Accretion and Dilution: Whether a Deal Adds to Earnings

Accretion and dilution measure one thing: what a deal does to the buyer's earnings per share. Mahasagar Industrial Group Limited, invented, buying Sankalp Industrial Systems Limited, invented, at Rs 115.00 a share lifts earnings per share by 3.74 per cent if it issues shares and cuts them by 1.73 per cent if it borrows. Same business, same price, opposite signs.

Opposite signs from one price are not a paradox and not a trick of presentation. The pair falls out of the shape of the measure. Earnings per share is a fraction, and a transaction pushes on both halves of it at the same time. The sign is decided by whichever half moves proportionately more. The sign therefore turns on the price paid against the funding cost, and not on the quality of the target. Nothing inside the fraction knows what the business is worth, and no amount of care with the arithmetic can put it in.

Accretion vs Dilution: what is moving, and whose number is it?

Start with the smallest possible version of the idea, away from any company. A household of four people lives on Rs 40,000 a month, so income per head is Rs 10,000. A fifth person moves in and starts contributing. If what they bring is Rs 12,000, the pot becomes Rs 52,000 across five heads and income per head rises to Rs 10,400. If what they bring is Rs 8,000, the pot becomes Rs 48,000 across five heads and income per head falls to Rs 9,600. The newcomer is the same person in both stories, working just as hard. Their contribution beat the Rs 10,000 the household was already running at, or it did not, and that alone decided the direction.

Accretion is a rise in the acquirer's earnings per share caused by the deal, and dilution is a fall in it, and both are measured on the buyer's own number rather than on anything belonging to the target. The comparison is always the same shape: the buyer's earnings per share as things stand, set against the buyer's earnings per share once the transaction has been put through the accounts. If the second number is higher, the deal is accretive. If it is lower, the deal is dilutive. If the two are identical the deal is earnings neutral. Earnings neutral is a real and useful answer, not a failure to reach one.

Three things follow from that definition that people routinely get wrong, and it is worth nailing all three down now. The target has an earnings per share of its own, and it plays no part: it disappears at completion because the target stops being a separately owned thing. The combined company's revenue, its assets, its headcount and its market position all change, and none of them is being measured either. And the word measures a movement, never a level: a deal that leaves earnings per share at Rs 10.37 is accretive if the buyer was on Rs 10.00 and dilutive if the buyer was on Rs 10.50.

Which three inputs decide the sign, and how many are about the target?

Once the fraction is in view, the list of things that can move it is short. Only three inputs matter, and it is worth counting how many of them describe the business being bought.

The first is the earnings the buyer actually acquires. The second is the price, and the price sets how much funding has to be raised. The third is the form of that funding, meaning whether the buyer hands over its own shares or hands over cash it has borrowed. Exactly one of those three inputs is a fact about the target, and even that one is an accounting line rather than a judgement about the business. The other two sit entirely on the buyer's side of the table, and one of them is a decision the buyer's treasury team makes.

The whole subject usually goes wrong at this point. A test that produces a plus or a minus feels as though it must be saying something about whether the acquisition was a good idea. It is not. The plus or the minus reports an arithmetic relationship between a price, a funding cost and a share count.

Which earnings are actually being bought, and which line gets missed?

Take the target's earnings apart line by line. The row that decides the answer sits right at the bottom, and readers rarely stay with it that far. Sankalp Industrial Systems Limited closed its base year with earnings before interest and tax of Rs 2,40,00,00,000. Its own borrowings cost it Rs 48,00,00,000 of interest, leaving profit before taxThe line reached once every cost including interest has been charged, but before the tax charge itself has been taken off. of Rs 1,92,00,00,000. A charge of Rs 48,00,00,000 then comes off at a rate of 25.0 per cent. The 25.0 per cent is assumed by this case and matches no published rate. Profit after tax lands at Rs 1,44,00,00,000.

Most people stop there and should not. Sankalp holds three quarters of Sankalp Coatings Private Limited, invented, and that subsidiary is fully consolidatedWhere a parent adds a subsidiary's whole revenue, cost and profit into its own statements line by line, even when it holds less than all of the subsidiary.. Every rupee the subsidiary earns is already sitting inside that Rs 1,44,00,00,000, and a quarter of Sankalp Coatings Private Limited sits with holders who are no part of the group at all. Their slice comes to Rs 6,00,00,000 a year. The outside quarter is not the buyer's to collect, it does not transfer when the parent's shares change hands, and it has no business being in the calculation.

The figure that belongs in an accretion test is the profit attributable to the owners of the parent, Rs 1,38,00,00,000, and not the group's profit after tax of Rs 1,44,00,00,000. On the target's 20,00,00,000 shares that is earnings per share of Rs 6.90. Using the wrong line credits the buyer with Rs 6,00,00,000 a year it will never see. The overstatement runs to 4.35 per cent of what is being bought, and it drags the multiple paid down from 16.67 times to 15.97 times. Neither error is large enough to look like an error, and that is what makes both dangerous.

