Trading Comps vs Precedent Transactions: Where the Gap Comes From

A trading multiple prices a small parcel of a similar listed business at today's market price. A precedent multiple is what one buyer paid once for control of a whole one. On this segment the two middle readings are 7.8 times and 9.5 times: a gap of 1.70 turns, 21.79 per cent of the trading figure, and Rs 4,89,60,00,000 on Sankalp Industrial Systems Limited, an invented manufacturer.

The two sets are answering different questions about different objects, and that is the whole of it. One is a price for a parcel of shares that carries no say over anything, remade every trading morning, sellable again tomorrow. The other is a single committed price for an entire business, struck once, by a named buyer, on a day that has passed. The distance between them is not an error in either set, and it is not one thing either. The distance is a leftover that holds several causes at once, and a leftover of that kind can be measured but never divided.

Most of the confusion about the gap starts with treating the two multiples as two estimates of the same quantity, so both objects have to be defined properly before they are compared. Then the distance gets measured, the four things inside it get named, and the reason the share belonging to each cannot be established is set out at some length.

What is a trading multiple a price for?

A screen shows, right now, what somebody will pay for a hundred shares of a listed manufacturer. A screen price multiplied by every share in issue, plus what the company borrowed, less its cash, gives a figure for the trading business itself: its enterprise valueOne price for the trading operation on its own. Two companies carrying very different borrowings can still be lined up beside each other at this level, and a multiple hangs off it for that reason.. Enterprise value divided by a year of earnings before interest, tax, depreciation and amortisation (EBITDA) is a trading multiple.

The screen price buys a hundred shares and nothing else. A hundred shares do not carry the right to change the dividend, refinance the borrowing, close a plant or replace the managing director. A parcel that size is a small slice, and the price paid is the price of a small slice. A trading multiple is therefore a price for a minority position in a going concern, quoted by people who can walk away from it before lunch.

A shop in a busy market row makes the same point. Stalls change hands constantly, so there is a going rate for taking over one stall for a season and everyone in the market knows roughly what that rate is. The stall rate is real, it is current, and it says nothing about what somebody would pay to buy the entire row, the parking behind it and the right to decide what gets sold there.

Two more properties of a trading multiple matter for what follows. A trading multiple is remade continuously: this morning's figure is this morning's, and by next month it will be a different figure without anybody transacting at all. And it is observable in quantity: six comparable companies give six readings today and will give six more tomorrow.

What is a precedent multiple a price for?

A completed transaction is a different object. A buyer agreed a price for the whole of a business, the money moved, the transaction closed, and the price is on the record. The enterprise value implied by that price, divided by the target's EBITDA, is a precedent multiple.

The object bought in a completed transaction is different in kind. The buyer did not acquire a slice. The buyer acquired the business entire, and with it every decision the business makes: what to do with the cash it generates, how much to borrow and from whom, who runs it, whether the factory in the second city stays open. A precedent multiple is a price for control of a whole business, agreed once, by one named party, under conditions that no longer exist.

Back to the market row. Somebody bought the entire row eighteen months ago. The price paid for the row is a fact. The price is also a fact about eighteen months ago, about that particular row, and about one buyer who had a reason for wanting it that they never wrote down anywhere.

And the supply of these is thin. Whole businesses in one industrial segment do not change hands weekly. Five completed transactions is a normal set to work with; sometimes it is three. A sixth cannot be produced by refreshing anything.

How big is the gap, and how should it be stated?

Year 0 EBITDA at Sankalp Industrial Systems Limited is Rs 2,88,00,00,000, and both sets get applied to that one denominator, so no further adjustment stands between them and they can be compared directly. Everything below rests on that one fact.

On the trading side there are six listed comparable companies, and their multiples of enterprise value to EBITDA run 6.6, 7.1, 7.6, 8.0, 8.7 and 13.8 times. The medianA middle reading. Half a set stands at or below it and half at or above, and rank is what it reports rather than size. of six is the average of the third and fourth readings, which is 7.8 times. Lay that over Rs 2,88,00,00,000 of EBITDA and the indication comes out at Rs 22,46,40,00,000.

On the precedent side there are five completed transactions, all in the same industrial segment, at 8.6, 9.1, 9.5, 9.9 and 11.4 times. The median of five is simply the third reading, 9.5 times, and applied to the same Rs 2,88,00,00,000 that indicates Rs 27,36,00,00,000. The arithmetic meanTotal a set and share the total equally among its members. Size enters this calculation and rank does not. of the five is 9.70 times, which is close enough to the median that nothing turns on the choice here.

