The Reservation Price: The Number Each Side Will Not Cross

A reservation price is the number a side will not cross: the most a buyer will pay, or the least a seller will accept. The number is decided rather than computed, though a stated test can produce a candidate ceiling. Holding this buyer's funding rule and assuming no synergy arrives, earnings per share is unchanged at about Rs 1,044 crore of equity value, and Rs 1,140 crore was agreed.

Start in a used car showroom. The shape of the thing is identical there, and nobody has to look at a spreadsheet to see it. A household has decided, before walking in, that it will pay eight lakh rupees for the car and not one rupee more. The dealer has decided, before the household arrived, that he will not let it go below seven lakh and twenty thousand. Neither of them says the number out loud. Neither is obliged to. Household and dealer talk about the tyres, the service history and the previous driver, and somewhere in that conversation a price gets agreed at seven lakh sixty.

Two things about that morning are worth holding on to. The first is that both numbers existed before the conversation started, and the conversation could not create them. The second is that the transaction happened only because the household's highest was above the dealer's lowest. Had the household stopped at seven lakh flat, there was no price either of them would sign, and no amount of talking about tyres would have produced one. The bargaining looks like an argument. The bargaining is actually a search, conducted blind, for a gap that either exists or does not.

Two hidden numbers and the gap between them are the whole idea, and the idea survives the move from a car to a company almost unchanged. The move adds arithmetic, and it adds the temptation, once the arithmetic is thick enough, to believe the arithmetic produced the number. It did not. Part of a walk-away number can be worked out on paper and part of it cannot. A transaction team that loses track of which side of that line it is standing on stops knowing what its own number means.

Harivansh Packaging Limited, an invented listed maker of rigid and flexible packaging, is buying the whole of Sundarban Polymers Private Limited, an unlisted maker of flexible packaging films that sells to some of the same customers. Devyani Kulkarni is the chief financial officer of Harivansh Packaging Limited and Ashwin Rege leads its transaction team. The equity value agreed is Rs 1,140 crore.

What is a reservation price, and who holds one?

A reservation priceThe number a party has settled it will not cross: the highest a buyer will pay or the lowest a seller will take. Each side holds its own, and neither is obliged to disclose it. is the number a party has settled, in advance, that it will not cross. For a buyer it is a ceiling. For a seller it is a floor. The reservation price is the price at which that party stops negotiating and does something else instead, so it is also called a walk-away priceThe same idea named from the other end: the point at which a party leaves the table rather than agree, because the next best thing it could do with its money or its business has become the better option.. Naming the action rather than the arithmetic makes the second name the more honest of the two.

Every negotiation over a business contains exactly two reservation prices, one held by each side, and neither side can see the other one. The blindness is not a defect in the process. The blindness is the process. If both numbers were published on the morning the talks opened, there would be nothing left to negotiate: either the ranges overlap, in which case the only remaining question is who captures the overlap, or they do not, in which case everyone can go home. Concealment is what makes the search necessary, and the search is what a negotiation is.

The space between the two numbers has a name. Where the buyer's highest sits above the seller's lowest, every price in between is one that both sides would sign rather than walk, and that band is the zone of agreementThe range of prices both parties would accept rather than walk away. The zone exists only when the buyer's highest sits above the seller's lowest, and neither party can see it from its own side.. Where the buyer's highest sits below the seller's lowest, the band is empty and no price exists that both would sign. Note what follows from that: a transaction failing to happen is not evidence that anyone behaved badly. The failure is often just evidence that two honest numbers did not overlap.

Who holds one, in a real purchase? Not the company, exactly. A board or a committee of it settles the ceiling, the chief financial officer and the transaction team build the case for wherever it lands, and the people in the room on the day are usually operating under a mandate that carries the number inside it. On the invented purchase here, that is Devyani Kulkarni and Ashwin Rege working to whatever Harivansh Packaging Limited's board settled. On the other side, an unlisted seller may be two or three individuals whose floor is bound up with what they want the next ten years of their lives to look like. Both are reservation prices. Only one of them will ever be written in a paper anybody files.

Is a reservation price computed, or is it decided?

