The Margin Build: Forecasting Cost Structure Honestly

A margin build forecasts every cost line from whatever actually moves it and lets the margin fall out at the end. Cost of materials comes from volume and input cost per unit. Employee cost comes from headcount and wage rates. Setting a cost at a percentage of revenue skips the mechanism and assumes the answer. The percentage is the very thing the build was meant to produce.

Underneath the definition sits one small idea. A margin is a ratio, and a ratio has two terms. Each cost line has a quantity of its own and a price of its own, and once those two are forecast the ratio has nowhere left to go: it is arithmetic by then, not judgement. Working in the other direction, from the ratio down to the line, supplies the answer in the first minute of the exercise. Everything after that is dressing.

Why is a margin an output and never an input?

A man selling tomatoes from a cart outside a railway station makes the point. Asked what his margin will be next month, he cannot honestly answer until he has guessed two things: what a crate will cost him at the mandi, and what he will be able to charge a kilo. Each guess can be argued with. Somebody who buys at the same mandi can tell him he is wrong about the crate. Somebody selling two carts down can tell him he is wrong about the kilo. If he skips both and simply says his margin will be about the same as last month, he has still made both guesses. He has just made them silently, and nobody can now argue with either one.

A margin assumption and a cost assumption are the same statement, and only one of the two can be checked against anything outside the model. That is the whole case for building costs from the bottom rather than setting a margin at the top. The cost assumption has a shape somebody can attack: a resin price, a wage settlement, a freight rate per tonne. The margin assumption has no shape at all. The margin assumption is a single number standing in for two prices that were never written down, and when the year comes in differently there is nothing in the file to explain why.

The difference changes what a review conversation can be about. If the build says materials cost per unit of output rises 4 per cent, a colleague can disagree with the 4 and both parties can look at where it came from. If the build says the gross margin holds, the only available disagreement is that it will not. A disagreement about a conclusion rather than about a reason goes nowhere.

How is the cost of materials built from one unit of output?

The cost of materials is units of output multiplied by what one unit of output consumes in bought inputs. Two things move it and there are only ever those two. Make more, and the line grows. Pay more for a litre of resin or a kilo of pigment, and the line grows. Nothing else touches it.

Now put the materials line next to revenue. Revenue is units sold multiplied by realisation per unitRevenue divided by the number of units sold, that is, the average price actually collected on one unit after discounts and rebates. Where realisation comes from, and how a revenue line is built out of it, is settled separately.. Take the ratio of the two, assume for the moment that a maker sells roughly what it makes in a year, and the units cancel. The materials share of revenue is simply input cost per unit divided by realisation per unit. The share therefore moves by the ratio of the two growth rates rather than by their difference.

Sarvani Coatings Limited, an invented maker of paints, makes the point better than any abstraction can. Between year two and year three its cost of materials fell to 54.0 per cent of revenue from 56.0 per cent. The gross margin therefore rose to 46.0 per cent from 44.0 per cent. Volume rose 6.0 per cent and revenue rose 13.92 per cent, so realisation per unit rose 7.467 per cent. Materials cost rose 9.86 per cent and output rose only 6.0 per cent. Input cost per unit is therefore up 3.638 per cent. Put those two into the relationship. 56.0 multiplied by 1.03638, divided by 1.07467, is 54.0 per cent, the published figure to the decimal.

Realisation per unit rose more than twice as fast as input cost per unit, so the gross margin widened even though the price of an input went up. Anybody who reads that two point margin gain and describes it as input prices coming down has the direction of the largest number in the working exactly backwards. The share of revenue fell. The price of a unit of input did not. A share is a ratio, and a ratio can fall in two completely different ways. Only the per unit working separates the two. Reading the share alone cannot do it.

The band is the honest picture of what a gross margin is. A gross margin is not a property of the company. The margin is the vertical distance between two prices set in two different places, one of them by whoever supplies resin and pigment and one of them by whatever the market will bear on a fifteen litre bucket of exterior emulsion. Neither of those two people has met the other. The margin is simply what is left over between their decisions.

