Share Buybacks: The Mechanics and What They Signal

A share buyback is a company buying its own shares with its own cash, so the count in issue falls. Sankalp Industrial Systems Limited, invented, bought 75,00,000 shares at Rs 80.00 for Rs 60,00,00,000, taking the count from 20,75,00,000 to 20,00,00,000. On the share count alone that lifts earnings per share by exactly 3.75 per cent. Net off the cash it spent and the honest figure is 1.76 per cent.

The shape of this is easier to see at a small size. Start with a bakery on a street corner. Four people put money into it years ago and each holds a quarter of it. The bakery has Rs 8,00,000 sitting in its current account doing nothing much. One of the four wants out. So the bakery itself buys her quarter for Rs 8,00,000, and now there are three holders instead of four, and the cash is gone.

Ask what changed and two answers appear, and only one of them is the interesting one. The obvious answer is that each remaining holder went from a quarter to a third of the bakery, and that sounds like a gain. The less obvious answer is that the bakery they now hold a third of is a bakery with Rs 8,00,000 less in the bank than the bakery they held a quarter of. Every buyback is a trade of a smaller number of holders against a smaller company, and the whole of the arithmetic in this guide is about counting both halves of that trade instead of one.

The trade between fewer holders and a smaller company is the entire subject. The same trade appears below at a scale with more commas in it, worked to the rupee on an invented listed company. Then comes the one step most write-ups of a buyback skip. The cash goes back into the calculation, and the improvement that survives gets counted.

What actually happens to the shares a company buys back?

In a share buybackA company purchasing its own shares, which returns cash to the holders who sell. the company itself is the buyer and its own holders are the sellers. Cash moves from the company to the holders who sold. The shares move the other way, from those holders back to the company that issued them in the first place.

Then something happens that has no equivalent in an ordinary trade between two investors. Holding its own shares as an asset would make a company partly a holder of itself, and every number built on the share count would start counting the same rupee twice. No company can sensibly do that. So in the ordinary case the shares bought are cancelled. The bought shares stop existing. The company does not resell them, does not keep them in a drawer, and does not bring them back.

So the share countThe number of shares in issue, which falls when bought shares are cancelled. falls permanently. Every per share figure the company reports afterwards is divided by a smaller number than before. A buyback is the only routine corporate action whose direct effect is to shrink the denominator of every per share figure the company will ever publish again. A dividend leaves the count exactly where it was. A buyback does not.

Watch what that does to the headline numbers. Earnings per shareProfit attributable to owners divided by the share count. is profit attributable to owners divided by the share count, so a smaller count raises it if profit holds still. Net assets per share works the same way and moves in the same direction. Neither of those movements required the business to sell one extra valve, win one extra customer or improve one margin by one basis point. The movement is division.

The phrase if profit holds still is doing more work in that sentence than it looks. The condition is the hinge the rest of the argument turns on, and it is almost never examined.

What are the three things that move at once?

Three things move on the day a buyback settles, and they move together rather than one after another. The standard calculation names one of the three. Naming all three is the whole discipline.

The first is that cash leaves. Sankalp Industrial Systems Limited, invented, paid Rs 60,00,00,000 to the holders who sold, and that Rs 60,00,00,000 left the company's bank account and did not come back. The company after the transaction is a company with Rs 60,00,00,000 less inside it. Nothing about that is subtle, and it is still the movement people forget.

The second is that the share count falls. Rs 60,00,00,000 at Rs 80.00 a share bought 75,00,000 shares, and cancelling them took the count from 20,75,00,000 to 20,00,00,000. The arithmetic of a per share figure puts the falling count in plain view. Everybody sees this movement.

The third is the one nobody writes down. The Rs 60,00,00,000 was doing something before it was spent. Money inside a company is not inert. The money sits on deposit and earns, or funds working capital, or waits to fund a machine. Whatever it was earning, it stops earning it the moment it is paid out, and that lost earning is a real reduction in next year's profit. A buyback removes shares from the denominator and it removes earnings from the numerator, and a calculation that changes only the denominator has silently decided the second removal was nil.

The everyday version of the omission is easier to feel than the corporate one. A household has Rs 5,00,000 in a deposit and a loan on which it pays interest. The household uses the deposit to clear part of the loan. The monthly outgoing on the loan drops. The drop feels like a gain, and somebody says the household is Rs 4,000 a month better off. Then somebody else asks what the deposit was paying, and the answer is that it was paying interest too, so the honest improvement is the difference between the two rates rather than the whole of the loan rate. Nobody in that conversation did bad arithmetic. One of them just stopped counting a line early.