What do 11,50,00,000 new shares actually do to the buyer?

Now put a buyer on the other side. Mahasagar Industrial Group Limited is listed. The buyer has 50,00,00,000 shares trading at Rs 200.00, and its market capitalisationThe share count multiplied by the traded share price. The market puts that figure on the whole of a company's equity on the day. is Rs 1,00,00,00,00,000. Mahasagar earns Rs 5,00,00,00,000 after tax, so its earnings per share is Rs 10.00 and its shares change hands at 20.00 times that.

The indicative offer for the whole of Sankalp is Rs 115.00 a share. Across 20,00,00,000 shares that is Rs 23,00,00,00,000 for the equity, and against attributable earnings per share of Rs 6.90 it is a multiple paid of 16.67 times.

Fund it entirely by issuing Mahasagar's own shares and the arithmetic is short. Rs 23,00,00,00,000 raised at Rs 200.00 a share is 11,50,00,000 new shares, exactly, with nothing left over. The share countHow many shares a company has in issue at a given moment. Put more into issue and every existing holder's slice of the same profit gets thinner. goes from 50,00,00,000 to 61,50,00,000. Combined profit, with no savings assumed anywhere, is Rs 5,00,00,00,000 plus Rs 1,38,00,00,000, being Rs 6,38,00,00,000. Divide and the answer is Rs 10.3740 a share against Rs 10.00 before, an accretion of 3.74 per cent.

Two growth rates make up the 3.74 per cent, so look at the growth rates rather than at the accretion figure. The profit pool grew by 27.60 per cent and the share count grew by 23.00 per cent, and the gap between those two percentages is the whole of the 3.74 per cent. Another way to see the same thing: the 11,50,00,000 new shares would each need to earn the old Rs 10.00 for earnings per share to stand still, which is Rs 1,15,00,00,000 of earnings they have to carry. Sankalp delivers Rs 1,38,00,00,000. The surplus of Rs 23,00,00,000 spread over the enlarged 61,50,00,000 shares is Rs 0.3740 a share, and there is the accretion, arrived at from a completely different direction.

What does borrowing really cost once the tax deduction is allowed for?

Change nothing about the target and nothing about the price. Mahasagar now borrows the Rs 23,00,00,00,000 instead, at a pre-tax cost of 8.50 per cent. The interest bill is Rs 1,95,50,00,000 a year.

The interest is not what reaches earnings, though, and this is the step readers most often drop. Interest reduces taxable profit, and a quarter of the charge comes back through a smaller tax bill, so what actually lands on the bottom line is the remaining three quarters: Rs 1,46,62,50,000. Combined profit becomes Rs 5,00,00,00,000 plus Rs 1,38,00,00,000 less Rs 1,46,62,50,000, being Rs 4,91,37,50,000. Nothing was issued, so the divisor is still 50,00,00,000 shares. Earnings per share is Rs 9.8275, against Rs 10.00 before, a dilution of 1.73 per cent.

The cash route pays for the deal above the line while the share route pays for it below the line, and that single structural difference is why one price can produce two answers with opposite signs. Notice also what the cash route does not do: it adds no shares at all, so every rupee of the target's earnings that survives the interest charge is spread over the same 50,00,00,000 holders as before. Cash deals therefore look wonderful when borrowing is cheap and turn ugly quickly when it is not.

Skipping the tax deduction is an expensive slip. Charge the full Rs 1,95,50,00,000 against profit and earnings per share reads Rs 8.85, a dilution of 11.50 per cent rather than 1.73 per cent. The gap between 1.73 and 11.50 separates a deal a board treats as marginal from one it treats as unaffordable, and a single missing multiplication opens it.

What do the two routes look like side by side at one price?

With the two routes in adjacent columns, the whole comparison is visible at once. Every row above the funding line is identical. The target is the same target, the price is the same Rs 115.00, the earnings acquired are the same Rs 1,38,00,00,000. Only the funding row differs, and only the funding row has to differ for the sign to flip.

At what borrowing cost does the cash route stop adding to earnings?

The cash route dilutes at 8.50 per cent. The same route would obviously accrete at a low enough rate. Somewhere between the two there is a rate at which it does neither, and finding it takes one line of algebra rather than a search.

Set the after-tax interest equal to the earnings acquired. At that point the numerator has gained exactly as much as it has lost, and the denominator has not moved at all. Interest on Rs 23,00,00,00,000 at 8.00 per cent runs to Rs 1,84,00,00,000, and once the tax deduction has done its work Rs 1,38,00,00,000 remains. Sankalp contributes precisely that. The breakeven borrowing cost is exactly 8.00 per cent, and the 8.50 per cent this deal was priced at sits fifty basis pointsA hundredth of one percentage point each. Rates get quoted this way so that a move from 8.00 to 8.50 is a clean fifty rather than a decimal argument. above it.