Splitting the move into its two halves makes the direction impossible to misread. Take the input cost rise on its own first. 56.0 multiplied by 1.03638 pushes the materials share up to 58.03 per cent, 2.04 percentage points worse than where it started. Then let realisation do its work: dividing 58.03 by 1.07467 pulls the share down 4.03 points to 54.0. The published two point fall in the materials share is a 2.04 point rise and a 4.03 point fall that happen to net out that way, and reporting only the net figure hides the larger of the two moves entirely.

Three settings on that control are worth visiting deliberately. Hold input cost per unit flat and the gross margin climbs to 47.9 per cent, worth Rs 1,157 crore of gross profit on the published revenue. Push it to plus 12 per cent and the margin drops to 41.6 per cent, or Rs 1,006 crore, a difference of over Rs 150 crore on a top line that never changed. Set it to 7.467, matching realisation exactly, and the margin lands on 44.0 per cent and Rs 1,063 crore, last year's margin carried forward untouched. The whole span reachable on that slider is 6.3 points of gross margin, and every point of it comes from one price moving against another.

What actually moves the employee cost line?

Employee cost is headcount multiplied by the average cost of one head. Headcount and cost per head are the whole of it, and the two behave very differently. A company hires a shift or opens a depot rather than adding a fifth of a person, so headcount moves in steps. Increments are annual and apply to nearly everybody at once, so cost per head moves smoothly.

Here is the household version. A house running on two salaries has a grocery bill that follows the number of people at the table and what a kilo of dal costs. The bill does not follow what the two earners were paid that month. If a cousin moves in for a year, the bill steps up and stays up. If dal gets dearer, the bill drifts up for everybody. A step and a drift are two different stories, and a household knows the difference instinctively. A model has to be told.

Sarvani Coatings' year three is a clean example of a line that is following neither of the numbers a lazy build would attach it to. Employee cost climbed to Rs 205 crore from Rs 186 crore, 10.22 per cent more. Revenue rose 13.92 per cent. Volume rose 6.0 per cent. The employee line tracked neither revenue nor volume but sat between them, and a line sitting between them is the signature of a headcount and wage story rather than an activity story. 1.1022 divided by 1.06 is 1.0398, so per unit of output the employee line rose about 4.0 per cent. Four per cent is a plausible increment on a payroll that grew a little. No share of revenue could ever have recovered that number.

What moves other expenses, and what does the disclosure allow to be said?

Other expenses is not a cost line at all. Other expenses is a drawer, and the things in the drawer have nothing to do with one another. Power and fuel follow units produced and a tariff. Freight follows tonnes moved and a rate per tonne kilometre. Advertising follows a decision somebody took in a meeting. Rent follows time and a contract signed years ago. Repairs follow how old the plant is. Travel follows how many people there are and how far they went.

Forecasting the drawer as one thing therefore means forecasting six or eight unrelated behaviours with one assumption, and the only defence for doing it is that the contents cannot be seen. The defence is real, and disclosure decides exactly how honest the work is allowed to be.

Look at what Sarvani Coatings published. Year three shows Rs 460 crore of other expenses. Inside that figure, two items are named on their own: Rs 121 crore against advertising and sales promotion, and Rs 138 crore against freight and distribution. The remaining Rs 201 crore is not broken out at all. Years one and two show a single undivided figure and nothing else. A line disclosed at one level of detail in one year and at a different level in the year before it cannot be trended across the two without saying so out loud, and saying so is the entire content of honesty on this line. The two named items can be built from their own drivers in year three. Year two does not contain them, so neither can be compared with it.

Why are a percentage of revenue and growth at the revenue growth rate the same method?

