How to Analyse Accretion and Dilution, Step by Step

Seven steps, in this order: take the target attributable earnings, fix the price, choose the consideration mix, cost the shares, cost the borrowing, tax and phase any claimed saving, then divide and hunt for both breakevens. On the worked case here the deal is earnings neutral at a pre-tax borrowing cost of exactly 8.00 per cent and at 72.73 per cent cash.

Every input into this test can be got wrong while the output still looks entirely reasonable, and the order of the steps is the defence against it. Taking the minority out late makes the multiple recorded against the price wrong before anything else happens. Putting the borrowing cost in before tax makes the reported dilution several times the honest figure. Adding a claimed saving before taxing it can turn the sign of the answer over on nothing at all. None of this is ritual: each step is here because the step behind it cannot be trusted until this one has been done.

Think of a household that runs a sweet shop and has the chance to buy the shop next door. Pay for it out of savings, and the same people share the profit of a bigger business, but the interest those savings were earning has gone. Bring in a cousin who puts up the money in exchange for a stake, and no savings are touched, but the profit of the bigger business is now split more ways. Same purchase, same price, two completely different effects on what each existing owner takes home. Paying out of savings and paying with a stake are the whole of what this test measures, and the seven steps are how it is measured without self-deception.

Step 1. Which earnings are actually being bought?

Start at the bottom of the target’s profit and loss account, then keep going. Sankalp Industrial Systems Limited, invented, reported operating profit of Rs 2,40,00,00,000 for Year 0, paid interest of Rs 48,00,00,000, and paid tax on the Rs 1,92,00,00,000 that was left at the 25.0 per cent effective rate assumed throughout. Group profit after tax comes to Rs 1,44,00,00,000. Rs 6,00,00,000 of that group profit belongs to somebody else, so Rs 1,44,00,00,000 is not the figure being bought.

Sankalp does not hold all of Sankalp Coatings Private Limited, invented, and the slice of Sankalp Coatings profit that belongs to the outside holders never reaches the parent shareholders. Strip it out and what remains is Rs 1,38,00,00,000 belonging to the parent owners. Divide by the 20,00,00,000 shares in issue and each one carries Rs 6.90. That Rs 6.90 is the only earnings line the acquirer is buying.

Two figures move when that subtraction is made, not one. The earnings acquired fall from Rs 1,44,00,00,000 to Rs 1,38,00,00,000, a cut of 4.17 per cent. The same Rs 115.00 now buys a smaller number, so the multiple recorded against the offer price moves the other way, from 15.97 times to 16.67 times. Both figures are read by steps that come later, and the check meant to catch a mistake here reads one of them.

Step 2. Which price is under test, and what multiple does it record?

Mahasagar Industrial Group Limited, invented, is offering Rs 115.00 a share for the 20,00,00,000 shares of Sankalp Industrial Systems Limited. The offer comes to Rs 23,00,00,00,000 in total. The price is an input to this test, never an output of it. Nothing in the seven steps decides whether Rs 115.00 is the right number to pay; the steps take the price as given and work out what happens to reported earnings once it is paid.

The one thing step 2 must produce is the multiple, and there is exactly one right way to compute it. Divide the offer price by the earnings figure step 1 produced, and by no other earnings figure. Rs 115.00 over Rs 6.90 gives 16.67 times. Write it down next to the price. The third of the four checks compares it with the multiple the acquirer itself carries, and that check only works if both multiples are built on comparable earnings.

Step 3. How is the consideration mix chosen, and what does the choice assume?

The mix is the split of the Rs 23,00,00,00,000 between cash the sellers receive and new acquirer shares they receive instead. The mix is a real negotiating variable, and it is also the single largest driver of the answer on this deal. Picking one and moving on is not enough. The two ends, all shares and all cash, are run first, before anything in between.

