Sum-of-the-Parts: Valuing a Company One Division at a Time

A sum-of-the-parts valuation values each division separately, at its own multiple, and adds the results. Sankalp Industrial Systems Limited, invented, has three divisions worth Rs 10,35,00,00,000, Rs 6,82,50,00,000 and Rs 7,56,00,00,000, less Rs 70,20,00,000 of capitalised corporate cost, giving an enterprise value of Rs 24,03,30,00,000 and an implied blended multiple of 8.34 times.

Begin with something a person can walk around. On one plot at the edge of a small town, a woman runs three things. There is a workshop with four lathes that turns out brass fittings to order. There is a shed at the back where a man and his two sons do rough casting for anyone who brings them a pattern. And at the gate there is a counter that sells spare parts and repairs pumps while the customer waits.

She wants to hand the whole plot over and retire. Somebody offers her eight times last year's profit for it.

Now ask what eight times is saying. The workshop earns steadily, and three factories account for nearly all of its order book, any one of which could change supplier next year. The casting shed is heavy work at thin margins on equipment that was second hand when it arrived. A pump that has stopped working gets repaired at whatever the counter asks that morning, so the counter at the gate never advertises, never chases anybody, and earns more paise on the rupee than the other two put together.

Eight times, applied to all three, says those are the same business. The workshop, the shed and the counter are not one business: they share no customers, no competitors and no reason for existing, and the only things they have in common are a plot number and the woman who signs for all of it. One number for all three is not a summary of the three. One number for all three is an average, and an average of things that were never alike loses information rather than compressing it.

A compound with three sheds holds the whole method. Everything below is the same idea run on a larger company with the arithmetic written out.

What is a sum-of-the-parts valuation actually doing?

A sum-of-the-parts valuation is refusing to average. The refusal is the entire idea, and every complication below comes out of it.

A group with more than one business reports one set of consolidated accounts. Apply one multiple to those consolidated earnings and the result is one number, and that number is a weighted average of businesses that may have nothing to do with one another. Where the businesses really are alike, the average loses nothing and the extra work of splitting them up buys nothing either. Where they genuinely differ, the average has thrown away the very thing that made the group interesting to value.

A sum-of-the-parts valuation puts that information back. The method is to take each segmentA division a company reports separately from the group total. the company reports, value it on its own terms at its own multiple, and add the answers. The method buys back the differences between the divisions, and the price of that purchase is that every division now needs a multiple that somebody has to choose and then defend.

The price is not small, and it is worth naming before any arithmetic starts. A consolidated valuation needs one arguable number. A three division valuation needs three, plus a decision about the costs that sit above all three, for a total of four. Every one of those four can be argued with, and a reader who does not know which four were chosen cannot argue with any of them.

When is valuing a company in pieces the right thing to do?

When three conditions hold at the same time. Not two of them, and not the two that happen to be easy to check.

Condition one: do the divisions really have different economics?

Different economics shows up in the numbers, so it is the condition that gets checked properly. On Sankalp Industrial Systems Limited, invented, the three divisions earn margins of 23.0 per cent, 25.0 per cent and 30.0 per cent, and those are different enough to matter. But margin alone is a weak test. The stronger question is whether the things a valuation actually reacts to differ: how fast each division is growing, how much capital each one has to put back in to keep growing, and how steady the earnings are from one year to the next.

Run the workshop test on it. The counter at the gate earns its margin because a broken pump has no patience and no alternatives. The workshop earns its margin by holding a low price and never missing a delivery for three large customers. Those are completely different reasons for earning money. Two divisions have different economics when the reason each one makes money is different, not merely when the percentages come out different.

Condition two: is there enough disclosed to value each division on its own?

Revenue and earnings are needed for each division, and they have to reconcile to the group. The requirement sounds obvious, and it is where most attempts stop. A company that reports three revenue lines and one profit line has given enough to size the divisions and nothing at all to value them with.

The test is arithmetic. Do the division revenues add to the consolidated revenue, and do the division earnings add to the consolidated earnings? On Sankalp Industrial Systems Limited the first of those reconciles exactly and the second does not. Earnings failing to reconcile is the normal state of affairs, and a whole section below is about it. The condition is satisfied when each division's earnings are visible along with exactly how far they are from the group total, not when the two happen to agree.

Condition three: is there a plausible route by which the pieces could be separated?

Nobody checks the third condition, and it is the one that decides whether the answer means anything at all.

Valuing the three sheds separately assumes somebody could end up with one of them. If the lathes, the casting shed and the repair counter share one electricity connection, one licence, one workforce and one customer contract that covers all three, then nobody is ever going to obtain the repair counter on its own at the repair counter's own multiple. The parts have prices in the arithmetic and no route to existing in life.

