How to Build a Sum-of-the-Parts Valuation

Six steps. Pull segment earnings out of what the company actually publishes, settle what happens to the head office cost that sits under no division, choose a multiple for each division and write down its defence, add the pieces and test the blend they imply, ask whether a holding company discount is established, then bridge to equity. Steps two and three carry the judgement.

The addition at the end is the part everybody can do. Two things before it are not, and a procedure earns its keep by making both of them visible rather than by making the arithmetic tidier. The first is that division earnings almost never add up to the group's earnings, and the shortfall is a real cost that has no division to sit under and therefore no multiple to be valued at. The second is that no listed business consists of exactly one division of somebody else's group, so a division multiple cannot be looked up anywhere. A division multiple can only be argued for.

What are the six steps, and which of them are hard?

Consider a household that runs three small shops out of one rented office. The rent, the accountant and the phone line serve all three shops and belong to none of them. Working out what each shop is worth on its own is an afternoon of addition. Deciding what to do about the rent takes longer, and deciding what a sweet shop with a loyal street is worth compared with a hardware shop with none takes longer still. The order of the six steps exists so that both of those judgements are made and written down before the addition, rather than discovered afterwards when the total already looks settled.

Sankalp Industrial Systems Limited, an invented manufacturer, runs three divisions. Here they are with what the company publishes about each. The whole build below uses these figures and nothing else.

Two of those totals are worth pausing on before anything else happens to them. Revenue adds to Rs 12,00,00,00,000, the consolidated revenue line exactly. Earnings add to Rs 2,97,00,00,000, and the consolidated earnings line for the same year is Rs 2,88,00,00,000. One of those two reconciliations holds and one does not, and the one that does not is where the method actually begins. All the figures relate to the same base year.

What does step 1 actually produce?

Step 1 arrives at segment earnings from what a company publishes. Put honestly: what disclosure hands over is what there is to take, not what an analyst would have asked for. Segment reportingThe requirement that a group publish figures for its separately managed parts as well as for itself as one whole. normally hands over revenue by division and some measure of division profit, along with a note reconciling that profit measure back to the group's reported line. A segment note rarely hands over a clean, fully loaded profit for each division that would stand up on its own if the division were sold tomorrow.

Segment earnings are not being built from first principles; the work is reading a disclosure that was prepared for a different purpose and deciding how far each line of it can be trusted. Two practical consequences follow. The first is that the division profit measure in a segment note is whatever management uses to run the business. Management's measure is a legitimate choice, and not necessarily the measure a buyer would price. The second is that the reconciling item in that note, the line that bridges division profit to group profit, is not an inconvenience to be tidied away. The reconciling item is the most informative number in the whole disclosure, and step 2 exists entirely because of it.

So step 1 finishes with two things written down: a revenue figure and an earnings figure for each division, and a note of exactly which measure of earnings is in hand. For Sankalp Industrial Systems Limited the measure is earnings before interest, tax, depreciation and amortisation (EBITDAProfit measured before interest, tax and the two write-down charges, so businesses with different borrowing and different asset ages can be lined up against each other.), so the three division figures are Rs 1,38,00,00,000, Rs 1,05,00,00,000 and Rs 54,00,00,000, on margins of 23.0, 25.0 and 30.0 per cent respectively.

What is the first check, and what does it find?

The addition is run against the consolidated line before anything is valued. Revenue behaves: 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, the group figure to the rupee. Earnings do not. Stacked, the three division figures total Rs 2,97,00,00,000. The group reported Rs 2,88,00,00,000. Head office cost of Rs 9,00,00,000 stands between those two totals, it is paid every year, and no division carries any of it.

The gap works out at exactly 3.125 per cent of consolidated earnings, taking the Rs 2,88,00,00,000 group line as the base. No rounding produces a difference that big, and nothing that small looks alarming either. A cost of that size gets absorbed precisely because it looks harmless. The two drawings below belong together. On a true scale the difference is a sliver no eye would notice, and on a scale that starts near the figures themselves it is unmissable. Both pictures are of the same Rs 9,00,00,000, and the reason the check has to be run as arithmetic rather than eyeballed is the left panel.

