The Deal Rationale: The Argument a Purchase Rests On

A deal rationale is the argument for why this buyer should hold this business at this price, written so that somebody can check it later. A rationale names what changes under new ownership, what that change is worth, what it costs to get, and what would show the argument was wrong. Drop the fourth and what remains is a description of the purchase with numbers attached.

An awkward observation sits underneath the whole subject. Almost every large purchase is approved. Boards say yes far more often than they say no, and they say yes on the strength of a document that runs to a few printed sides and is read once. If that document could not have produced any answer other than yes, then approving the purchase told the board nothing, and nobody will be able to say afterwards whether the thinking was sound or merely fortunate.

The household version of the same problem is worth feeling before it is worth calculating. A cousin wants to buy the sweet shop two streets away. Asked why, he says the shop is popular, the location is good, and the two shops together will do better than either alone. Every sentence is true. Not one of them can be wrong. He has said what he is buying and he has said that he likes it. Ask him eighteen months later whether it worked and he will have nothing to compare the answer against. He never said what the answer was supposed to be.

The four questions run differently. Which change on the day one owner holds both shops could not have happened while he held one? How much money does that change put in his hand in a year? How much has to be spent to make the change happen? And what does the money used to buy the shop cost, given that most of it was borrowed from a brother in law at an agreed rate? If he answers all four, he has a rationale. If he answers the first two, he has enthusiasm with figures in it.

Harivansh Packaging Limited, an invented listed maker of rigid and flexible packaging, is buying all of Sundarban Polymers Private Limited, an unlisted maker of flexible packaging films. Devyani Kulkarni is the chief financial officer of Harivansh Packaging Limited, and Ashwin Rege leads the transaction team. Every price, rate and multiple in the case is assumed rather than read off a market, and a market rate on the borrowing would move the gap without changing its shape.

What is a deal rationale, and what makes it an argument rather than a description?

A description states what is happening. A deal rationaleThe written case for a purchase, setting out what the buyer expects to be different afterwards and why that difference is worth the price and the money used. states why the person doing it expects to be better off, and does so in a form that some future observation could contradict. The possibility of contradiction is the whole distinction between a rationale and an account of what the purchase consists of.

Write out the description of this purchase and see how complete it looks. Harivansh Packaging Limited is acquiring 100 per cent of Sundarban Polymers Private Limited at an enterprise value of Rs 1,320 crore. The price is 10.0 times the target's earnings before interest, tax, depreciation and amortisation (EBITDA) of Rs 132 crore. Deduct Sundarban Polymers' own net debtBorrowings less cash. It is deducted from enterprise value because the buyer inherits the borrowings and the cash along with the business. of Rs 180 crore and the equity valueThe amount that actually reaches the sellers for their shares, after the business's own borrowings have been taken off the enterprise value. is Rs 1,140 crore. Rs 1,140 crore is the amount that actually reaches the sellers. The considerationWhat the buyer hands over: cash, shares, deferred amounts, or a mixture. Here it is entirely cash. is all cash, funded with Rs 140 crore of the buyer's own cash and Rs 1,000 crore of new borrowing at the buyer's own contracted rate of 9.0 per cent.

The description is precise, it is verifiable, it will survive any amount of scrutiny, and it is not an argument. The description makes no claim about the future at all, so nothing in it could turn out to have been mistaken. A description of this kind is a photograph of the transaction. A reader could return to it in three years and learn exactly what was done and nothing whatever about whether it should have been.

A rationale is the document that can be wrong, and being the document that can be wrong makes it the harder one to write and the one nobody keeps a copy of. The description survives in the filings and the accounts and the press coverage. The rationale, if it existed as a separate thing at all, tends to disappear into a board pack that is archived and never reopened. Ask anybody who has worked on a purchase to produce the rationale two years afterwards and watch what happens.