A reservation price is decided. Decided is doing real work in that sentence, and most of the confusion in practice comes from getting this one distinction wrong, so it is worth holding still for a moment before the arithmetic starts.

A ceiling rests on three things, each of which can be tested. First, what the money would otherwise have done: Rs 1,140 crore not spent here is Rs 1,140 crore available for a different purchase, for the company's own factories, for paying down borrowing, or for sitting in the bank while somebody waits for a better idea. Second, how badly this particular business is wanted. The wanting covers everything from a customer relationship that is hard to build from scratch to a competitor who would take the target if this buyer does not. Third, what the buyer believes about the future of the combined business. A belief is not a measurement.

None of those three appears in any figure a transaction produces. So a reservation price cannot be computed out of transaction figures, however many of them are available. Revenue, earnings before interest, tax, depreciation and amortisation (EBITDA), net debt, the multiple, the profit ladder and the funding cost are all facts about what exists. A ceiling is a statement about what a party is willing to do. The missing ingredients are preferences and expectations that live inside the buyer rather than inside the accounts. A ceiling can be informed by the facts, and should be, but it cannot be derived from them.

Go back to the showroom to feel it. Why was the household's ceiling eight lakh rather than eight lakh fifty? Partly because of what the same money buys elsewhere, partly because there is another car two streets away that would just about do, partly because a wedding is coming and the cash has a competing claim on it. None of that is in the car. Somebody could examine the car for a week with a torch and never find the number eight lakh anywhere on it. The number was decided by the household and merely tested against the car.

A test always produced it. So when somebody produces a document headed with a computed reservation price, the first thing to establish is what that test was. A computed reservation price is always something else that has been relabelled. The useful question is never whether the number is right, but what was held constant to get it. Usually the something else is a break-even price under one metric, which is a genuinely useful object as long as nobody promotes it into a decision it cannot make.

What can be computed, and what shape does that computation take?

Plenty can be computed, and none of it is wasted. A stated test produces a candidate ceilingA maximum price produced by one stated test, offered as an input to a decision rather than as the decision. A candidate ceiling is only as wide as the test that made it.: a price at which some named thing stops being true. Cross it and the named thing breaks. Such a statement about the world is real, checkable and arguable, and it is worth far more than an unsupported assertion that the buyer should stop at Rs 1,100 crore on a feeling.

Every such test has the same three parts, and one that is missing any of them is not worth reading. Part one, something held constant: earnings per share, a leverage ratio, a coverage ratio, a return on the capital employed, a credit rating band. Part two, a named set of assumptions: the funding, the tax rate, the share count, what the target contributes, and what is assumed not to happen. Part three, a solved price: the number at which the thing held constant gives way.

A candidate ceiling that does not name what it holds constant and what it assumes leaves nothing in it for anybody to disagree with, so it is not a ceiling at all. That last clause is the point. The value of the assumptions is not that they are correct. The value is that a reader who thinks the tax rate is wrong, or who thinks some synergy will arrive, can move exactly one input and see the ceiling move. A number without its test attached is immune to argument, and a number immune to argument is useless in a room where people are trying to decide something.

Notice too how narrow the output is. A ceiling from an earnings test is a boundary on earnings and nothing else. An earnings ceiling says nothing about whether the borrowing is prudent, nothing about whether the combined business can be run, nothing about what a competitor would pay. A different test would produce a different ceiling, and both would be correct about different things. Narrowness is not a weakness to be apologised for, as long as nobody quietly widens the claim on the way to the meeting.

What does the earnings test hold constant, and what does it assume?

State the test before running it, in one sentence a reader can accept or reject on the spot. At what equity price is Harivansh Packaging Limited's earnings per share unchanged, holding the funding ruleThe stated order in which a purchase is paid for. Here, the buyer's own cash goes in first and everything above it is borrowed at the buyer's contracted rate. of the transaction and assuming no synergy arrives?

Now the assumptions, every one of them named before any arithmetic happens. The buyer puts in its own Rs 140 crore of cash first and borrows everything above that at its own contracted 9.0 per cent. Tax is 25.0 per cent, the effective rate in the accounts used here. This purchase is being paid for in cash and no shares are issued, so the share count stays at 18.00 crore. Sundarban Polymers Private Limited brings profit after tax of Rs 61 crore. And no synergy arrives at any price on the line.