What did this invented company buy, and for how much?

Everything from here runs on one transaction at one invented company, and it is worth writing the transaction out before doing anything clever with it. Sankalp Industrial Systems Limited, invented, is a listed manufacturer of industrial valves, precision castings and the aftermarket parts and service that go with them.

At the end of year minus 2, counting back from the base year, it bought 75,00,000 of its own shares at Rs 80.00 each. Cash out was Rs 60,00,00,000. The 75,00,000 shares were cancelled, so the count in issue went from 20,75,00,000 to 20,00,00,000 and has stayed there through year minus 1 and the base year. Four figures describe the whole transaction, and every calculation that follows is built out of those four and nothing else.

Two more figures come from the same locked record and both are needed. The base year is the last completed year, and profit attributable to owners in it was Rs 1,38,00,00,000. Profit attributable to owners is profit after tax after taking out the Rs 6,00,00,000 that belongs to the minority holders of the subsidiary, Sankalp Coatings Private Limited, invented, and it is the number that belongs to the holders of the parent. Divided by the 20,00,00,000 shares now in issue it gives earnings per share of Rs 6.90.

One thing on that table deserves a second look. The price paid was Rs 80.00 a share and the share is priced at Rs 90.00 in the base year. The two prices do two different jobs, both are locked in this invented record, and confusing them will put every breakeven figure that follows wrong by a wide margin. The price that matters for a buyback is the price the buyback actually paid.

Why is the naive effect exactly 3.75 per cent rather than approximately?

Here is the calculation almost everybody runs, and it is worth naming it before criticising it. Take the profit the company actually reported. Divide it by the count that would have been outstanding if the buyback had never happened. Compare that against the earnings per share actually reported. The difference is what the buyback did. Call it the naive effectThe change in earnings per share computed from the lower share count alone., not because the person running it is naive but because it takes exactly one of the three movements at face value and asks nothing further.

Run it. Rs 1,38,00,00,000 over 20,00,00,000 shares is Rs 6.90, the figure the company reported. Rs 1,38,00,00,000 over the 20,75,00,000 shares that would otherwise have been in issue is Rs 6.6506. Rs 6.90 against Rs 6.6506 is a rise of 3.75 per cent.

Now the part that is genuinely elegant, and it is worth pausing on because it explains why that figure is exact rather than rounded. Both earnings per share figures have the same numerator. Dividing one by the other cancels the Rs 1,38,00,00,000 completely, and what is left is nothing but the ratio of the two share counts, the other way up. 20,75,00,000 divided by 20,00,00,000 is 1.0375, exactly, with no decimals hiding behind it. The naive effect of any buyback is nothing but the ratio of the old share count to the new one, so it does not depend on the profit figure at all and it is exact whenever that ratio is.

Test the claim by breaking it. Suppose profit had been Rs 2,00,00,00,000 instead. Then earnings per share would have been Rs 10.00 on the new count and Rs 9.6386 on the old one, and Rs 10.00 against Rs 9.6386 is a rise of 3.75 per cent. Same answer. Suppose profit had been Rs 50,00,00,000. Rs 2.50 against Rs 2.4096 is a rise of 3.75 per cent. Same answer again. The profit figure is scenery.

The cancelling of the profit figure says something about the calculation. A number that does not move when profit moves is not measuring anything about the business. The naive effect measures the size of the buyback relative to the company. The same 3.75 per cent would come out if the company had earned nothing at all that year, and a 3.75 per cent rise in a loss is not an improvement in anybody's language.

What was the cash doing before it was spent?

The naive calculation never asks what the cash was doing, and asking it is the whole of the method. Rs 60,00,00,000 sat inside Sankalp Industrial Systems Limited, invented, until the day it did not. The money was not sitting in a sack. Wherever it was, it was earning something.

The record this guide works from assumes that cash held by this invented company earns 6.00 per cent a year before tax. The 6.00 per cent is an assumption of the invented record, labelled as one every time it appears. The rate is not a market rate, not a rate any reader can go and get, and not a fact about deposits in India. The number was chosen so the arithmetic can be followed. The whole of the honest calculation moves when the assumed return moves, and the controls below let it move.