There is a word for the property being asked for here, borrowed from how careful people talk about any claim at all. FalsifiabilityThe property of a claim that some possible future observation could show it to be false. A claim nothing could contradict is not thereby true; it simply has not said anything checkable. means there exists an observation which, if made, would show the claim to be false. Falsifiability is not a demand for pessimism and not a prediction of failure. Falsifiability is a demand that the claim be about something. A rationale which no possible outcome could contradict has not made a claim, and cannot be graded later, and therefore cannot teach the team that wrote it anything at all.

What are the four parts every rationale has to contain?

Four, and they are not a style guide. The four quantities have to exist before the question can even be asked, and the reason most rationales fail is not that the reasoning is poor but that two of the four are simply absent from the document.

The first is the change. Something has to be different once one holder runs both businesses, and it has to be something that could not have happened while they were separate. Every rationale carries the change, and the change is the part people enjoy writing. The second is the amount the change is worth, stated over a period. Most rationales carry this one too, and it is where the number that gets quoted in the room comes from.

The third is the cost to achieveThe money and effort spent to bring a promised benefit into existence: severance, system migration, relocation, rebranding, retraining, the people who do nothing else for a year.. Benefits do not arrive because a purchase completed. Somebody has to merge two order books, move a warehouse, retrain a sales team, or run one system where two ran before, and all of that costs money in the year it is done. The fourth is what the money used costs. The borrowing carries a rate and the cash could have been somewhere else, so the cost of the money exists whether anybody writes it down or not.

Most rationales carry the first two parts and skip the third and the fourth, and skipping them is exactly what lets any purchase at all look justified. A document containing only parts one and two says that a good thing will happen and states how big it is. There is no subtraction anywhere in it. A statement with no subtraction in it is not being measured against anything, so it clears every hurdle.

The household version again. The cousin says the two shops together will sell an extra Rs 40,000/- of sweets a month. Wonderful. The next question is what it costs to get that extra Rs 40,000/-: a second delivery run, one more person on the counter, a new sign. And after that, what the money costs: he borrowed most of the purchase price and is paying interest on it every month. The extra Rs 40,000/- was never the answer. The extra Rs 40,000/- was the first of four numbers, and he stopped after one.

What is the purchase this rationale is arguing about?

Before the argument can be tested it has to be attached to figures that are already fixed. Otherwise the test measures the assumptions rather than the argument. The figures below come from the valuation and the funding terms settled before the rationale was written, and none of them moves.

Harivansh Packaging Limited runs its own business at a revenue of Rs 3,180 crore and an EBITDA of Rs 477 crore, a margin of 15.0 per cent. After depreciation and amortisation of Rs 138 crore, finance cost of Rs 60 crore and other income of Rs 21 crore, profit before tax is Rs 300 crore, tax at an effective 25.0 per cent is Rs 75 crore, and profit after tax is Rs 225 crore. On 18.00 crore shares that is earnings per share of Rs 12.50/-. Its share price is Rs 300/-, an assumed level rather than a reading taken from a market.

Sundarban Polymers Private Limited earns revenue of Rs 880 crore and EBITDA of Rs 132 crore, also a margin of 15.0 per cent. The matching margin is not an accident, and it matters more than it looks: because both businesses run at the same margin, no rationale for this purchase can be built out of the claim that the buyer is more efficient than the target. The argument has to come from price, funding and structure, exactly where an honest rationale has to look anyway.

The target's own profit after tax is the figure the rest of this guide leans on. Its earnings before interest and tax (EBIT) is Rs 98 crore, its finance cost on its own borrowings at a contracted 9.0 per cent is about Rs 16.2 crore, so profit before tax is about Rs 81.8 crore and profit after tax is about Rs 61 crore. Rs 61 crore is rounded: the chain above gives Rs 61.35 crore, and Rs 61 crore is the value used consistently across this sequence. The direction of the answer is the same on either figure.

Now the funding, the part that fixes the arithmetic. The buyer pays Rs 1,140 crore of equity value in cash, using Rs 140 crore of its own cash and Rs 1,000 crore of new borrowing at its own contracted rate of 9.0 per cent. Interest on that borrowing is Rs 90 crore a year, and at the 25.0 per cent effective tax rate the after-tax cost of debtThe interest cost after the tax saved by deducting it. At a 9.0 per cent rate and a 25.0 per cent effective tax rate, the rate becomes 6.75 per cent. is 6.75 per cent, so the annual charge is Rs 67.5 crore. Its own borrowings move from Rs 740 crore to Rs 1,740 crore and its cash goes to nil.