The test asks about structure rather than about numbers, and people skip it for exactly that reason. Could a division be sold, listed, spun out or run by somebody else without the other two coming along? If the honest answer is no, then a sum-of-the-parts figure is a price for something that is not available. The third condition asks whether the pieces could be pieces, and a valuation of parts that cannot be parted is careful arithmetic on a hypothetical.

What does it cost to run the method where a condition does not hold?

Not an error message. The absence of one is the difficulty. A build with a broken condition produces a perfectly presentable number with four decimal places and a tidy table behind it, and nothing anywhere in the arithmetic complains.

Taken one at a time, the conditions show what breaks. If the divisions are not genuinely different, the build has done four times the work to reach an answer the consolidated multiple would have given, and it has introduced three chances to be wrong where there was one. The extra work is a waste rather than a distortion, and it is the least damaging of the three.

If the disclosure is not there, the gaps have been filled in by somebody. Somebody had to allocate group costs to divisions, or estimate a division margin from an industry figure, or split a revenue line by judgement. Every one of those is a real decision and none of them appears in the output. The output shows three clean division values and gives no sign at all of how much of them was constructed.

And if the parts cannot be separated, the answer is a price for something nobody can buy. That third failure is both the most common and the quietest of the three, and a failure block further down treats it at length. The method never refuses to run, so a build that fails a condition looks exactly like a build that passes one, and the only thing standing between the two is somebody asking the question out loud.

How does the build run, division by division?

Four lines, three of which are additions. Each division gets its revenue, its margin, the earnings before interest, tax, depreciation and amortisation (EBITDA) that those two produce, and a multiple applied to those earnings.

Here is the whole build for Sankalp Industrial Systems Limited, invented. Every figure below comes from the same invented record and none of it is a market observation. The multiples are choices; where a multiple for a division would be sourced from is covered separately, and the three are taken as given here so that the arithmetic can be seen clearly.

Two things in that bottom row are worth stopping on, and they behave completely differently.

The revenue check passes. Rs 6,00,00,00,000 plus Rs 4,20,00,00,000 plus Rs 1,80,00,00,000 is Rs 12,00,00,00,000, exactly the consolidated revenue of Sankalp Industrial Systems Limited. Revenue reconciles because every rupee a group sells was sold by one division or another, so there is nothing left over for the sum to miss. If a set of division revenues does not add to the group figure, either a division is missing or something has been counted twice, and the build stops until that is settled.

The earnings check does not pass, and it was never going to. Segment EBITDAEarnings before interest, tax, depreciation and amortisation for one division. across the three divisions adds to Rs 2,97,00,00,000. The consolidated EBITDA of Sankalp Industrial Systems Limited, invented, is Rs 2,88,00,00,000. The three divisions have between them produced Rs 9,00,00,000 more earnings than the group reports.

Rs 9,00,00,000 against a consolidated Rs 2,88,00,00,000 is 3.13 per cent, and against the Rs 2,97,00,00,000 of added segment earnings the same amount is 3.03 per cent, so quoting either figure means saying which one it was divided by. On either base, it is small enough to be waved away and consequential enough that waving it away is the most arguable thing a build like this can do. The next section is about what happens to it.

What happens to the cost that belongs to no division?

The cost gets its own line, and that line is a deduction.

Go back to the compound. The woman who runs the three sheds also keeps a small office by the gate. There is an accountant who comes twice a month, an electricity bill for the office itself, a licence renewal, a phone. None of that belongs to the lathes, or to the casting shed, or to the repair counter. The office cost belongs to the fact that all three are one business with one person signing for them.

The office by the gate is unallocated corporate costHead office cost that belongs to no division and has no multiple of its own.. On Sankalp Industrial Systems Limited, invented, it is the Rs 9,00,00,000 by which segment earnings exceed consolidated earnings. Unallocated corporate cost is real money leaving the group every year, and it has one property that makes it awkward: because it belongs to no division, it has no multiple of its own, and every treatment of it is therefore a choice somebody made rather than a calculation somebody performed.

One treatment is used here, and it is a choice rather than a rule. The Rs 9,00,00,000 is capitalisedTurning a recurring annual amount into a single value by applying a multiple to it. at the blended 7.8 times to give Rs 70,20,00,000, and that amount is deducted as a separate line. The logic is that a cost which recurs every year is worth something in the same way an earnings stream is worth something, and if a rupee of group earnings is worth 7.8 times, then a rupee of group cost costs 7.8 times as well.