One honesty note before the chain runs. The rounding below matters to anyone who rebuilds this. The Rs 61 crore is a rounded figure. Sundarban Polymers Private Limited has earnings before interest and tax (EBIT) of Rs 98 crore and interest of about Rs 16.2 crore on its own borrowings at a contracted 9.0 per cent, giving profit before tax of about Rs 81.8 crore and profit after tax of Rs 61.35 crore at 25.0 per cent. Rs 61 crore is the locked value used everywhere in this material, and it is used here too, but a reader working from Rs 61.35 crore will land a few crore higher on the ceiling. The ceiling is solved directly from that number rather than merely compared with it, so the rounding is load bearing here in particular.

The chain runs at the agreed price first, so the method can be watched reproducing an answer already in hand. At an equity price of Rs 1,140 crore, the cash covers Rs 140 crore and the borrowing is Rs 1,000 crore. Interest at 9.0 per cent is Rs 90 crore. At 25.0 per cent tax the interest costs Rs 67.50 crore after tax. Combined profit after tax is Rs 225 crore from Harivansh Packaging, plus Rs 61 crore from Sundarban Polymers, less that Rs 67.50 crore. The total is Rs 218.50 crore. Across an unchanged 18.00 crore shares that is Rs 12.14/-, against Rs 12.50/- before, a fall of 2.9 per cent measured on the Rs 12.50/- base. The fall is a dilutionA fall in earnings per share caused by a transaction. A rise is called accretion. Both are arithmetic about one metric and neither is a verdict on the transaction., and the arithmetic behind it was settled in the acquisitions material rather than here.

Where does the line cross, and what price is that?

The solve is one line of arithmetic, short enough to carry in the head. So the crossing can be worked out rather than read off the picture.

Earnings per share is unchanged exactly when the two things the transaction adds to the numerator cancel. The target adds Rs 61 crore of profit after tax. The borrowing subtracts interest after tax. So the crossing is the borrowing whose after-tax interest is exactly Rs 61 crore. A quarter of the interest comes back as reduced tax, so interest at 9.0 per cent costs 6.75 per cent after tax at 25.0 per cent. Rs 61 crore divided by 0.0675 is Rs 903.70 crore of borrowing. Add the Rs 140 crore of cash that went in first and the equity price is Rs 1,043.70 crore, or about Rs 1,044 crore. The crossing is the earnings-neutral priceThe price at which a purchase leaves the buyer's earnings per share exactly where it started, given a stated funding rule and a stated set of assumptions..

The crossing is where what the target earns exactly pays for what the borrowing costs, and every rupee of price above it is a rupee the buyer is funding out of its existing earnings. Read it that way and the whole line makes sense without any chart at all: below the crossing the target is carrying its own funding and some of the buyer's, above it the buyer is carrying some of the target's.

One more step before anyone quotes this number in a room. An equity price is not comparable with the multiples people talk in, so convert it. Rs 1,043.70 crore of equity value plus the Rs 180 crore of net debt that Sundarban Polymers Private Limited carries is an enterprise value of Rs 1,223.70 crore, and against the target's EBITDA of Rs 132 crore that is 9.27 times. The transaction as agreed is Rs 1,320 crore of enterprise value, or 10.0 times the same Rs 132 crore. So the earnings test says the buyer stopped somewhere around 9.27 times and it agreed 10.0 times, a difference of about three quarters of a turn.

A multiple quoted without naming what it was struck on is the single most common fault in this whole subject. So say both the numerator and the denominator in the same sentence, every time. Nine point two seven times what? The Rs 132 crore of EBITDA the target actually earned. And on what enterprise value? Rs 1,223.70 crore, being the derived equity price plus the Rs 180 crore of net debt that comes across with a purchase of the whole company. Both halves, every time, or the number travels around the building meaning whatever the reader assumes.

Why is a derived ceiling not the reservation price itself?

Because the test that produced it left three things out, and all three are things a buyer would weigh next. Take them one at a time, and notice that each one is a reason the true ceiling could sit above the derived one rather than below it.