What changes under new ownership here, and why is it not priced?

The change in this purchase is easy to name and it is real. Harivansh Packaging Limited and Sundarban Polymers Private Limited sell to some of the same customers. A buyer at one of those customers who currently manages two supply relationships, two quality processes, two negotiations and two sets of paperwork would afterwards manage one. One relationship replacing two is a genuine difference that could not exist while the two businesses were separate, and it is the reason the transaction exists at all rather than a story told after the fact.

The second of the four parts stays open in this case. Nobody has sized the change, and naming the part as unpriced is more honest than manufacturing an amount. The whole lesson of the four parts is that the second and third numbers are hard, contested and easy to make up.

An absent figure is worth more here than an invented one. A figure would be remembered as a figure: a sense that a single relationship replacing two is worth roughly some amount, when the amount was chosen to make the arithmetic close. The shape of the obligation remains even with the amount missing. Somebody has to produce that number, defend the method behind it, and put a date on it, and if nobody has, the rationale has a hole in it that no amount of confidence fills.

The cost of obtaining the change stands in the same position. Merging two customer relationships into one is not free. Somebody negotiates, somebody rewrites contracts, somebody loses a little price to keep a customer through the transition. All of that is real spend in a real year, and no figure for it exists in this record either. Two of the four parts are therefore open, and naming them as open is worth more than filling them with invention.

The fourth part is the one that is not open, and it is therefore the one that can be tested properly. The money used costs a known amount. The cost of the money is the half of the rationale where nothing has to be estimated, believed or negotiated, and it is where a rationale can be held to account with complete confidence.

What arithmetic does a rationale have to beat?

Here is where a rationale stops being a story. The buyer has handed over Rs 1,140 crore and in exchange has bought a stream of earnings. The money handed over was not free. Rs 1,000 crore of it carries interest at 9.0 per cent, and after tax that interest is Rs 67.5 crore a year. So there are two amounts, and the rationale has to explain the distance between them.

The earnings bought are Sundarban Polymers' profit after tax of Rs 61 crore. Expressed against what was paid, that is an earnings yieldEarnings divided by the amount paid for them, written as a percentage. It answers how much profit a rupee of purchase price brings in a year. of Rs 61 crore over Rs 1,140 crore, or 5.35 per cent. The after-tax cost of the money is Rs 67.5 crore, and struck on that same Rs 1,140 crore it is 5.92 per cent.

The gap is 0.57 percentage points. On the Rs 1,140 crore paid that gap is Rs 6.50 crore a year, and Rs 6.50 crore is precisely what the rationale has to account for. Not describe. Account for, with a change that produces at least that much and a cost of obtaining it that leaves at least that much standing.

Notice what this does to the conversation. The question is no longer whether the purchase feels sensible or whether the businesses fit. The question is whether the argument in the document produces more than Rs 6.50 crore a year, net of what it costs to produce. A question in that form has an answer, and a document that does not attempt it has not engaged with the purchase at all.

Notice too the claim the gap does not make. The gap is not a claim that the purchase destroys value. The gap is a claim that on day one, before anything changes, the earnings bought fall short of the cost of the money by Rs 6.50 crore, and every rupee of the argument has to be spent closing that gap before a single rupee counts as gain. Rs 6.50 crore is the honest starting line, and starting anywhere else is how a rationale ends up unable to fail.

Why does the base the two figures sit on decide whether the argument ties?

Rationales quietly stop reconciling at this step, and the step is worth slowing down for. The error looks like nothing at all on a quick reading.

There are two perfectly true statements about the cost of this money. The after-tax rate on the new borrowing is 6.75 per cent. And the after-tax charge of Rs 67.5 crore, expressed against the Rs 1,140 crore actually paid, is 5.92 per cent. Both are correct. The two rates are struck on different bases, so they are not interchangeable. The first is struck on the Rs 1,000 crore borrowed and the second on the whole Rs 1,140 crore paid, and the whole Rs 1,140 crore includes the Rs 140 crore of the buyer's own cash.