So the forgone returnWhat the cash used for the buyback would have earned had it stayed in the company. is Rs 60,00,00,000 at 6.00 per cent, or Rs 3,60,00,000 a year before tax. But profit attributable to owners is an after-taxA figure stated after the company's own assumed effective tax rate of 25.0 per cent has been applied. figure, so the comparison has to be made after tax as well. This company's own effective rate of 25.0 per cent is again an assumption of the invented record rather than any statutory rate. At that rate, Rs 3,60,00,000 before tax is Rs 2,70,00,000 after it.

Rs 2,70,00,000 a year is what the buyback cost the profit line. An account records what happened rather than what stopped happening, so the cost appears in no line of any account. There is no entry anywhere in the financial statements headed interest no longer earned. The cash left, the interest line got smaller, and the two events sit a year apart in most people's reading.

Think about how ordinary that omission is. A shopkeeper who spends the cash box on a new shutter does not book a loss for the interest the cash box was making. He notices a nicer shutter. The interest was small, it arrived quietly, and its absence arrives even more quietly. Companies are the same at four more zeroes.

What is the honest effect, worked line by line?

The repair is one line long and it is entirely mechanical. Before the division by the smaller share count, profit takes back what the spent cash would have earned, and the comparison is made against that. Everything else about the calculation stays where it was. The result is the honest effectThe same change once the return the spent cash would have earned is taken out of profit., and four lines do the work.

Look at what moved between the two calculations. The naive one compared Rs 6.90 against Rs 6.6506. The honest one compares Rs 6.90 against Rs 6.7807. The number being reported did not change at all. The whole of the difference between 3.75 per cent and 1.76 per cent lies in the counterfactual, in the claim about what the company would have reported had it not done the buyback, and that is a claim about the world rather than an arithmetic step.

The counterfactual is why the honest figure is a judgement and the naive one only pretends not to be. Both calculations rest on an assumption about what the Rs 60,00,00,000 would have earned. The honest one says 6.00 per cent before tax and states the assumption openly. The naive one says nil and states nothing. The assumption is embedded in the act of leaving the numerator alone. The naive calculation is not assumption-free; it is the assumption that the cash was worth nothing, wearing the clothes of a simple division.

How far apart are 3.75 and 1.76, and which one gets printed?

Put the two figures beside each other and the gap is 1.99 points on a headline of 3.75. More than half of the reported improvement in earnings per share, about 53 per cent of it, is not the buyback at all; it is the unexamined assumption that the Rs 60,00,00,000 was earning nothing. Only about 47 per cent of the headline, being the 1.76 points, survives once the cash is counted.

The two figures are not rivals but one subtraction. Both are the same calculation, with one line added. Starting at 3.75 points and taking away the 1.99 points that come from assuming the cash was idle leaves 1.76 points. There is no third figure and no room for argument about which is right; there is only a question about what the cash would have earned, and the assumption made here is stated out loud.

Now the same thing in rupees rather than in percentages. The rupee view carries a warning the percentage view hides. The three earnings per share figures in play are Rs 6.6506, Rs 6.7807 and Rs 6.90. The whole argument of this guide lives inside a span of Rs 0.2494 on a figure of Rs 6.90. The span is under four per cent of the number, and drawn on a scale starting at nil the three points would show as a single dot.

An argument whose entire claim is that one number overstates another has an obligation not to overstate the difference itself. So the scale below starts at Rs 6.60 rather than at nil, and says so on its own face. Read the positions as relative, not as sizes.

Which of the two percentages gets printed in practice? The larger one, almost always, and usually with no intention to mislead at all. A company preparing a note on its own buyback runs the calculation everybody runs, gets 3.75 per cent, and prints it. The alternative requires an explicit statement about what the cash would have earned, and somebody has to defend that statement. The 3.75 per cent looks like a fact, so it requires defending nothing. An account that prints 3.75 per cent alone has printed the number a company would print, and the only defence against that is to print both and say which is which.

At what return would the buyback have changed nothing at all?

Now for the part that turns this from a story about one transaction into something that carries to any transaction. The honest effect depends on what the cash would have earned. At an assumed return of nil it is 3.75 per cent. At an assumed 6.00 per cent before tax it is 1.76 per cent. As the assumed return is pushed higher the effect keeps shrinking, and at some particular rate it must hit exactly zero.

For this transaction that rate is 11.50 per cent before tax, and the check is quick. Rs 60,00,00,000 at 11.50 per cent is Rs 6,90,00,000 before tax, and at the assumed 25.0 per cent rate that is Rs 5,17,50,000 after it. Added to Rs 1,38,00,00,000, profit without the buyback would have been Rs 1,43,17,50,000. Divided by 20,75,00,000 shares that is Rs 6.900000, the same figure to six decimal places that the buyback actually produced. The effect is nil.