The first is synergy. The test assumed none arrives at any price on the line. The assumption is severe rather than neutral. If the two businesses share customers, and Sundarban Polymers Private Limited does sell to some of the same food and personal care customers as Harivansh Packaging Limited, some combination of buying, freight, plant loading or cross-selling may be available. How much and at what cost to achieve it is worked in the acquisitions material and is not rebuilt here. The size of the hole is what matters for the test: the gap to be closed is Rs 6.50 crore of profit after tax, or about Rs 8.67 crore of extra EBITDA before tax at 25.0 per cent. The extra EBITDA is 6.6 per cent of the target's Rs 132 crore. Whether that is easy or heroic is a judgement, and the test refuses to make it.

The second is patience. The test holds earnings per share constant, and so it quietly assumes the buyer is unwilling to accept any fall at all in that one metric, ever. Real buyers routinely are willing, for a stated period, for a stated reason. A board that has decided it will accept two years of slightly lower earnings per share in return for a plant, a customer list and a second production site has not made an error. The board has made a different decision from the one the test encodes, and the test has no way of representing it.

The third is the alternative. Rs 1,140 crore not spent here would have done something else inside Harivansh Packaging Limited. Built capacity, retired borrowing, sat in the bank, or bought a different target that is not in this record at all. The earnings test compares this purchase with doing nothing at all and financing nothing at all. The test never compares this purchase with the next best thing, and the next best thing is exactly what a walk-away number is measured against.

The derived ceiling is one input to a decision and never the decision itself, and promoting it to the decision is the specific misuse to guard against. Used properly it is excellent: it names what is being bought when it is crossed, in the precise currency of a metric everybody watches. Used improperly it arrives with a decimal point and becomes an authority nobody can question.

What does a seller's reservation price rest on, and where is it here?

A seller's floorThe least a seller will take, resting on what continuing to hold the business is worth to them, on any competing offer, and on their own tax and personal position. is built from three ingredients, and none of them looks much like the buyer's list. The first is the value of simply carrying on. A seller who holds a business earning Rs 132 crore of EBITDA and expects to hold it for another decade is comparing an offer against a stream of profits it already has, not against nothing. The second is any competing offer. A competing offer converts a floor from a belief into a fact, and nothing else a seller holds is that powerful. The third is the tax and personal position of the individual sellers: what they keep after tax, what they want to be doing in three years, and whether one of them wants out while another does not.

Now the honest part. The record for this purchase contains not one of those three, so the seller's floor cannot be computed from it. There is no competing offer in the figures. There is no statement of what holding on would be worth to the people who built Sundarban Polymers Private Limited. No individual seller has a name in this record, so there is no tax position for one either. The record has a target's profit ladder, its net debt and its net worth, and a floor cannot be built out of those.

An absence stated is a finding and an absence hidden is a hole. A reader who is told the seller's side is empty knows exactly how much of the negotiation has been explained. One half of it. A reader who is simply shown a buyer's ceiling and nothing else may walk away believing that a transaction price is set by the buyer's arithmetic. The belief is close to the opposite of the truth. Prices land where they land because two numbers overlapped and one side negotiated better inside the overlap.

The seller's ingredients are structurally harder to compute than the buyer's, not just missing here. The worth of holding on is a forecast. A competing bidder's price is somebody else's private ceiling. The individuals' wishes for the next decade are not a financial quantity at all. So even a fully documented purchase would leave a seller's floor mostly undocumented. Of the two numbers, the buyer's ceiling is the only one anybody was ever going to write down, and that is why it gets all the attention.

What happens to a ceiling that was never written down?

It moves. Not sometimes, and not in a random direction. Every pressure in the room points one way and nothing points back, so an unrecorded ceiling drifts upward during a negotiation. The clock is running. Work has been done and people want it to count for something. A competitor may be circling. The seller has just said something encouraging about next year. And the ceiling itself, being a number in somebody's head, has no edges anybody can point at.

Sit with what a written ceiling actually does. A written ceiling is easy to mistake for a control on behaviour, and it does not stop anybody crossing it. A board can cross its own ceiling in an afternoon and be entirely within its rights, and sometimes it should. The written number forces the crossing to become an event. Somebody has to look at a document, see Rs 1,043.70 crore under a stated test, and say out loud that the transaction team is now proposing Rs 1,140 crore. The sentence has to be said out loud, and once it is said it can be answered.