Rs 1,140 crore is what was handed over to get the Rs 61 crore, so the earnings yield of 5.35 per cent is struck on the Rs 1,140 crore paid. So the cost it is compared against has to be struck on the same Rs 1,140 crore. Set the 5.35 per cent yield against the 5.92 per cent cost and the spread of minus 0.57 points multiplies out to minus Rs 6.50 crore. Combined profit after tax falls by exactly that amount. Set the same 5.35 per cent against the 6.75 per cent rate and the spread is minus 1.40 points. On Rs 1,140 crore the spread comes to minus Rs 15.95 crore, and that figure reconciles to nothing on the earnings line at all.

The mismatch does something else to a reader as well. Rs 15.95 crore looks like a bigger, more conservative, more responsible number, and a rationale carrying it would look more rigorous than one carrying Rs 6.50 crore. The bigger figure is not more conservative. The bigger figure is a comparison between a yield on one base and a rate on another, and it will not tie to the earnings per share the accounts actually report. A more alarming number arrived at incorrectly is not caution; it is an error that happens to point the same way as caution.

The discipline is one sentence long and it is worth memorising. When two percentages are compared, name the base under each of them out loud before subtracting. If the two bases differ, one of the two percentages has to be restated before the subtraction means anything.

What does the Rs 6.50 crore actually do to earnings per share?

Run the chain and watch the gap turn into the number a holder sees. Harivansh Packaging Limited's own profit after tax is Rs 225 crore. Add Sundarban Polymers' Rs 61 crore. Deduct the Rs 67.5 crore of after-tax interest on the new borrowing. Combined profit after tax is Rs 218.5 crore. The consideration was entirely cash and no shares were issued, so the share count does not move and stays at 18.00 crore.

Rs 218.5 crore over 18.00 crore shares is Rs 12.14/-, against Rs 12.50/- before. The move is a fall of Rs 0.36/- a share, or 2.9 per cent. The Rs 6.50 crore gap divided by 18.00 crore shares is Rs 0.36/- exactly, and the funding gap and the earnings per share move are therefore the same fact stated twice.

The identity between the two is the test of whether the arithmetic is sound. If the gap figure does not divide by the share count into the earnings per share move, the two sides of the comparison are sitting on different bases and the error described in the section above has been made. The Rs 15.95 crore figure, divided by 18.00 crore shares, gives Rs 0.89/- and corresponds to no reported number anywhere.

The word for what has happened will be used against this transaction, so it is worth naming. AccretionA purchase is accretive when it raises the buyer's earnings per share and dilutive when it lowers them, measured in the first full year and before any change in how either business is run. is the test of whether a purchase raises or lowers earnings per share, and this one lowers it. The transaction is dilutive on the locked Rs 61 crore, and it is also dilutive on the exact Rs 61.35 crore, where combined profit after tax is Rs 218.85 crore and earnings per share is Rs 12.16/-, a fall of 2.7 per cent. The rounding changes the size of the headline and not the direction, and that is exactly why the rounding is stated rather than hidden.

And here is the observation that should stop anybody reaching for the multiple as a shortcut. Sundarban Polymers is being bought at 10.0 times its EBITDA while Harivansh Packaging trades at an illustrative 12.58 times its own. On that comparison alone the purchase looks cheap. The purchase is still dilutive. The multiple comparison and the cost of the funding are two different questions, and neither one answers the other.

How much more would the business have to earn to close the gap?

Turn the gap around and ask it as a requirement. If the argument in the rationale is to hold earnings per share where it was, how much extra does the combined business have to produce? The number people mean is the hurdleThe amount a benefit has to reach before the thing that produced it is worth doing, set by what the money used costs rather than by preference., and there are two of them here, and they answer different questions.

