Diluted EPS: Computing Earnings Per Share After Dilution

Diluted earnings per share (EPS) divides the profit attributable to the owners by the share count that would exist if every instrument capable of becoming a share did become one. The result is what a share would have earned on that fuller count. Anything whose inclusion would raise the figure is left out, so the diluted result never sits above the basic result.

Here is the mechanical part underneath that definition. Two of the three quantities in the calculation are printed somewhere in the accounts and one of them has to be assembled. The profit is printed. The share count as it stood through the year is printed. The extra shares that have not been issued yet are printed too, but in a different note, and putting them into the same fraction as the profit is the whole of the work. Finding those three quantities in the right places and dividing once is the entire calculation.

Anjani Stationers, an invented stationery business with a single option grant outstanding, supplies the numbers throughout, and the one wrong input that inflates its result by 75 paise a share is a profit figure taken from the wrong line of the consolidated statement.

What does the diluted figure answer?

The diluted figure answers one narrow question: if everything that can turn into a share turned into one tomorrow, and the profit stayed where it is, what would each share have earned? The basic earnings per shareThe profit for the period divided by the number of shares actually in issue, weighted for how much of the period each was in issue. figure answers the same question on the shares that genuinely exist today. Both are printed, both are correct, and they are different answers to two different questions rather than a right one and a rough one.

The diluted figure is the cautious count and the basic figure is the current count. Because the two answer different questions, the standards require both to be shown rather than letting a preparer choose. Consider a household of four sharing a pot of rice. Divided four ways, the pot shows what each person gets tonight. Now suppose two cousins have a standing arrangement to join the meal whenever they like. The pot does not get bigger when they arrive, so anyone planning the household's food does the sum on six rather than four, and does it before the cousins turn up rather than after. Both sums are true. One of them is the sum to plan around. The household's two sums stand to each other exactly as the basic and the diluted figures do, and Anjani Stationers has one such standing arrangement in it: Meera Rao, the operations manager, holds share optionsA right, given to somebody under an agreed set of terms, to acquire shares in the business at a stated price at some point in the future. over 25,000 shares.

What goes on top of the fraction, and where is it found?

The profit attributable to the owners. On a standalone statement of profit and loss the profit attributable to the owners is simply the profit after tax line at the foot of the statement, and for Anjani Stationers' year two that line reads Rs 30,00,000. On a consolidated statement it is not the profit for the year: it is one of the two amounts the profit for the year is split into, printed immediately below the total under a heading naming who each part belongs to. Anjani Stationers' consolidated profit for year two is Rs 40,00,000, split Rs 37,00,000 to the owners of Anjani Stationers and Rs 3,00,000 to the non-controlling interestThe share of a subsidiary that the parent business does not hold, and therefore the part of that subsidiary's profit belonging to somebody outside the group's shareholders.. The figure that goes on top of the fraction is Rs 37,00,000.

On a consolidated statement the required number is never the largest number printed there, and it is always printed two lines below that largest number. The reason the split is printed at all is that the statement above it has added in the whole of Chitra Binding's revenue and the whole of Chitra Binding's costs, and Chitra Binding is a subsidiary with a founder still holding 30 per cent of it. The split is where the statement hands that 30 per cent back. Taking the line above the split takes the founder's Rs 3,00,000 with it, and that Rs 3,00,000 is then divided among shares that have no claim on a rupee of it.

What goes underneath it, and where is that found?

Two numbers added together, and they come from two different notes. The first is the weighted averageAn average in which each figure is counted in proportion to how long it applied, so a share issued halfway through the year counts as half a share for that year. number of equity shares in issue. The note on earnings per share states the count. The share capital note lists every issue and buy-back during the year, and the count reconciles to that list. Anjani Stationers had 4,00,000 equity shares of Rs 10 each in issue for the whole of year two and issued none, so the weighted average is the same 4,00,000. The second is the number of shares the potential instruments would add. The note on employee share options discloses that number along with the terms of each grant. For Anjani Stationers that number is 25,000, so the count underneath the fraction becomes 4,25,000.

Four inputs, four places to look, and not one of them requires working out what an instrument is or how it was priced: the count required has already been disclosed by the preparer. The instruments themselves can be intricate, so the point is worth saying plainly. A convertible instrumentA borrowing or a preference share carrying a right to be exchanged for ordinary shares on stated terms, so the holder can end up as a shareholder rather than a creditor. has a conversion ratio buried in its terms, an option grant has a vesting schedule and an exercise price, and the arithmetic that turns those terms into a share count belongs to the preparer and the standard. The reader assembling this fraction goes to the disclosure, reads the number of shares stated there, and adds it.

One assumption behind the arithmetic has to be stated rather than buried. The count used here adds the full 25,000 shares disclosed as being under option. The method a preparer applies under the accounting standard adjusts that number for the consideration the option holder will pay, and the adjusted figure is itself part of what the earnings per share note discloses. The figure added in this calculation is the disclosed potential share count taken as given. A reader with the accounts in front of them does exactly that, and the disclosed count is not a substitute for the preparer's own computation. Where the two differ, the disclosure is the authority and the standard behind it is named in the references below.