One closed form removes the need to solve for that rate ever again, and it is worth memorising. The breakeven pre-tax return is the earnings yield at the price the buyback paid, divided by one less the tax rate. Earnings per share of Rs 6.90 over a buyback price of Rs 80.00 is 8.625 per cent. Divided by 0.75 that is 11.50 per cent, exactly. Two divisions, no algebra, and it works on any buyback.

Why does the tax rate appear at all? Because the two things being compared sit on opposite sides of the tax line. Earnings per share is an after-tax figure, so the earnings yield is an after-tax yield. The return the cash would have earned is quoted before tax. Grossing the earnings yield up by one less the tax rate puts both on the same footing, and once they are on the same footing the comparison is a straight one.

Read the closed form again and notice what is in it and what is not. The closed form contains earnings per share and the price paid. Absent are the size of the buyback, the number of shares, the profit total and anything about the business at all. The line that decides whether a buyback lifts or lowers earnings per share moves with the price paid and with nothing else, so the same company doing the same buyback at a different price crosses the line at a different rate. Buy below the line and earnings per share rises; buy above it and earnings per share falls.

Why is that 11.50 per cent not a rule for deciding anything?

The 11.50 per cent is a breakeven for one thing only, the arithmetic of earnings per share. The rate is not a hurdle, not a test, not a threshold and not a decision rule. Earnings per share is not value, and a transaction can lift earnings per share while making the company worth less.

Two other figures in this same invented record make the identical point from two other directions, and it is worth naming both in one line each so the pattern is visible rather than asserted. First, an acquisition: the invented acquirer Mahasagar Industrial Group Limited paying Rs 115.00 a share for this company entirely in its own shares would lift its own earnings per share by 3.74 per cent with no synergies whatever, purely because the multiple it pays is below the multiple it trades on, and nothing about that arithmetic says the deal created anything. Second, leverage: on the modelled figures in this record, firm value peaks at a 40.0 per cent debt share. Earnings per share there would be Rs 6.8250, below today's Rs 6.90, so the value-maximising financing move is the one that lowers earnings per share.

Three separate transactions, three directions, one conclusion. A per share earnings figure can be pushed around by the share count, by the funding mix and by the price paid in a transaction, none of which is the business getting better or worse. Anything that can be moved by arithmetic alone cannot be the quantity the measurement was after. The effect can be computed correctly and still settle nothing, because the effect on earnings per share is not the question.

What happens to both effects as the buyback gets bigger?

Everything so far has been one transaction at one size. Now hold the price at Rs 80.00, hold the profit at Rs 1,38,00,00,000, hold the assumed return on cash at 6.00 per cent before tax, and vary only how much the company spends. Both effects rise, as anybody would predict. The interesting part is what happens to the distance between them.

At Rs 20,00,00,000 the company would buy 25,00,000 shares, the count would fall to 20,50,00,000, the naive effect reads 1.22 per cent and the honest one 0.56 per cent. The gap is 0.66 points. At Rs 1,00,00,00,000 it would buy 1,25,00,000 shares, the count would fall to 19,50,00,000, the naive effect reads 6.41 per cent and the honest one 3.05 per cent. The gap is 3.36 points.

The gap widens with the size of the buyback. Intuition says the opposite, that a bigger transaction is harder to overstate. It widens for a plain reason: the more cash is spent, the more return is given up, and the return given up is the entire content of the correction. Doubling the spend doubles the forgone earnings while the share count effect grows only a little faster than in proportion. So the larger the buyback, the more flattering the headline figure becomes.

What does a buyback state about the company that did it?

Now leave the arithmetic and ask the other half of the question, the half about what the action itself communicates. Most writing about buybacks stops being description at this point and starts being flattery. The discipline is to say only what the transaction structurally establishes.

A buyback establishes something narrow. On the day it happened, the company had cash it was not putting to work inside the business at the return it wants from a rupee, and it chose to send that cash to holders through the share register rather than through the dividend line. A buyback states that a specific quantity of cash was not deployed inside the business, and it states the price at which the board was willing to buy the company's own shares. Both of those are facts about the transaction rather than opinions about the future.

The second half of that sentence carries more than it looks. A board that buys at Rs 80.00 a share has made a decision at Rs 80.00 a share, and any reader can compute what that price implies using the closed form given above. Computing that implication uses the information rather than reading anybody's mind. It is a statement about the arithmetic of the transaction, not about what anybody believed.