Why does head office cost have no multiple of its own?

Step 2 starts here, with a question that reads as hair splitting until it is followed through. A multiple is a claim about what a stream of earnings is worth. A valve business is valued at 7.5 times because of an assertion that a rupee of valve earnings, repeating and growing as valve earnings do, is worth seven and a half rupees of capital. The head office produces no earnings. It eats them. Not one of the three divisions has economics that could price a line which only consumes, so each treatment set out below is a fallback rather than an answer.

The absence of an obvious answer is exactly the condition under which people invent a convention and then forget it was invented. The head office question matters more than it first appears for that reason. All three of the treatments below are described as standard practice by somebody. None of them is wrong. None of them is settled either, and the difference between saying so and not saying so is the difference between a valuation a reader can interrogate and one that has to be taken on trust.

Treatment A: what does capitalising the cost once do to the answer?

The first treatment leaves the three divisions exactly as they are, values them at their own multiples, adds them, and then subtracts the head office as a single capitalised line at the end. The gross sum of the three divisions is Rs 10,35,00,00,000 plus Rs 6,82,50,00,000 plus Rs 7,56,00,00,000, being Rs 24,73,50,00,000. Capitalising the head office line, all Rs 9,00,00,000 of it, calls for a rate of 7.80 times. The rate used is the peer medianThe middle reading in a lined-up set of similar quoted businesses, which one extreme member of the set cannot drag away from the centre. for this manufacturer's quoted comparators and is taken here as given rather than rebuilt. Capitalising at that rate gives Rs 70,20,00,000, and deducting it leaves Rs 24,03,30,00,000.

Treatment A says the head office is a group-level burden and should be valued at a group-level multiple. The position is defensible precisely because it refuses to pretend the cost belongs anywhere in particular. Its weakness is the mirror image of its strength: 7.80 times is a multiple built from businesses that all have head offices of their own, so it is a reasonable stand-in rather than a measurement. Treatment A is the reference answer that every comparison below is measured against.

Treatment B: what changes if the divisions carry the cost themselves?

The second treatment says the head office exists to serve the divisions, so the divisions should carry it. Split the Rs 9,00,00,000 across them in proportion to revenue, reduce each division's earnings by its share, and then value each reduced division at its own multiple. Revenue shares of 50.00, 35.00 and 15.00 per cent give allocations of Rs 4,50,00,000, Rs 3,15,00,000 and Rs 1,35,00,000, and those three add back to the whole Rs 9,00,00,000.

Treatment B has one property no other treatment has. Because the head office has been pushed into the divisions rather than left outside them, the earnings it values add to the consolidated line exactly. The exact tie is a real argument in its favour, and it is why careful people reach for it. Its weakness is the allocation basis. Revenue is one basis. Headcount is another, assets employed is a third, and management time is a fourth that nobody can measure. Each produces a different answer, and none of them is a measurement of anything.

Treatment C: what does a build produce when nobody decides at all?

The third treatment is not really a treatment. Treatment C is what a build does by default when nobody runs the reconciliation at step 1: add the three divisions, get Rs 24,73,50,00,000, and stop. The head office never appears because nobody ever looked for it. Leaving the cost out puts a valuation on a manufacturer that has no head office, and that is not the manufacturer being valued.

The reason treatment C is the serious one deserves precision. The head office cost is not a modelling nicety. The cost is rent, salaries, an audit fee and a legal department, all of them paid in cash every year and all of them continuing under any owner. A valuation that quietly assumes them away has not made a defensible judgement badly; it has failed to notice that a judgement was required.

What do the three answers look like side by side?

Read the scale at the bottom of that drawing before reading the panels. Treatments A and B are the two positions a review meeting will actually argue between. Measured against treatment A, at 0.12 per cent, the distance separating them comes to Rs 2,92,50,000. Nobody argues for treatment C because nobody chooses it, and it sits Rs 70,20,00,000 above treatment A, or 2.92 per cent of the same base. Dividing one by the other, the omission is worth exactly twenty four times the argument.

Why is the argument between the two treatments worth so little?