Now the distance. 9.5 against 7.8 is 1.70 turnsThe unit multiples get counted in. Moving something from 9.5 times to 10.5 times is one of them, and what it is worth in money depends wholly on what sits underneath.. As a share of the trading median that is 21.79 per cent. On Sankalp's Rs 2,88,00,00,000 of EBITDA it is Rs 4,89,60,00,000 of enterprise value. The turns, the percentage and the rupee figure are three statements of one measurement, not three measurements.

A figure like this one gets copied without being checked, so it is worth checking both ways round. Multiplying 1.70 by Rs 2,88,00,00,000 gives Rs 4,89,60,00,000. Dividing Rs 4,89,60,00,000 by the trading indication of Rs 22,46,40,00,000 gives 21.79 per cent, the same number the turns route gives. Two roads, one answer.

And here is the part everybody drops. A percentage gap is meaningless until the base it was divided by is stated. The same 1.70 turns against the precedent median of 9.5 is 17.89 per cent. The gap is 21.79 per cent or 17.89 per cent depending on the base, and a figure quoted without its base cannot be compared with anybody else's.

A reader takes colour in before words, so every drawing here uses one colour for one meaning and the whole of the scheme is set out below.

Red is the one worth watching. Red appears exactly once, on the drawing about the split, and it never means loss, error or anything else.

Why does the gap exist at all? Reason one, control

Behind every price in the precedent set stands a buyer who took the entire business. The whole business brings the power to decide with it. Whether the cash generated next year goes into a new furnace, into repaying the term loan or out to shareholders. Whether the borrowing gets refinanced. Whether the managing director stays. Whether the loss-making service branch closes.

A holder of a parcel of listed shares has none of that, and the screen price is a price for exactly that condition of powerlessness. Control is the cleanest of the four reasons: a genuine difference in what is being bought rather than a difference in circumstance.

The household version runs like this. A room in a house can be rented, and there is a going rate for that. The tenant cannot knock through a wall, cannot relet it to somebody else, and moves out if the landlord decides to sell. Buying the house costs more per square foot than renting the room implies, and nobody thinks that is strange. Nobody calls it an anomaly in the rental market.

One qualification that matters. Saying control is inside the gap is not the same as saying how much of the gap it is worth. The amount a buyer pays above an unaffected priceThe level a share stood at while the market still had no idea an approach was coming. for the power to run a business, and how that relates to the discount at the other end, has arithmetic of its own and is covered separately. Control is a cause of the gap; sizing it is a separate exercise.

Reason two: what did each buyer actually want?

Look again at who paid these five prices. Four of the five buyers were strategic buyersA purchaser already running something in the same line of work, and one that keeps what it buys rather than selling it on. already operating in the industry. One, on the lowest multiple in the set, was a financial buyerA purchaser from outside the trade. A financial buyer holds for a period, is measured on what its own money earned over that period, and leaves. that underwrote no savings and claimed none.

Each of those four had a reason for wanting that particular business, and the reasons were not the same reason. One was buying a first manufacturing base in a country it had not made anything in before. One was buying a pure service business quite different in mix from the other four. One found itself in a second round with a rival still bidding. Each buyer's plan for the business afterwards differed from every other buyer's, is disclosed in none of the five, and cannot be reconstructed from a multiple.

Notice the shape of that sentence. Every clause in it is doing real work. The sentence is not saying that synergyWhatever a purchaser reckons two businesses will produce jointly that the pair of them, kept apart, would not. Synergy is a belief held before the fact, not a measurement made after it. is absent. The claim is that whatever was there was different in each case and was never written down. A multiple is a single ratio. Any number of different beliefs about the future produce the same ratio, and once the ratio is in hand the process cannot be run backwards.

The everyday version: four households on one street each paid a different price for the same model of second-hand car. One needed it that week. One knew the seller. One was replacing a car that had died. The four prices can be averaged. The average cannot recover how much of anybody's price was urgency.

Reason three: are the two sets even looking at the same day?

A trading multiple is remade every morning. The figure is today's, whatever today happens to be like. A completed price is fixed at the moment it was agreed and never updates: the conditions that produced it, whatever they were, are sealed inside it.

The two sets are therefore not observing the same conditions, and no adjustment can make them. The precedent multiples can be age-adjusted, and people do adjust them, but every adjustment needs an assumption about how the segment repriced between then and now, and that assumption is exactly as unmeasured as the thing it is correcting.