Here is what a buyback does not establish, and each of these gets asserted routinely. A buyback does not establish that the board thinks the shares are worth more than the price it paid. A board may be doing many things at once, and intent cannot be read from a transaction. Nor does a buyback establish anything about next year's profit. Nothing in the mechanics touches the business, so nothing establishes that the business improved. And it establishes nothing about what any share is worth.

Nothing about a market reaction is recorded in this invented case, so the market's response to this buyback is unknown.

What does a buyback not commit the company to?

Commitment is the structural difference between the two routes cash can take back to holders, and commitment is why a board has a genuine choice rather than a preference. A buyback happens and is finished. Rs 60,00,00,000 went out, 75,00,000 shares were cancelled, and the following year begins with the company owing nobody a repeat.

Now imagine the same Rs 60,00,00,000 going out as a rise in the regular dividend instead. The cash movement in that year is identical to the rupee. The next year is not identical. A regular dividend is read as a level, so a company that raised it to a new level will be measured against that level next year, and cutting back to where it was is a visible event that requires explaining. The same rupees leaving by the two routes create completely different obligations for the year after, and that difference in commitment, not the arithmetic, is usually what a board is actually choosing between.

The household version is immediate. Handing a parent Rs 50,000 once because a good year happened is one thing. Setting up a standing instruction for Rs 4,167 a month is a different thing, made of the same rupees, and everybody in that house knows the second one is a promise and the first one is not. Stopping the standing instruction is a conversation. Not repeating the one-off is not.

Two more differences follow from the mechanics rather than from the commitment. First, a dividend reaches every holder in proportion to what they hold, wanted or not. A buyback reaches only those holders who chose to sell into it. Second, a dividend leaves the share count exactly where it was, so every per share figure afterwards is divided by the same number. A buyback permanently lowers the count.

What conditions attach to a buyback, and who sets them?

Every reader who reaches this point wants a number. How much may a company buy back. Who has to approve it. How often may it be repeated. How is the money treated for tax when it reaches the person who sold. Every one of those is the right question, and the answers lie outside the arithmetic.

All of those conditions are set by law and by the authorities that administer it, not by the arithmetic. The conditions are written down, they are public, and they change. A threshold printed in a teaching text becomes wrong on a day nobody records, and a reader has no way of detecting that it went wrong. A plausible wrong number is more damaging than no number at all.

Every question about a buyback sorts into one of two piles. If the question is arithmetic, it has one answer and it does not change with the year: how many shares Rs 60,00,00,000 buys at Rs 80.00, what the count becomes, what earnings per share does both ways, and at what assumed return the effect is nil. If the question is a condition, it has an answer that is current rather than permanent, and only the current text of it is of any use.

What does a lender, an analyst or a household actually do with this?

Three readers pick up the same buyback and want three different things from it, and the arithmetic in this guide serves all three differently. The calculation is the same for all three and the use is not, so each one is worth walking.

A lender reads a buyback as cash that has left and is not coming back. The lender's reading is the plainest of the three and the least interested in earnings per share. Rs 60,00,00,000 of cash went out of Sankalp Industrial Systems Limited, invented, and the assets standing behind the lender's claim are Rs 60,00,00,000 smaller for it. The Rs 6,00,00,000 of gross debt this invented company carries did not change at all. A lender's question is therefore not what happened to a per share figure; it is what the cushion looked like before and after, and whether anything in the loan documentation had something to say about a distribution of that size. Every buyback is a transfer from the claim that sits behind to the claim that sits in front.

An analyst reads it as a correction to make before comparing anything. Two things need fixing. First, part of the growth in earnings per share across the buyback year is the denominator moving, so that growth rate is contaminated. The honest way to see the business is to look at profit rather than profit per share across that boundary. Second, any comparison against a company that did not buy back is a comparison of two things measured differently. The analyst's job is to compute both the 3.75 and the 1.76, state which assumption produced the second, and put the assumption in the note rather than in the footnote.

A household that holds shares in a company that has bought back reads it as a change in what it holds rather than as cash received, and this is the reading most likely to go wrong. A holder who did not sell into the buyback received nothing. The holding is now a slightly larger fraction of a company that has slightly less cash in it. The change is not a gain and not a loss on the face of it. It is a change in the shape of what is held, and any statement about whether the holder ended up better off requires a view about value.

The same four figures serve a lender asking about the cushion, an analyst asking whether a growth rate is real, and a holder asking what changed, and none of the three needs to know what anybody intended.