8,00,000 over the profit before tax of Rs 38,00,000, and the division gives 21.1 per cent.

The multiplication is by one less the rate, not by the rate, and that single detail is where a first attempt at this arithmetic usually goes wrong. Multiplying Rs 41,50,000 by 0.211 gives the tax, not the profit. Multiplying it by 0.789 gives what is left, and what is left is NOPAT. Written out, Rs 41,50,000 times 0.789 is Rs 32,74,350, or about Rs 32,74,000 rounded. Both routes reach the same place, so either one serves. Taking the tax off in two steps works equally well, computing Rs 8,75,650 of tax first and subtracting it, with the two answers checked against each other before anything further is done.

A careful reader will at this point think two computations disagree, so one precision has to be stated rather than buried. The Rs 8,75,650 is a notionalComputed for a purpose rather than reported. A notional amount is one the arithmetic requires, not one printed anywhere in the accounts. figure and it is larger than the Rs 8,00,000 of tax the accounts actually report. The difference is not an error in either place. The reported charge was levied on profit before tax of Rs 38,00,000, a figure already struck after the finance cost. The whole intention of NOPAT is to measure what the operations produced before any question of how they were funded, so NOPAT applies the rate to the bigger operating profit figure of Rs 41,50,000. So the tax in this computation is what the operating profit would have carried, and it is larger than the printed charge for exactly that reason.

What is invested capital, and where is it found?

Invested capital is the capital standing in the business for the long term, and here it is held at capital employedTotal assets less current liabilities, read from the balance sheet. Capital employed is one of several bases for a return ratio. of Rs 1,52,00,000, the figure already published for Anjani Stationers' year two. The Rs 1,52,00,000 is taken from the balance sheet, not computed. Assembled from a published set of accounts, it comes off the assets and liabilities side rather than the statement of profit and loss, and it is a balance at a date rather than a total for a year.

There is no single definition of invested capital that everybody uses, and the rule that matters is not which one is chosen but that the choice is stated and then kept. Three constructions turn up constantly. One is capital employed, total assets less current liabilities, the base used here. A second is total equity plus interest-bearing debt, built from the funding side rather than the asset side. A third is net operating assets, where cash and anything else not used in trading is stripped out first. The three constructions will not give the same answer on the same business. Set a return computed on one beside a return computed on another without saying so, and the difference in the answer measures the definition rather than the business.

There is a second choice hiding under the first, and it is the one that quietly moves a trend. The balance sheet gives a closing figure at the year end. The profit on top was earned across the whole year. Some preparers therefore use an average of the opening and closing capital as the denominatorIn a division, the figure underneath: the quantity everything above the line is being measured against.. The published pre-tax return was built on the closing figure of Rs 1,52,00,000, and the same closing figure is used throughout so the two answers reconcile. Which of the two was used is stated beside the answer, every time.

Why does this come out below the 27.3 per cent published earlier?

Because the tax step sits in this numerator and not in that one, and for no other reason. The return on capital employed already published for Anjani Stationers' year two is 27.3 per cent, and it is the same Rs 41,50,000 of operating profit over the same Rs 1,52,00,000 of capital, with the tax left on. Taking the tax off the top and leaving the bottom untouched gives 21.5 per cent. The two figures are not a disagreement between two computations and not two attempts at one number. Both are one subtotalA running total struck part of the way down a statement, before further items are added or deducted. measured once before tax and once after it.

The relationship is exact rather than approximate: the after-tax return is the pre-tax return multiplied by one less the effective tax rate, so 27.3 per cent times 0.789 gives 21.5 per cent and the pair is self-checking. The check runs in the other direction too. Dividing 21.54 by 27.30 gives 0.789, and 0.789 is one less the 21.1 per cent rate the arithmetic started with. Where the two returns do not reproduce the rate when one is divided by the other, something other than tax has moved between them, and the usual something is that the denominator was assembled differently in the two computations. The gap, in points, is 5.8, and that gap is the tax measured against the same capital.

What does Anjani Stationers' calculation come to?

The table below holds the entire computation with nothing left implicit: three inputs, their sources, and the two operations that turn them into an answer. The middle column is a set of directions to a printed statement and to nothing else: which statement to open and which line to run an eye down. A source column is not there to say what an amount means, and this one does not try.

Notice that the denominator is identical in the last two rows. An identical denominator is what makes the reconciliation a single line rather than an investigation. Had the pre-tax return been built on capital employed and the after-tax one on net operating assets, the two answers would still have differed by roughly the tax, and there would have been no way to prove it, because two things would have moved at once. Holding the denominator still and moving one thing leaves the difference with exactly one cause. Anjani Kulkarni can be shown the pair in a single sentence: the operations produced 27.3 per cent on the capital before tax, and 21.5 after it.

Anything shown only through a control is lost to a reader working from a printout, so the settings are set down here in words as well. Strip the tax out entirely and NOPAT is the full Rs 41,50,000, putting the after-tax return exactly on the pre-tax 27.3 per cent with no gap left to measure. Set the rate at 10 per cent and NOPAT is Rs 37,35,000, giving 24.6 per cent. At the reported 21.1 per cent the answer is 21.5. Push on to 30 per cent and NOPAT falls to Rs 29,05,000 for a return of 19.1 per cent, and at 40 per cent it is Rs 24,90,000 for 16.4. The rate cannot reach either input of the pre-tax return, so through every one of those settings the pre-tax return refuses to leave 27.3 per cent. The immobility is the plainest evidence available that the two measures are asking different questions of one set of accounts.

Who runs this computation, and what do they open next?

Step out of the arithmetic for a moment. Nobody produces these numbers for their own sake. Somebody computes them and then has to do something, and what they do next differs by who they are. A lender assessing a term facility computes the after-tax figure because tax is a claim that lands before anything is available to service the loan, and having computed it the lender turns to the tax note to see whether the rate used is one the business is likely to keep bearing. An analyst setting several years of one business side by side computes the after-tax return because tax regimes differ between the years and the after-tax figure is the one that stays comparable, and turns next to the year-by-year effective rates to see how much of any movement was tax rather than trading.

The finished pair delivers a direction of travel and not a judgement: how wide the gap is decides whether the tax note or the balance sheet is the thing to open next. Where the two returns sit close together, the rate was low and there is little for the tax note to explain, so the reader stays with the balance sheet and the construction of the capital figure. Where they sit far apart, most of the distance is the rate, and the tax note is the next thing to open. The gap is a statement about where to look next. Whether the return is high enough for anything is a different question with its own comparison, covered under the cost of capital.

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