There is at least one other defensible treatment and it is worth naming. The Rs 9,00,00,000 could instead be allocated across the three divisions in proportion to revenue, reducing each division's earnings before its own multiple is applied, and the answer would come out differently because the three multiples differ. Neither treatment is more correct than the other. The argument between them is covered separately; what matters is that whichever one is used, it is shown.

Which is the reason the deduction gets its own line. Folded into the three division values, Rs 70,20,00,000 leaves an output of three tidy numbers and a total, and a reader has no way of knowing that a decision was made at all, let alone of disagreeing with it. A choice buried inside three division valuations cannot be challenged by anybody reading the output. The most arguable line in the build is precisely the one that has to stay visible.

The two rows above the magnified strip show how little the deduction takes off. Rs 70,20,00,000 against a gross of Rs 24,73,50,00,000 is 2.84 per cent of the gross, or around twenty three pixels at the width drawn here. Smallness of that order is exactly why the deduction disappears from so many builds. The strip at the bottom is the same amount drawn on a piece of the same scale stretched out about twenty one times, and it is the same deduction either way.

What kind of value has the build actually produced?

An enterprise value. Not a share price, not a market capitalisation, and not what the shareholders' claim is worth.

Rs 24,73,50,00,000 gross, less Rs 70,20,00,000 of capitalised corporate cost, gives Rs 24,03,30,00,000. The figure describes the operating divisions of Sankalp Industrial Systems Limited valued as businesses. The divisions are worth that much to everybody who funded them, the lenders as well as the shareholders, and the figure takes no view at all on how the funding is split between the two.

Every one of the three inputs points the same way. Each division was valued on its earnings before interest, before tax, before depreciation and before amortisation, and earnings measured before interest belong to funders of every kind. So the total belongs to funders of every kind too. The earnings a sum-of-the-parts figure is built on have not yet paid anybody, so the figure can only be an enterprise value.

Getting from there to what a share is worth is the same walk as for any other enterprise value, and it is covered separately. The only thing that matters at this point is that the walk has not happened. On this invented company the four lines of that walk net to less Rs 4,40,00,00,000, so anybody quoting Rs 24,03,30,00,000 as though it were the shareholders' number is out by that amount, being 18.31 per cent of the built figure. Two people comparing division-by-division valuations of the same company can be Rs 4,40,00,00,000 apart with neither of them having made a single arithmetic error, purely because one of them walked and the other did not.

What can the implied blended multiple check in one question?

The whole build, without opening any of it. Checking the whole build is why the figure is worth computing, even though nothing in the method requires it.

Take the answer and divide it by the group's own consolidated earnings. Rs 24,03,30,00,000 over Rs 2,88,00,00,000 is 8.34 times. The 8.34 times is the implied blended multipleThe group multiple a divided-up valuation works out to, used as a check on the whole build.: the single number that this four line build has, without ever saying so, decided the whole of Sankalp Industrial Systems Limited, invented, is worth.

Something has happened that is worth marking. The build started by refusing to apply one multiple to the group, went to the trouble of choosing three, deducted a fourth thing, and arrived back at one multiple anyway. Arriving back at one multiple is not a failure of the method. The method is handing over a receipt. Every division-by-division valuation implies a group multiple whether it prints one or not, and printing it turns a four line build into a single claim a reader can accept or reject in one breath.

Now use it. The question is simply whether 8.34 times is a defensible number for this company as a whole. If a reader thinks it is not, then at least one of the three division multiples is wrong, or the corporate cost treatment is, and they have learnt that without checking a single line of the build. If they think it is defensible, the build has passed its cheapest available test and they can go and argue about the individual multiples knowing the total is not absurd.

The comparison a reader will reach for immediately is the group as it actually trades. Sankalp Industrial Systems Limited, invented, carries a traded enterprise value of Rs 22,40,00,00,000, being 7.78 times the same Rs 2,88,00,00,000 of consolidated earnings. The two figures are Rs 1,63,30,00,000 apart, or 6.79 per cent of the built figure and 7.29 per cent of the traded one. Quoting either percentage requires saying which of the two it was divided by, or the number means nothing.

And then it has to stop, and stopping is the hard part. The build and the market have produced two numbers. One of them was constructed from three chosen multiples and one chosen treatment of corporate cost; the other is what a market is producing. A difference between a built number and an observed number is a difference between a built number and an observed number. Whether that difference means anything, and what would have to be true for it to, is covered separately. Both figures stand as they are.

Where does the sensitivity in this build actually live?

In one place, and it is calculable exactly rather than guessable. Move one division's multiple by a full turnOne unit of a multiple, as in one turn of EBITDA. and the answer moves by that division's own earnings. Nothing else about it is complicated.