The narrow hurdle holds earnings per share at Rs 12.50/-. The narrow hurdle needs the Rs 6.50 crore of missing profit after tax to be found. Before tax at 25.0 per cent, Rs 6.50 crore of profit after tax requires Rs 8.67 crore of extra EBITDA, and with that added, earnings per share sits back at Rs 12.50/-. As a proportion of what the target already earns, Rs 8.67 crore is 6.6 per cent of Sundarban Polymers' Rs 132 crore of EBITDA.

The full hurdle asks something else. The full hurdle refuses to treat the buyer's own Rs 140 crore of cash as free, and charges it at the same 6.75 per cent after-tax rate that the borrowing carries, on the reasoning that the cash had somewhere else to be. On that basis the whole Rs 1,140 crore of money used carries a cost of Rs 76.95 crore rather than the Rs 67.5 crore the borrowing alone costs. The acquired earnings would have to reach Rs 76.95 crore against the Rs 61 crore they are, a shortfall of Rs 15.95 crore of profit after tax. Before tax that shortfall is Rs 21.27 crore of EBITDA, or 16.1 per cent of the target's Rs 132 crore.

The two hurdles are Rs 8.67 crore and Rs 21.27 crore, they are two and a half times apart, and a rationale that does not say which one it cleared has not answered the question. Neither is the right one and neither is a stricter version of the other. The first asks whether the reported earnings per share is held. The second asks whether every rupee of money used earns its keep, including the rupees that were already sitting in the buyer's account.

Two warnings belong beside these figures. The first is that Rs 15.95 crore is not the day one funding gap. The day one gap is Rs 6.50 crore, and the two differ only because the fuller hurdle also charges the buyer's cash. The second is the one from the previous section, restated because it produces the same number by accident: a rationale that reaches Rs 15.95 crore by setting a yield struck on Rs 1,140 crore against a rate struck on the Rs 1,000 crore borrowed has arrived at the right figure for entirely the wrong reason, and will reconcile to no earnings per share number at all. Getting a defensible answer by an indefensible route is not a smaller error than getting the wrong answer.

The idea underneath the full hurdle is why the second question is asked at all, and it is worth naming. The opportunity cost of cashWhat the money gives up by being used here rather than anywhere else. Cash on a balance sheet feels free because no interest is paid on it, but it is not free to the people whose money it is. is invisible in the accounts and real in every other sense. Charging it at 6.75 per cent is a choice, not a fact, and a rationale is entitled to make either choice as long as it says which one it made.

What would show the argument was wrong?

The falsification line is the part that makes the other three testable, and it is the part almost nobody writes. The line is one sentence, and it has three components: a figure, a date, and a direction. Miss any one of the three and the sentence stops being checkable.

Written for this purchase, it reads like this. If the combined business has not delivered Rs 8.67 crore of EBITDA from the change described above, net of what it cost to obtain and measured against a baselineThe reading fixed before the purchase completes, so that a later measurement has something to be compared against. Without one, any later number can be explained as having always been there. fixed before completion, by 31 March of the second year after completion, then the argument set out in this rationale was wrong.

Take the sentence apart. The figure is Rs 8.67 crore, and it is not chosen for effect: it is the narrow hurdle computed above, so the rationale is measuring itself against the arithmetic rather than against an ambition. The date is stated, so the argument cannot be extended indefinitely by the people who wrote it. The direction is stated, so there is no argument later about whether a given outcome counts. And the baseline clause is what stops the whole thing being defeated by a business that would have grown anyway.

A rationale that no future observation could contradict has not made a claim, and no amount of confidence, detail or length in the rest of the document repairs that. One test applies to any rationale. Which observation would make the author say, out loud, that they were wrong? If nothing would, then approving the purchase and rejecting it were never distinguishable decisions.

Notice what the falsification line does to the people writing it. Most of its value sits there. Anybody can write that a purchase will strengthen the combined position in the market. Nobody enjoys writing that the combined business will produce Rs 8.67 crore of extra EBITDA net of costs by a named date, or the argument was wrong. The discomfort is the mechanism working. The discomfort forces the change to be sized, the cost of obtaining it to be estimated, and somebody to accept that the estimate will be checked.