Two assumptions attach to the mix and both belong in the open rather than inside the arithmetic. The first is that the acquirer’s share price used to convert rupees into shares is the right one. The second is that the borrowing needed for the cash half is available at the rate assumed. Neither is a fact about the deal; each is a choice being made, and the reader is entitled to see both. Where a deal is quoted as an exchange ratioA way of quoting share funded consideration as a count of acquirer shares handed over for each share of the company being bought, instead of as a rupee amount. rather than as a rupee amount, that first assumption is still there; it has simply been converted into a ratio before the reader saw it.

Step 4. What does the share half cost?

Costing the share half is division, and the divisor is the acquirer’s own market price. Mahasagar shares are at Rs 200.00, so funding the whole Rs 23,00,00,00,000 in shares takes 11,50,00,000 new shares. The existing count of 50,00,00,000 becomes 61,50,00,000. No interest arises and no tax arises. Every rupee of combined profit is now shared 23 per cent more widely.

One assumption carries this step, and it is stated rather than buried. The share price of the acquirer is taken as Rs 200.00 and is assumed not to move between the announcement and the issue. That is a convenience, and it is the assumption most likely to fail in a real transaction, because an announcement itself moves prices. If the shares were worth less than Rs 200.00 at the moment of issue, more of them would be needed, the count would be higher and the answer would be worse. If they were worth more, fewer would be needed. The arithmetic does not know which; the analyst does, and says so.

Step 5. What does the cash half cost, and why is the tax line not optional?

Costing the cash half is multiplication followed by a subtraction that people forget. Borrowing the full Rs 23,00,00,00,000 at 8.50 per cent before tax runs up interest of Rs 1,95,50,00,000 a year. Interest is deductible against profit, so once the 25.0 per cent effective rate is applied, the amount actually reaching the combined earnings line is Rs 1,46,62,50,000. The figure that belongs in the numerator is the after-tax cost, and putting the pre-tax figure there reports dilution of 11.50 per cent instead of 1.73 per cent.

Two smaller things sit inside this step. The first is drawdownTaking money down off a loan facility that has been agreed but not yet used. A facility can be arranged in one year and drawn in another. timing. A facility arranged in March and drawn in October does not cost a full year of interest in the year it is drawn. A Year 1 answer built on twelve months of interest overstates the cost, and an answer built on the year the deal closes and the year after is not comparing like with like. The second is that the tax rate used here has to be the same rate used in every other line. Mixing a statutory rate into one line and an effective rate into another produces an answer nobody can reconcile, including its author, three weeks later.

Step 6. What becomes of a claimed saving?

Mahasagar has told the market it expects Rs 45,00,00,000 a year of cost savings from procurement and a shared service centre, phased in fully by Year 2. Three things happen to that number before it is allowed near the earnings line, and they happen in this order. A saved cost lifts taxable profit like any other, so the saving is taxed first. Rs 45,00,00,000 becomes Rs 33,75,00,000. Only the part that has arrived by Year 1 may be carried into a Year 1 answer, so the saving is phased next. And the taxed, phased figure goes on a line of its own.

The separate line is the part that matters most, and it is the part most often skipped. Of all the inputs the seven steps take, a claimed saving is the one most likely to be wrong. It is a forecast made by the party that wants the transaction to happen. An answer that carries the saving buried inside a combined profit figure cannot be re-read without it. An answer that carries it on its own line can be re-read by anybody in four seconds: the line is set to zero and the answer read again. On the all-cash case here, counting the saving lifts earnings per share to Rs 10.5025 and turns 1.73 per cent dilution into 5.03 per cent accretion, so one line decides which of two opposite reports of the same transaction gets filed.

Watch the language too. A saving quoted as a run rateA figure quoted as though it applied to a full year, even though only part of a year has actually been observed. Useful shorthand, and easy to read as more than it is. is a full year figure that may never have been earned for a full year. A run rate belongs in the Year 2 line, not the Year 1 line, unless somebody can show the months.

Step 7. Where does the division happen, and why not stop at the answer?