The reason is that the three division values are independent additions. The valves division is worth its earnings times a number; a turn added to the number adds its earnings once. The other two divisions were not consulted and the corporate cost line did not move. So the whole build is three straight lines added together, and each line's steepness is fixed by the size of the division under it.

Here are the three ladders. In every one of them, only the named division's multiple moves; the other two stay at their locked values and the Rs 70,20,00,000 corporate cost line is completely still.

Ladder one: the industrial valves multiple, on Rs 1,38,00,00,000 of earnings

Each half turn moves the answer Rs 69,00,00,000, so a full turn moves it Rs 1,38,00,00,000, exactly this division's earnings.

Ladder two: the precision castings multiple, on Rs 1,05,00,00,000 of earnings

Each half turn moves the answer Rs 52,50,00,000, so a full turn moves it Rs 1,05,00,00,000, again this division's earnings.

Ladder three: the aftermarket multiple, on Rs 54,00,00,000 of earnings

Each full turn moves the answer Rs 54,00,00,000, this division's earnings. The ladder runs across four turns rather than two. A plausible argument about an aftermarket multiple can cover a much wider span than one about a valve multiple, and the width of that span is an assumption rather than an observation, worth arguing with.

Read across the three ladders and the arithmetic is the same in all of them: the sensitivityHow much the answer moves for a given move in one input. of the answer to a division's multiple is exactly that division's earnings, so the biggest division moves the answer most per turn and there is nothing else to know about it. Rs 1,38,00,00,000 for valves, Rs 1,05,00,00,000 for castings, Rs 54,00,00,000 for the aftermarket division.

So why is the smallest of the three the one to look at hardest?

Because sensitivity is only half of the question, and it is the half that is easy to compute. The other half is how wrong the input could plausibly be, and the two point at different divisions.

Where each multiple comes from is the next question. A multiple for an industrial valve business can be argued about, but the argument has walls: there are other valve businesses, they are visible, and a number well outside their range needs defending. Two turns out, and somebody will ask why. The same is true of castings.

The aftermarket multiple has no such walls. A parts and service operation attached to an industrial group is not a thing that trades on its own in any quantity, so the number applied to it is reasoned rather than observed. Fourteen times can be argued for; so can twelve, and so can sixteen, by people who are all being honest. The valve multiple could plausibly be wrong by about a turn. The aftermarket multiple could plausibly be wrong by two turns in either direction, and that difference is not visible anywhere in the sensitivity arithmetic.

The two multiplied together give something more useful, best named exposureSensitivity multiplied by how wrong the input could plausibly be.: what one turn is worth, times the number of turns the estimate could plausibly be out by. On the ranges assumed here, valves comes to Rs 1,38,00,00,000, the aftermarket division to Rs 1,08,00,00,000, and castings to Rs 1,05,00,00,000.

Look at what that does to the ordering. By sensitivity the aftermarket division is a distant third, worth less than half of what a turn on valves is worth. By exposure it moves up to second, and it passes castings. The gap between them is small: Rs 1,08,00,00,000 against Rs 1,05,00,00,000 leaves Rs 3,00,00,000, and nothing to build an argument on. But the move from third to second is real and it changes where the attention should go.

Two warnings travel with this. The first is that the plausible ranges are an assumption rather than a fact about the world, and somebody who thinks a valve multiple can move two turns gets a different ordering. The second is that the ranges are wide enough to matter a great deal. Moving the aftermarket multiple alone from 14.0 to 12.0 times takes Rs 1,08,00,00,000 off the answer, on its own 66.14 per cent of the entire Rs 1,63,30,00,000 that separates this build from the group as it trades. One input, moved within its plausible range, accounts for two thirds of the whole difference.

What still has to be done to Rs 24,03,30,00,000 before it means anything to a shareholder?

The walk to a shareholders' figure is covered separately, and the size of it is worth knowing even so.

The figure the build produced belongs to everybody who funded the operating divisions. A shareholder in Sankalp Industrial Systems Limited, invented, does not hold that. A shareholder holds what is left after the lenders are satisfied, plus anything the group holds that the three divisions do not contain and did not earn. On this invented company those adjustments net to less Rs 4,40,00,00,000, being 18.31 per cent of the built figure, and every one of the lines behind that amount is covered separately.

The reason this deserves a failure block of its own is that the mistake produces no visible error. A number quoted without a label is still a number. An unlabelled number has the right digits, the right currency and a defensible build behind it, and nothing about it announces that it is answering a different question from the one the reader had. A sum-of-the-parts figure quoted as though it were a shareholders' figure is one of the most common reasons two people comparing division-by-division valuations of the same company find themselves hundreds of crore apart for no reason either of them can locate.