Here is the arithmetic that settles it, and it is worth working through slowly because it turns a methodological argument into a number. Under treatment B, the Rs 4,50,00,000 allocated to valves is removed from earnings valued at 7.5 times, so it takes Rs 33,75,00,000 of value with it. The Rs 3,15,00,000 allocated to castings is removed at 6.5 times, taking Rs 20,47,50,000. The Rs 1,35,00,000 allocated to the aftermarket division is removed at 14.0 times, taking Rs 18,90,00,000. The three removals add to Rs 73,12,50,000.

Rs 73,12,50,000 divided by the Rs 9,00,00,000 of head office cost is 8.125. Allocating the head office across the divisions by revenue is arithmetically identical to capitalising the whole of it at 8.125 times, so the entire argument between treatments A and B is an argument about 0.325 of a turnTraders count multiples in these. Repricing something from eight times earnings up to nine times has moved it by exactly one.. Reach the same 8.125 from a different direction and the reason shows itself. Take the three division multiples and average them, weighting each by its share of revenue: 7.5 weighted at 50.00 per cent plus 6.5 at 35.00 per cent plus 14.0 at 15.00 per cent. Allocating a cost by revenue and then valuing at division multiples always resolves to capitalising it at a revenue-weighted multiple, whatever the numbers happen to be.

So the two candidate multiples for the same Rs 9,00,00,000 are 7.80 and 8.125. A third of a turn separates them. A third of a turn applied to Rs 9,00,00,000 is Rs 2,92,50,000, and there the matter ends. The argument is real, both sides are defensible, and it decides roughly a tenth of one per cent.

Push the control all the way to 14.0 times and the deduction reaches Rs 1,26,00,00,000, leaving Rs 23,47,50,00,000. Rs 1,26,00,00,000 is therefore the entire range this decision can produce, being 5.24 per cent when treatment A is the base, or 2.33 turns of the aftermarket multiple. Making the head office question cost as much as two turns of error on one division would mean capitalising it at 12.0 times, and nobody has ever proposed that. The reason to run the control is not to find a better treatment; it is to see the size of the whole question before spending an afternoon inside it.

What must a division multiple be defended against?

Step 3 decides the answer, and it starts from an uncomfortable fact. The third division of Sankalp Industrial Systems Limited is its aftermarket arm, selling parts and selling service. Nothing listed consists of exactly that description, so no multiple for such a business can be observed anywhere. Every multiple available to look up belongs to a company that is a mixture of something, and the division being valued is a different mixture. So the multiple cannot be measured. The multiple can only be argued for, and an argument has parts.

The first defence is naming: which businesses, or which completed purchases of a whole business, involved only that kind of activity. A precedent transactionA completed purchase of a whole business, read afterwards as evidence of what one buyer was actually willing to pay for something of that kind. is often more useful than a quoted comparator. A purchase of a stand-alone aftermarket business is closer to the division being valued than a quoted group that happens to have an aftermarket arm.

The second defence is resemblance, and it has to be resemblance on the things that actually drive a multiple: growth, margin and capital intensityHow much money has to sit inside a business, in plant and stock and receivables, for every rupee of sales it produces.. Two businesses described by the same industry word can be entirely different on all three. The third defence is stating each adjustment made for the differences, in direction and rough size, out loud rather than buried inside a number.

The fourth defence is saying what the answer becomes if the multiple is wrong by two turns, and it is simultaneously the cheapest of the four to produce and the one most reliably absent. It takes a single line. On the third division here it reads: two turns down, from 14.0 times to 12.0, removes Rs 1,08,00,00,000 and leaves Rs 22,95,30,00,000. The two-turn line converts an input nobody can verify into a stated range, and a stated range is the only honest form the input has.

Why does the smallest division deserve the most attention?

The aftermarket parts and service division is the smallest of the three by revenue and by earnings. The aftermarket division is also the one whose multiple is furthest from anything that can be looked up, and it is where the value quietly concentrates. One column of the next drawing, followed from left to right, makes the point on its own.