Notice the asymmetry in the two failure modes. Crossing a written ceiling badly leaves a record of a bad decision. A record is unpleasant and reviewable, and reviewable is how anybody gets better at this. Crossing an unwritten ceiling badly leaves nothing at all: no test, no date, no argument, no way to tell six months later whether the price moved because somebody learned something or because it was four in the morning and everybody wanted to go home. A recorded ceiling that was later crossed still leaves evidence of a decision, and an unrecorded one leaves nothing to examine, so the recording matters more than the number.

The household version is familiar to anyone who has ever renovated a kitchen. Two people agree a budget in the car on the way to the shop. Nobody writes it down. Three hours later they have spent thirty per cent more, and neither can reconstruct which item did it. No moment ever came at which anyone said the budget was being exceeded. Written on the back of an envelope, the same thirty per cent might still have been spent, but somebody would have had to say why.

How does a lender, an analyst or a household use a walk-away number?

Three readers, three different first questions, and it is worth seeing that none of them is asking what a valuer would ask. Start with the lender who is being asked to fund the Rs 1,000 crore of new borrowing. A lender does not care very much where the buyer's ceiling sat in the abstract. The lender cares whether the buyer had one, whether it was tested, and whether the price finally agreed still leaves the combined business able to service what it is borrowing. A buyer that cannot produce a ceiling with a test attached is telling the lender something about how it makes decisions, and that is read as a fact about the borrower rather than a fact about the price.

The analyst reading the announcement afterwards works the other way round. The price is known and the test is not, so the analyst rebuilds a ceiling of their own to see what the buyer must have been assuming. Rs 1,140 crore against a crossing of Rs 1,043.70 crore says the buyer either expects at least Rs 8.67 crore of extra EBITDA, or accepts a fall in earnings per share for a period, or values something the earnings test cannot see. The three doors are the only ones, and the analyst's job is to ask which one the buyer walked through and whether it has said so publicly.

The investor already on the register asks the narrowest question of the three: what happened to my earnings per share, and for how long. Rs 12.50/- to Rs 12.14/- is a 2.9 per cent fall on the Rs 12.50/- base, and that is an arithmetic fact about the first year on stated assumptions, not a forecast and not a verdict. Whether it reverses depends on the synergy actually arriving and on what the combined business does with the plants it now runs, neither of which is settled on the day of the announcement.

All three readers are checking the same thing in different words: whether a number that was decided came with a test attached, and whether the test was allowed to be wrong out loud. The household version is the same reflex again. When a relative asks how much a household would pay for the flat it is looking at, the useful answer is not a figure. The useful answer is a figure plus the sentence that follows it, naming the rent it must replace, the loan it must carry, or the school it must be near. A figure with its reason attached can be argued with over dinner. A figure alone can only be agreed or disagreed with. Agreement is not argument.

What cannot be said about Rs 1,140 crore?

Whether Rs 1,140 crore sat above or below where Harivansh Packaging Limited should have stopped is not a question arithmetic can settle. The silence on it is not modesty and not a hedge. Everything the earnings test leaves out forces it.

To say the price was too high would require knowing what the money would otherwise have done, and no published figure contains it. To say it was fine would require knowing what synergy will actually arrive net of what it costs to achieve, and that is a forecast rather than a measurement. The arithmetic of this purchase is checkable and the merit of it is not, so an honest account stops exactly where the checkable part stops.

The checkable part is precise enough to be useful. On a test that holds earnings per share at Rs 12.50/-, holds the funding rule of Rs 140 crore of cash and then borrowing at a contracted 9.0 per cent, and assumes no synergy at all, the crossing sits at Rs 1,043.70 crore of equity value, or Rs 1,223.70 crore of enterprise value and 9.27 times the target's Rs 132 crore of EBITDA. The transaction was agreed at Rs 1,140 crore of equity value, Rs 1,320 crore of enterprise value and 10.0 times the same EBITDA. The distance is Rs 96.30 crore. Anybody with those assumptions in front of them can rebuild every one of those figures. A ceiling written any other way cannot be checked at all.