A great many working models contain both, and their builders believe they have two independent views of the same line. The equality is worth proving rather than asserting. The first method, written out in full, holds the cost at last year's share, so the forecast cost is last year's cost divided by last year's revenue, multiplied by this year's revenue. The second grows the cost at the revenue growth rate, so the forecast cost is last year's cost multiplied by this year's revenue divided by last year's revenue. Both routes use the same three quantities in a different order.

Sarvani Coatings' materials line settles it in rupees. Last year's share was Rs 1,187 crore over Rs 2,120 crore, or 55.9906 per cent. Applied to Rs 2,415 crore, that gives Rs 1,352.17 crore. By the other route, Rs 1,187 crore multiplied by the revenue factor of 1.139151 is Rs 1,352.17 crore. Two methods that agree to the rupee on every line in every year are not two methods, and the agreement is not evidence of anything except that division and multiplication behave as expected.

How large is the error that shortcut makes, line by line?

Sizing it is the only way to know where an afternoon is worth spending. Take Sarvani Coatings' year two ladder, hold each cost line at its own share of revenue, apply each share to year three revenue as published, Rs 2,415 crore, and set every answer beside what the company actually reported. The last column sizes each error against year three earnings before interest, tax, depreciation and amortisation (EBITDA).

The shortcut is nearly harmless on the two operating lines and very large on the materials line, exactly backwards from where modelling effort usually goes. An analyst will spend an hour arguing about whether advertising is 5.0 or 5.2 per cent of revenue, a distinction worth about Rs 5 crore, and pass over the materials line in a minute because a share of revenue felt like a reasonable placeholder. Rs 48.17 crore is nearly ten times the prize on the smaller argument.

Now the part that should end the argument. Hold all three lines at last year's share at once and the EBITDAOperating profit before depreciation, amortisation, interest and tax are taken off. EBITDA is one rung of the published profit ladder, and what belongs in it is settled in the accounting notes rather than here. that falls out is Rs 387.3 crore of EBITDA against published revenue of Rs 2,415 crore, a margin of 16.04 per cent. The 16.04 per cent is year two's margin, to the second decimal. The number could not have been anything else. If every cost is a fixed share of revenue then the sum of the costs is a fixed share of revenue, so what is left over is a fixed share too. The percentage of revenue method does not forecast a margin at all: it copies last year's, and the model then prints that copy back as though it were a result.

What is operating leverage, once it is written as arithmetic?

Operating leverage is not a virtue and not a quality of a business. Operating leverage is a division. If a cost grows more slowly than revenue, then that cost is a smaller share of revenue than it was, and whatever sits below it in the ladder is a larger share. Margin widens. Nothing else has happened.

The household version is a rent. A house paying Rs 18,000/- a month in rent on Rs 60,000/- of income is spending 30.0 per cent of what comes in on rent. If income rises to Rs 70,000/- and the rent is unchanged, rent is now 25.7 per cent of income and the house has 4.3 points more of everything else. Nobody negotiated anything. The rent is a fixed costA cost that does not change when activity changes, at least over the period under examination. A rent, an insurance premium and a licence fee behave this way. Which costs are genuinely fixed and which only look fixed is settled in the cost accounting material rather than here. and the calendar did the work.

Sarvani Coatings shows the same arithmetic in both directions on its two operating lines. Employee cost grew 10.22 per cent against revenue at 13.92 per cent, so its share of revenue slipped from 8.77 to 8.49 per cent and handed 0.28 points to the EBITDA margin. Other expenses grew 13.02 per cent, only just below revenue, so its share slipped from 19.20 to 19.05 per cent and handed over 0.15 points. Added to the 1.99 points the gross margin contributed, those account for the whole of the 2.43 point EBITDA margin gain, with nothing left over and nothing borrowed.

The closure matters more than the parts. Look closely at it. At full precision the three contributions are 1.9947, 0.2850 and 0.1505 points, and they sum to 2.4302, the gain exactly. Round each part to two decimals first and they print as 1.99, 0.28 and 0.15, adding to 2.42 rather than 2.43. Rounding the parts is the commonest way a decomposition that closes perfectly is made to look as though something is missing, so check a margin decomposition before rounding it.