Revenue puts the aftermarket division at 15.00 per cent of the manufacturer; value puts it at 30.56 per cent, so the least verifiable number in the whole build is doing roughly twice the work its size would suggest. Two turns on it moves the answer Rs 1,08,00,00,000, or 4.49 per cent of treatment A. Set that against Rs 2,92,50,000, being 0.12 per cent of the same base, for the entire head office argument, and the ratio is close to thirty-seven to one.

Be careful about what that does and does not say. Two turns of error on the valves division would move the answer Rs 2,76,00,00,000, larger still, simply because valves carry more earnings. The reason attention belongs on the aftermarket multiple is not that a turn there is worth more; it is that 14.0 times is the multiple furthest from anything anybody has observed, so an error there is the one most likely to be present and least likely to be noticed. Exposure is one thing and the chance of being wrong is another, and a defence has to consider both.

What does the implied blended multiple establish?

Step 4 is the addition and the check that goes with it. Take the answer, Rs 24,03,30,00,000, and divide it by the consolidated earnings the whole manufacturer actually reported, Rs 2,88,00,00,000. Dividing gives 8.34 times, the multiple the whole build implies for the group as one thing. A reader who has never opened the working can now test the entire valuation with one question: is 8.34 times a defensible figure for this manufacturer as it stands?

How the check behaves against the three treatments shows what it is sensitive to. Treatment A implies 8.34 times, treatment B implies 8.33 times, and the check cannot really tell them apart. Treatment C implies 8.59 times, visibly different. And an aftermarket multiple of 12.0 rather than 14.0 implies 7.97 times, different again. The blend check is nearly blind to the argument people have and clearly sensitive to the two things nobody checks, and that is exactly the property a sanity test needs to have.

One honest limit. The check can fail a build but it cannot confirm one. An implied blend that looks perfectly reasonable is entirely consistent with three division multiples that are each wrong and happen to offset one another. The blend check is a cheap test that catches a class of error, not a proof.

What is a holding company discount, and why does this build apply none?

Step 5 asks a question that has to be asked and, on this manufacturer, has to be answered with a refusal. Where the pieces of a group sit inside one listed structure that cannot easily be taken apart, a shareholder cannot get at the pieces separately even though the valuation has just priced them separately. A further reduction is sometimes applied to reflect that, and it is usually called a holding company discount.

Nothing in the record for Sankalp Industrial Systems Limited establishes such a discount for this structure, so this build applies none, names the adjustment, and stops there. Refusing is not fastidiousness. A build like this one gets reused: the Rs 24,03,30,00,000 travels into other work, gets compared against other figures, and becomes an input somebody else relies on. A discount invented here because such discounts are common would ride along inside every one of those uses, carrying no evidence at all and looking exactly like a measured adjustment.

How does the sum become an equity value?

Step 6 is the shortest of the six steps, and its shortness is deliberate. Rs 24,03,30,00,000 is an enterprise valueA price put on the trading business itself, sized so that it would satisfy every funder holding a claim over it, lenders as much as shareholders.. Every funder has a claim on that figure between them, and none of them holds it alone, so it is not what a share is worth. Getting from one to the other means adding cash and anything the forecast never earned from, taking out borrowings, and taking out the slice of a subsidiary the group does not hold, the minority interestWhere a parent holds most of a subsidiary but not all of it, somebody else holds the rest, and their portion of profit runs through the group accounts and has to come back out..

The bridge to equity is identical for a sum-of-the-parts answer and for any other enterprise value, so it belongs with enterprise value rather than with this method. Saying out loud that Rs 24,03,30,00,000 is an enterprise value is the discipline worth keeping. The single most damaging thing a reader can do with a number like this is treat it as what the shares are worth.

What does a finished valuation have to say out loud?

Four sentences, and a build that carries them can be argued with while a build that does not has to be trusted instead. Name the three division multiples. Name the treatment of head office cost. State the implied blended multiple. State what two turns on the most sensitive division would do.

Without those four lines a reader cannot separate which part of Rs 24,03,30,00,000 is the manufacturer and which part is the analyst, and that separation is the only thing that makes a valuation reviewable. The four lines take about ten minutes to produce, and all four are already sitting in the working by the time step 4 is done.

Sankalp Industrial Systems Limited is invented.
Educational material. Not advice on any investment, tax, budget or market position.