The fifty basis points are worth pricing on their own, and they turn out to be the whole story. Rs 23,00,00,00,000 at half a percentage point is Rs 11,50,00,000 of extra interest, or Rs 8,62,50,000 after tax. Spread over 50,00,00,000 shares that is Rs 0.1725 a share, or 1.725 per cent of Rs 10.00. The entire dilution on the cash route is fifty basis points of borrowing cost, and none of it is a statement about Sankalp.

Why does the printed column of changes not step evenly?

Run across a ladder of borrowing costs, the same arithmetic throws up something odd in the printed figures. Each fifty basis points costs exactly Rs 8,62,50,000 after tax. On 50,00,00,000 shares that is exactly Rs 0.1725 a share, and exactly 1.725 percentage points of earnings per share. The underlying step never varies. Yet subtracting one printed cell from the printed cell above it gives 1.72 at some rungs and 1.73 at others.

The unevenness is entirely a printing effect. Two decimals get applied to every cell separately, and only afterwards does anybody subtract, so a constant underlying difference does not survive. The rungs that print 1.73 are 6.50 to 7.00, 7.50 to 8.00, 8.00 to 8.50, 9.00 to 9.50 and 10.00 to 10.50. The rungs that print 1.72 are 6.00 to 6.50, 7.00 to 7.50, 8.50 to 9.00, 9.50 to 10.00 and 10.50 to 11.00. Five each, alternating almost but not quite regularly. The only place the pattern doubles back is either side of the crossing at 8.00.

The rounding is not a small point of housekeeping. A difference should always be computed from the unrounded figures and rounded once, never computed by subtracting two figures that have already been rounded. A reader who takes the printed column at face value will conclude that the relationship bends, and it is dead straight.

What single condition settles the sign of a share-funded deal?

Go back to the share route and ask what decides its sign in general, not just in this case. Write out the pro forma earnings per share, insist that it beat the old one, and cancel what cancels. The surviving condition is startlingly bare.

Read the condition as a swap rather than as algebra and it stops feeling like a coincidence. Mahasagar is handing over paper that the market prices at 20.00 times its earnings, and receiving earnings priced at 16.67 times. Mahasagar gives up less earnings per share than it collects, so its own per share figure has to rise. Turn the two multiples around and the trade runs the other way, and the deal dilutes, whatever either business happens to be like.

Be precise about what the condition settles and what it leaves open: the two multiples decide the sign, and they do not decide the size. The size also depends on how large the purchase is relative to the buyer. Hold both multiples exactly where they are and double the size of the target, and the accretion grows well past 3.74 per cent. The same proportional advantage is being applied to a bigger slice of the buyer. Any statement that a given pair of multiples always produces a given percentage is wrong, and it is a common thing to say.

Three conditions have to be held still for the rule to hold at all, and every one of them is regularly broken in practice. No savings are assumed. A large enough saving turns a dilutive share deal accretive on its own. The acquirer's share price is assumed not to move on the announcement, and that assumption fixes how many shares the purchase costs. And there is assumed to be nothing else in the consideration, no deferred slice and no cash top-up. All three conditions are named whenever the rule is used.

What do expected cost savings do, and what gets to them first?

Deals are rarely presented without a claimed saving, and this one is no exception. The case assumes Rs 45,00,00,000 a year, pre-tax, from combined buying and a shared administrative function, fully in place by the second year. Two businesses that each run a payroll team, a ledger team and a purchasing desk can plausibly run one of each instead, and buying steel through one order rather than two plausibly costs less per tonne.

The trap is not in the saving itself. The trap is in carrying the saving straight to earnings per share. A rupee saved raises taxable profit exactly as a rupee earned does, so a claimed pre-tax shared service centreOne combined back office running the payroll, ledgers and administration that two separate companies would otherwise each staff and each pay for. saving reaches the per share line only after tax has taken its quarter. Rs 45,00,00,000 becomes Rs 33,75,00,000. Using the untaxed figure overstates the effect by a third. A third is not a rounding slip.

The taxed figure does something drastic to the cash route. Combined profit goes from Rs 4,91,37,50,000 to Rs 5,25,12,50,000, earnings per share goes from Rs 9.8275 to Rs 10.5025, and the answer moves from 1.73 per cent dilutive to 5.03 per cent accretive. The sign turned over. Nothing about the target changed, nothing about the price changed and nothing about the borrowing changed; a single assumed line did all of it. A claimed saving therefore deserves more scrutiny than any other input in the model, and the size of the claim needed to flip a sign is worth computing and stating.

What warning has to travel with every accretion figure?