Tomatoes, in one line. Today's price is on the board at the market this morning. A neighbour's price for a crate last November is also a real price, and a real price about last November.

Reason four: how much rests on six readings and five?

Six continuously priced companies against five one-off observations. The difference is not only about the count. The difference is about whether a set can be looked at again.

Removing one company from the peer set moves the median by exactly 0.20 turns. Which company is removed does not matter: with six readings the median sits between the third and fourth, and removing any one of them leaves five readings whose middle is either the old third or the old fourth. Removing one transaction from the precedent set moves its median by up to 0.20 turns as well. The two moves sound like the same fragility and are not.

The peer median can be re-observed tomorrow; the precedent median cannot. If a comparable company is dropped because somebody argues it is not really comparable, six other companies are still being priced this morning and the argument can be reopened with fresh readings. If a completed transaction is dropped, or if there simply never were more than five, that is the end of it. A missing transaction stays missing, and a stale one gets staler.

There is one asymmetry inside the precedent set worth pausing on. Deal 3 at 9.5 times is itself the middle reading, and removing it shifts nothing: the four survivors have a middle of exactly 9.5 times. Removing either of the cheaper two lifts the middle reading by 0.20 turns; removing either of the dearer two drops it by 0.20. Sensitivity is not spread evenly, so which observation is lost matters more than how many were there to begin with.

Play with it for a moment and the point lands harder than any sentence. Remove one comparable company and one completed transaction, one from each set, and the gap can be made as wide as 2.10 turns, or Rs 6,04,80,00,000, or as narrow as 1.30 turns, or Rs 3,74,40,00,000. One observation out of each of two small sets moves the measured gap across a range of Rs 2,30,40,00,000, and every one of those readings is as defensible as the 1.70 turns the full sets give. That is what working with six and five observations is actually like.

Can the gap be split into a part for control and a part for savings?

The 1.70 turns does not divide into a fixed share for control and a fixed share for expected savings. The obstacle is not that the splitting is difficult. The obstacle is that the record does not support the split, and neither does any published transaction record.

The space between the two medians is a leftover, and a leftover holds everything that differs between two questions, all at once and without internal edges. Control is in there. So are five different buyers' reasons for wanting five different businesses. So is the age of each of the five prices. So is the accident of which six companies and which five transactions ended up in the two sets. The four causes do not queue up in order, each contributing its own measured slice. The causes overlap, they interact, and nothing that has been disclosed distinguishes them.

Here is the domestic version, and it is exact rather than merely illustrative. An electricity bill comes in Rs 900/- higher this month than last. The household bought a second-hand refrigerator, and it was also a much hotter month. How much of the Rs 900/- is the refrigerator? The total is known to the rupee because the meter measured it. Neither part was measured, and the two are not independent: the hotter month made the refrigerator work harder. Somebody who says it was Rs 500/- for the refrigerator and Rs 400/- for the weather has invented two numbers and made them add up to one that is actually known.

What would have to be published before a split could be defended?

The conditions can be stated exactly. A defensible split of the gap would need, for every transaction in the set, three things that none of the five discloses.

None of the five transactions discloses any of the three, and invented substitutes would carry three fabricated numbers into every valuation that relied on them. That is what makes this a position rather than a dodge: the conditions are stated, they are checkable, and if a record ever appeared that carried all three for every transaction in a set, the split would become ordinary arithmetic.

The second row of that table asks for something worth being clear about. An unaffected price is the level a share stood at before anybody in the market knew an approach was coming, and pinning that date down is contested even when the data exists. For a private target there is no share price at all. So the second condition is not merely undisclosed here; for several kinds of target it is not observable in principle.

What makes each set unreliable, and are the two failures alike?

A trading set fails by containing a company that is not really comparable. Peer 6 is the argument, and it was built to be one. At 13.8 times it is an outlierOne member standing a long way from where the rest of its set gathers. Distance by itself is not evidence of a mistake. by a distance, and the four rows below say why.

Whether a company like that belongs in the set at all is a genuine argument with two defensible sides, and it is settled separately. The effect of its presence on the two measures is what matters here.

So what does peer 6 do to the two measures? The mean of the six is 8.63 times; the mean of the other five is 7.60 times. One company out of six shifts the average by 1.03 turns, more than a whole turn. The median of the six stays at 7.8 times however far above the fourth reading that one company sits. Push it from 13.8 times to 30.0 times, a figure no company in this set carries, and the median of the six is still 7.8 times. Absorbing a reading like that is what a median is for.