What counts as dilutive, and what is left out?

Treat it as a step in the computation rather than a category of instrument. Compute the figure with the potential shares added. Compare the result with the basic figure. If the recomputed figure is lower, the instrument is dilutiveDescribes an instrument whose inclusion in the calculation pulls the per-share result down rather than up. and it stays in the count. If the recomputed figure is higher, the instrument is anti-dilutiveDescribes an instrument whose inclusion would push the per-share result up, which is why the calculation leaves it out.. The step drops it and the count stays where it was. The comparison is the entire test, and it is performed on the arithmetic rather than on the paperwork.

The test is a comparison, not a judgement, and it is the reason a diluted figure equal to the basic figure is a perfectly ordinary result rather than a sign that something was missed. Meera Rao's options are in the moneySaid of an option whose exercise price sits below the current value of the share, so exercising it is worth doing. at an assumed exercise price of Rs 40 a share, so adding them takes Anjani Stationers' standalone figure from Rs 7.50 to Rs 7.06 and the step keeps them. Now imagine a grant on the other side of the line, priced so far above the share's value that including it would push the figure up rather than down. The step would drop it, the count would stay at 4,00,000, and the two printed figures would be identical. A business with no potential shares at all reaches that same place by a shorter route.

What does Anjani Stationers' calculation give?

Two profits and two counts make four figures, and every one of the four gets printed somewhere. Take them in order. The standalone profit after tax of Rs 30,00,000 over the 4,00,000 shares in issue gives basic earnings per share of Rs 7.50. The same Rs 30,00,000 over 4,25,000 gives Rs 7.06. On the consolidated numbers, Rs 37,00,000 over 4,00,000 gives Rs 9.25, and Rs 37,00,000 over 4,25,000 gives Rs 8.71. Nothing else is computed and nothing else is needed.

The dilution takes 44 paise off the standalone figure and 54 paise off the consolidated one, and yet it is exactly the same 5.88 per cent in both cases. The count is the only thing the options changed. The equal percentage is the single most useful property of the calculation. The percentage a set of potential shares takes out is fixed by the share arithmetic alone: 25,000 over a count of 4,25,000 is 5.88 per cent, whatever profit sits on top. Change the profit and the paise change; the percentage does not move at all. Notice too that 25,000 shares over the existing 4,00,000 is 6.25 per cent, a different number. The dilution is measured against the enlarged count and not against the count it started from.

At four settings the calculator above produces the following. With no options at all, both bars end in the same place and the standalone figure is Rs 7.50 twice over. At the reported 25,000, the diluted figure is Rs 7.06 and the gap is 44 paise. At 50,000 shares under option the count reaches 4,50,000 and the diluted figure falls to Rs 6.67, a gap of 83 paise or 11.11 per cent. At 1,00,000 the count reaches 5,00,000 and the figure falls to Rs 6.00, a gap of Rs 1.50 or a full 20 per cent. Switch the picker to the consolidated profit. Every percentage in that list is unchanged and every paise figure grows, the clearest demonstration available that dilution is a property of the count and not of the profit.

How far does the fall go as the option count keeps rising?

Not in a straight line, and the shape is worth seeing once. Each new block of potential shares is divided into a profit that has already been divided among more shares than before, so each block takes less off the figure than the block before it. The first 25,000 shares under option cost 44 paise. The second 25,000 cost 39 paise, taking the figure from Rs 7.06 to Rs 6.67. The third cost 34 paise and the fourth 33 paise, ending at Rs 6.00. Dividing by a larger number always leaves something, so the fall never stops and never reaches zero either.

A curve that flattens as it falls is why a very large grant is a smaller shock per share than the first arithmetic suggests, and why a small grant on a small share count is a bigger one than most readers expect. Look at the two lines in the figure below and notice they never touch: the vertical distance between them at any point is the whole of the difference between the standalone profit and the profit attributable to the owners, spread over whatever count sits underneath. The numerators differ by Rs 7,00,000 all the way along, so at no option count does the standalone line reach the consolidated one.

How does a reader actually use the two figures?

Nobody computes this for the pleasure of computing it. Four kinds of reader pick a per-share figure off a set of accounts, and each of them has a reason for picking one of the four rather than another. None of those reasons is that one figure is more accurate. All four are correct and answer different questions, and picking the wrong one answers a question that was not asked.

Somebody buying shares plans on the diluted figure. The count they will be sharing with is the count that includes the option shares, and those shares arrive without their permission. Suppose a cousin of Anjani Kulkarni is offered a parcel of shares in the business. The basic consolidated figure of Rs 9.25 describes a share of profit that assumes Meera Rao never exercises. The diluted figure of Rs 8.71 describes the share of profit that survives if she does. Since the decision belongs to Meera Rao and not to the buyer, the buyer plans on Rs 8.71 and treats the 54 paise as something they may get back rather than something they are entitled to. The same reasoning is why the two figures always appear together: printing only the higher one would hide a claim that already exists.

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