What are the common rationales, and which of them can be tested?

There are perhaps six arguments that carry most purchases, and it is useful to sort them by a single property: does this argument, written honestly, produce a figure with a date on it, or does it produce a sentence?

Scale in purchasing produces a figure. Two businesses buying the same film, resin or freight now buy it as one, and the saving is a volume times a price difference that can be computed and dated. Buying capacity rather than building it produces a figure too, and a very clean one: the capacity has a quantity, and building it would have had a cost and a timetable, both of which are known. Filling a gap in a range produces a figure with more effort. The revenue from the missing product to existing customers can be estimated, though the estimate is softer.

Reaching customers the buyer does not have produces something in between. The customer list is real and countable, but what those customers will buy from the enlarged offering is a projection. The value of a team or a technique resists being written as an amount by a date, so acquiring people or a capability usually produces a sentence. Removing a competitor produces a sentence too, and often one that cannot be written down at all for reasons that have nothing to do with arithmetic.

The arguments that produce a sentence rather than a figure are not thereby wrong, they are simply harder to hold anybody to, and a rationale resting on one has to say so in the document rather than dress it as a number. A team acquired for a capability may be the best purchase a business ever makes. Such a purchase will not be checkable eighteen months later against a line somebody wrote before completion, and pretending otherwise by attaching a confident figure to it is worse than admitting it.

The everyday version is the same distinction. If a household buys a second scooter because the elder child now travels to a college eleven kilometres away, that is a figure with a date: the auto fare saved is countable from the first month. If the same household buys a laptop because it will help the child's prospects, that may be entirely right and there is no month in which anyone can check it. Both can be good decisions. Only one can be graded.

What does a wish look like when it is dressed as a rationale?

Every experienced reader of these documents has a feeling that something is wrong before they can say what. The tells are not matters of tone at all, so the useful move is to stop trusting the feeling and convert it into a checklist. Each one is a missing part from the list of four.

The first tell is a change that is named but never sized. The document says the combined business will be stronger with shared customers, and no amount appears anywhere near the claim. Part two is missing. The second tell is that the cost of achieving the change appears nowhere. Nothing is said about who does the merging of the two relationships, what it costs, or in which year it is spent. Part three is missing.

The third tell is timing described as over time, in due course, or as the businesses come together. The date has gone missing from the falsification line. A claim with no date can never be overdue, and that makes the missing date the most effective of all the omissions. The fourth tell is the case resting on what the combined business will be able to do rather than on what it will do. Capability is not an outcome. Every business is able to do a great many things it does not do.

Each tell is a missing part rather than a matter of style, so the fix is never rewriting the prose and is always supplying the number that was left out. The checklist is therefore more useful than the instinct. An instinct says this document feels thin. The checklist says part three is absent and the date is absent, a specific request the author can actually answer.

Who writes the rationale, and who signs it?

An argument nobody stands behind is not an argument, it is a document. So the last question about a rationale is not about its contents at all. The last question is about the names on it.

Follow the usual path. The rationale is drafted by the transaction team, led here by Ashwin Rege, who have worked on the purchase for months and whose work is complete when it completes. It is reviewed by the chief financial officer, Devyani Kulkarni, whose accounts will carry the result. It is signed by the board, who approve it. And it is delivered, if it is delivered at all, by the people who run the plants, negotiate with the customers and sit on the sales desks, most of whom have never seen the document and many of whom did not know the purchase was happening.

A rationale produced by the people who are paid when the purchase completes, and never read by the people who will have to deliver it, is an argument with nobody standing behind it. Say clearly what that is and what it is not. The point is not an accusation of bad faith. A transaction team producing an optimistic estimate is behaving exactly as anyone would when they are close to something they have worked on for months and will not be measured on afterwards. The optimism is a structural fact about who is in the room, and it is fixed structurally rather than by asking people to try harder.