Now take peer 6 out of the set altogether and watch both measures move. A percentage without its base is not a comparable quantity, so each move below is quoted on its own starting figure.

And look at where the five survivors leave the two measures: 7.6 times on one and exactly 7.60 times on the other. Take out the single company responsible for the drag and the average stops disagreeing with the middle. No demonstration of what peer 6 had been doing to the average is tidier.

A precedent set fails in ways a median cannot absorb. A precedent set fails by containing a price that is not comparable, as deal 5 at 11.4 times might be, a pure aftermarket service business where the other four were not. A set of five also fails by being too small to survive one removal, as the panel above shows directly. And it fails silently through staleness. A trading set refreshes itself and a set of completed transactions does not, so staleness has no equivalent on the trading side at all.

So the checks do not transfer. Choosing a median rather than an average is a real protection against the trading set's characteristic failure and no protection whatever against either of the precedent set's.

Which question is each set the right answer to?

Neither multiple is the correct one. Each is the correct answer to a different question, and the mistake worth avoiding is reaching for whichever one is higher.

A range built from both, with each end labelled by the question it answers, is complete work; a single figure picked from whichever set reads higher is not. A range that is written down carries its label with it. The reader who receives Rs 22,46,40,00,000 to Rs 27,36,00,00,000 with no note about what each end assumes has been given two numbers and no information.

Where does this company sit against both?

Sankalp Industrial Systems Limited has a traded enterprise value of Rs 22,40,00,00,000 against Year 0 EBITDA of Rs 2,88,00,00,000, or 7.78 times. The traded figure sits Rs 6,40,00,000 below the trading indication of Rs 22,46,40,00,000, essentially on the trading median, and Rs 4,96,00,00,000 below the precedent indication of Rs 27,36,00,00,000.

The only claim made about that placement is where the traded figure sits. Not that the company is cheap or expensive. Not that it is undervalued or overvalued. Not that the distance to the precedent indication is an opportunity, and not that anything at all is likely to happen. A traded multiple sitting near a trading median is what routinely appears when a listed company has listed comparables; it is what would be expected, and it is a fact about the arithmetic rather than a finding about the business.

Two things are not true of the Rs 4,96,00,00,000. The distance is not a percentage over the traded figure, and it is not a premium. A premium is measured against a price that was unaffected by news of an approach, an indicated value is not an offer, and neither of those objects is present here. Confusing an indication with a price somebody has actually put on a table is the single easiest way to turn a range into a claim.

Who actually uses this, and for what?

Three people read the same two medians and use them for three different jobs, and none of the three jobs is picking a winner.

The readers of an equity analyst's note on a listed manufacturer are buying parcels, so the analyst works mostly off the trading set. The precedent set appears in the same note as a second reference point, labelled as the level at which control has changed hands in the segment, and the labelling is the whole of the value. An analyst who prints the two numbers without printing what each one prices has produced a range that cannot be read.

A lender sizing borrowing against a business looks at both for a different reason. A lender's security is worth whatever somebody would hand over for the business under pressure, and a pressured sale transfers control rather than parcels. But the lender also knows that a precedent median is thin, aged, and drawn from transactions run under conditions nobody promises to repeat. So a cautious lender anchors on the trading side and treats the distance to the precedent side as headroom that may or may not be there, rather than as collateral it has counted.

A person on the inside of a business uses it in the plainest way of all. If the segment's completed transactions have run at 8.6 to 11.4 times and the business trades near 7.8 times, that says something about the shape of the market the business sits in, and nothing whatever about what the business should do next week. Directors get told this figure regularly. The useful version of the sentence names both sets, both medians and the four things inside the distance, and stops.

And the household version, a familiar exercise. A resident looks up what flats in the building have sold for, and separately hears that a developer bought the whole plot next door for a price per square foot nobody in the building could match. Both figures are real. Neither settles what the resident's flat is worth, and averaging them says less than either one did on its own.

Sankalp Industrial Systems Limited, Aravalli Flow Controls Limited, Satpura Engineering Works Limited, Kaimur Industrial Limited, Girnar Precision Limited, Shivalik Systems Limited, Nallamala Components Limited, Marudhar Valve Industries Limited, Palani Castings Private Limited, Bhima Flow Systems Limited, Chenab Industrial Products Limited and Tapti Service Partners Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.