Now the arithmetic closes. Combined profit is the acquirer’s Rs 5,00,00,00,000 plus the target’s Rs 1,38,00,00,000, less whatever the cash half costs after tax, plus whatever the claimed saving contributes after tax and after phasing. The share count is the acquirer’s 50,00,00,000 plus whatever the share half issues. Divide, and compare against the Rs 10.00 the acquirer was already earning on its own.

At the all-share end, with no saving counted, Rs 6,38,00,00,000 over 61,50,00,000 shares is Rs 10.3740, or 3.74 per cent above Rs 10.00. At the all-cash end, again with no saving counted, Rs 4,91,37,50,000 over the unchanged 50,00,00,000 shares is Rs 9.8275, or 1.73 per cent below. Same price, same target, same year, and two answers of opposite sign. The mix has to be stated wherever the accretion figure is quoted.

Stopping there would waste most of the work. The two cases give two points on a path, and the useful question is where that path crosses the level at which nothing changes. There are two such crossings, one on the borrowing cost and one on the mix, and they are found by algebra rather than by trial.

There is a second route to that same 8.00 per cent, and it is worth knowing because it takes no algebra at all. The earnings acquired per share, Rs 6.90, divided by the price paid per share, Rs 115.00, is an earnings yieldEarnings per share divided by the price, which is the price to earnings multiple turned upside down and read as a percentage. of 6.00 per cent. Grossing upWorking back from an amount measured after tax to the larger before-tax amount that would leave it once tax has been taken. that yield for the tax deduction, by dividing by 0.75, gives 8.00 per cent on the nose. The cash breakeven rate is nothing more than the earnings yield on the price, grossed up for the tax relief on the borrowing.

Eight elevenths is a derived figure rather than an asserted one, and one line checks it. Eight elevenths of Rs 23,00,00,00,000 is Rs 16,72,72,72,727 of cash, rounded to the nearest rupee, whose after-tax interest is Rs 1,06,63,63,636. Combined profit is therefore Rs 5,31,36,36,364. The remaining Rs 6,27,27,27,273 of share consideration issues 3,13,63,636 shares, taking the count to 53,13,63,636. Dividing gives Rs 10.0000 exactly. Eight elevenths of anything rarely comes out whole, so the share count at the exact crossing is not a whole number. The crossing is a boundary in the arithmetic rather than a deal anybody could strike to the last share.

Reading down the accretion column, the spacing is the thing to catch: the fall is 0.45 points across the first ten points of cash and 0.66 points across the last ten. The numerator and the denominator are both moving, and they move at different speeds, so the path is close to straight without ever being straight.

The near straightness of that path invites a shortcut that does not work, and the shortcut is worth walking into once. If the path really were straight, the crossing could be found by linear interpolationEstimating a value in between two known readings by assuming a straight line joins them. Quick, and wrong by however much the real relationship bends. alone: the accretive end is 3.74 points and the dilutive end 1.73 points, and a straight line joining them meets the unchanged level 68.43 per cent of the way across. The interpolated answer is out by 4.29 points of cash. The real path bows above the straight line by about three paise a share at its widest. Three paise does not sound like much, and it moves the crossing by more than four points of the consideration.

Which four checks show the arithmetic is sound?

Four checks, one line each, and each one catches a specific error rather than offering general reassurance. All four are run before the answer leaves the desk. Between them they catch every mistake the seven steps can hide, and they cost about a minute.

The fourth check leans on a property worth naming. Across the whole range of mixes, earnings per share is monotoneMoving one way for the whole distance, with no turn back at any point in between. A relationship with a hump or a dip somewhere in the middle is not monotone. in the cash share: it only ever falls as cash rises, so it crosses the unchanged level once and never returns to it. An interior mix that beats the all-share end is therefore an arithmetic error rather than an interesting finding, and that is the whole value of the check.