The fix is one step and it is unglamorous. Before the rationale goes to the board, the person who will be accountable for delivering each part of the argument reads the figure they are going to be measured against, and says whether they accept it. Not approves the purchase. Accepts the number. If the head of the packaging plant has read that the change is worth a stated amount by a stated date, and has said the amount is achievable, then somebody is standing behind it. If nobody has, then the number in the board pack is an estimate produced by people who will not be present when it is checked.

There is a household version of this too, and it is the reason the point lands. A wedding budget agreed between two people who will not do any of the buying is not a budget. A budget of that kind is a hope with subtotals. The moment the person who will actually negotiate with the caterer says yes, that amount is achievable, it becomes something else entirely.

How do a lender, an analyst and an existing holder read a rationale?

Three readers, three different first questions, and none of them reads the document the way its authors expect. Watching all three is the fastest way to see what a rationale is actually for.

A lender reads the rationale as a question about the borrowing it is being asked to provide. Harivansh Packaging Limited is taking on Rs 1,000 crore of new debt, moving its own borrowings from Rs 740 crore to Rs 1,740 crore and its cash to nil. The lender's first move is to strip the promised benefit out entirely and ask whether the combined business services the debt without it, because the benefit is exactly the part of the argument that the lender cannot verify and does not control. The rationale matters to the lender chiefly as evidence that somebody has thought about the Rs 67.5 crore, not as a source of comfort about what will be earned.

An analyst reads it as a set of claims to be marked against later. The useful analyst behaviour is to write the promised figure and the promised date into a note and then look at it in eighteen months, which is the only way anybody ever learns whether a management team's estimates mean anything. An analyst who has done this for a few purchases in a row knows something genuinely valuable that no single set of accounts contains: whether this particular team's rationales come true.

An existing holder reads it as a question about their own earnings per share, and gets an immediate answer they will not enjoy: Rs 12.50/- becomes Rs 12.14/-. The holder's real question is not whether the fall happened but what the argument says will close it, and how they will know a year from now whether it did. A rationale that offers a benefit with no size and no date has told an existing holder that their earnings per share fell and that they will never be able to check whether the reason was good.

The household version once more. When a relative proposes a shop purchase funded by a loan, the person who has lent the money asks whether the household can pay the instalment even if the shop does nothing new. The neighbour who is curious asks how much more it will earn and by when, and remembers the answer. And the wife or husband who is on the loan asks the only question that matters to them: what changed for the household this month, and what is supposed to change by next Diwali? All three are reading the same argument for different reasons, and all three deserve a document that can be checked.

What can a rationale never become?

Two things, and holding both of them steady is what keeps this whole discipline honest rather than ceremonial.

A rationale is not a promise that the purchase will work. A rationale is an argument made in advance with the information available in advance, and arguments made that way are sometimes wrong for reasons nobody could have known. A rationale that fails its own test has not necessarily been dishonest or careless. Such a rationale has been checked, and being checked is more than most of them ever manage.

And a rationale is not evidence that the purchase did work. A well written argument that cleared a hurdle on paper is a well written argument, and the results are a separate matter entirely, settled by what the combined business actually earns. Confusing the two is how a good document becomes a defence rather than a test.

The whole function of a rationale is to be a written record of what was believed and why, available to be checked later, and any use that is not that use degrades it. Used as a sales document it becomes optimistic. Used as a defence it becomes vague. A record has no incentive to be anything else, so used as a record it stays honest.

The arithmetic in this guide goes this far and no further. Rs 61 crore of acquired earnings against Rs 67.5 crore of after-tax interest, both struck on the Rs 1,140 crore paid, leaves a gap of Rs 6.50 crore a year. The gap is Rs 0.36/- a share and takes earnings per share from Rs 12.50/- to Rs 12.14/-. Closing it needs Rs 8.67 crore of extra EBITDA on the narrow question, or Rs 21.27 crore on the fuller one. Every one of those figures is computable and every one of them is now computed.

And none of them says whether this purchase was a good idea. The merit of the purchase turns on what the Rs 1,140 crore would otherwise have done and on what the combined business goes on to achieve, and no published figure settles either. The arithmetic settles the funding gap and the two hurdles, and the judgement about what the money should have been used for belongs to whoever has to defend it.