Check three is not a rule of thumb dressed up as a check, and one more sentence shows why. Solve for the offer price at which the all-share deal is exactly neutral and it comes out at Rs 138.00 a share, precisely 20.00 times the Rs 6.90 the target earns. Verify it: at Rs 138.00 the acquirer issues 13,80,00,000 shares, the count reaches 63,80,00,000, and Rs 6,38,00,00,000 over that count is Rs 10.0000 to the paisa. The statement that an all-share deal with no claimed saving accretes when the acquirer’s multiple is above the multiple paid is arithmetic, not observation.

Why is a single accretion figure the least useful form of the answer?

A report that the deal is 3.74 per cent accretive says something true and almost useless. The figure is true only at one mix, at one borrowing rate, with one treatment of one claimed saving. Which of those three the sign is resting on stays invisible to whoever reads it. A report that the deal runs from 3.74 per cent accretive to 1.73 per cent dilutive across the consideration mix, turns at 72.73 per cent cash, and turns again at a borrowing cost of 8.00 per cent, tells the same reader what the answer depends on. The range with its turning points carries the information; the single figure carries only the conclusion.

There is a discipline hiding inside that. Reporting the range requires the range to have been computed, computing the range requires both ends to have been run, and running both ends is what makes the fourth check possible. The reporting rule and the checking rule are the same rule seen from two sides.

What happens when one of the inputs is missing?

Three inputs go missing often, and the answer in every case is to widen the output rather than to invent the input. A stated range with its turning point named is a better answer than a single figure resting on an invented number.

Take them one at a time. Where nobody will quote a borrowing rate, the cash case is run across a range stated openly, say from 7.00 to 10.00 per cent, and reported as earnings neutral at exactly 8.00 per cent, accretive below and dilutive above. One sentence of that shape carries everything the missing input could have told the reader. Where the claimed saving is a headline with no detail behind it, the answer is reported twice, once with the saving line at zero and once with it in, leaving the reader to decide how much of it to believe. Where the accounts show group profit but not the split, the report says the split is unavailable, carries both figures, and notes that about one point of reported accretion sits in the difference between them.

How does somebody actually use this on a live transaction?

The two ends are the map the negotiation happens on, so an analyst on a deal team runs them before anybody has agreed a mix. Knowing that the sign flips at 72.73 per cent cash tells the team, in one number, how much cash they can put into the consideration before the earnings story changes shape. The crossing is not a view about whether the price is right. The crossing is a boundary the price conversation can be held inside.

A lender looks at the cash case for a different reason. The cash case is the one that adds interest to the combined business, and the breakeven rate is the point at which the earnings being bought exactly pay for the money borrowed to buy them. A rate above that turning point means the acquirer is funding part of the purchase out of what it already earned. The breakeven borrowing cost is the sharpest single sentence a lender and an acquirer can have in front of them at the same time.

An investor reading an announcement gets the most out of one habit: looking for the mix before looking for the accretion figure. An announcement quoting accretion without stating the mix, the borrowing rate and the treatment of claimed savings has given a conclusion and withheld all three of the choices behind it. Running the two ends from the announced price and share counts takes about five minutes and gives the width of the range the announcement is quoting one point from. Looking for the mix first is the pro formaFigures rebuilt on the footing that a purchase is already done, so what were two separate sets of accounts are presented as one. discipline in miniature: never accept a combined figure without knowing which combining assumptions produced it.

What can this test not tell?

Three things, and they are worth stating plainly rather than leaving anybody to infer them.

The test cannot say whether Rs 115.00 a share is a sensible price. The price is an input; the test only reports what happens to earnings once it is paid. Worth is built from cash flows and a rate, and this arithmetic touches neither, so the test cannot say what Sankalp Industrial Systems Limited is worth. And it cannot say whether the Rs 45,00,00,000 of claimed savings will arrive. They sit on a line of their own for that reason, where a reader can set them to zero. An accretive deal can destroy value and a dilutive deal can create it, so the sign of this test is never a verdict on the transaction.

Mahasagar Industrial Group Limited, Sankalp Industrial Systems Limited and Sankalp Coatings Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.