The arithmetic widens a margin whether the reason is good, bad or accidental, so a widening margin is not by itself evidence that anything improved. A cost that grew slowly because a supply contract has not been renegotiated yet widens the margin exactly as much as a cost that grew slowly because a new line runs with fewer people. One of those reverses next year and the other does not, and the margin move looks identical in both cases. The question worth asking is never how much did the margin widen. The question is always why that cost grew more slowly than revenue. A build writes the cost and its driver down separately, and that separation is what makes the question askable.

What does a margin build hand on, and what does it refuse to settle?

A margin build hands on something small and specific: a cost structure for the year ahead, and beside every line the driver it was built from, with units. Rupees per litre of input. Rupees per litre sold. Heads. Rupees per head. Each of those is a sentence somebody can disagree with, and the disagreement lands on one cell rather than on the whole model. The set of statements is the entire product. A build is not a view but a set of arguable statements arranged so that the arithmetic between them is visible.

A margin build refuses more than it hands on. The per unit work on Sarvani Coatings shows exactly what happened between year two and year three: realisation per unit rose 7.467 per cent, input cost per unit rose 3.638 per cent, and the gap between the two is the entire 2.0 point gross margin gain. The same working shows nothing whatever about why. Three explanations fit that gap equally well. Perhaps every maker in the field was able to price ahead of its raw material bill that year, and this company simply went along with the weather. Perhaps Sarvani Coatings priced ahead of the field on its own strength. Or perhaps a mix shiftWhen the blend of what a company sells moves, so that its average price and its average cost both change even though no single product was repriced. How this is read across a business is settled in the sector material. towards industrial lifted realisation and input intensity at the same time.

Only one of the three can be pushed aside, and it is not pushed aside by the per unit arithmetic. The segment reportingThe part of an annual report that splits revenue, and sometimes profit, across the separately identified parts of a business. The rules on what must be reported there, and how far it can be pushed, are settled in the accounting notes. shows the industrial share of revenue moving from 24.06 to 25.01 per cent, a shift of about 0.95 percentage points in the year. A shift that small is nowhere near large enough to carry a 2.0 point gross margin gain on its own, so mix is not the main story. The other two remain, and the published statements contain nothing that tells them apart. The per unit arithmetic settles the what completely and settles none of the why, and any account that pretends otherwise is selling a conclusion it does not have.

Naming what would actually separate them is the honest end of the exercise, and the alternative is a shrug. Gross margins for the same one year across the peer setThe other listed companies a reader compares against, chosen because they face similar demand and similar input costs. How a peer set is assembled and where it misleads is settled in the sector material. would show whether the whole field widened together, and those are not in this record. A realisation series by product, or an input price series, would show whether this company's prices moved differently from everybody's, and the statements do not publish either. Say that the evidence is absent. Do not build a figure that stands in for it.

How does an analyst use a margin build on an ordinary working morning?

Meghna Iyer does not start with a spreadsheet. She starts by writing three cost lines down the side of a sheet and, next to each one, the two things that move it and the units they are measured in. Then she goes looking for those things. Volume, from whatever the company chooses to disclose. An input price, from whatever it says about its raw material basket. A wage increment, from the employee note and the headcount if there is one. Only when that column is full does she open the model, and the model is then mostly arithmetic on numbers she has already argued about.

The second thing she does is mark every cell as one of two kinds: an assumption she chose, or a result the sheet computed. Margins live entirely in the second group. If a margin ever appears in the first, something has gone wrong upstream and she goes and finds it. Marking every cell sounds like housekeeping, and it is the whole discipline.

A lender reading the same company uses the build differently and asks a narrower question. He is not trying to forecast the margin at all. He wants to know how far the margin can fall before interest cover stops working, and a build lets him move one price rather than guessing at a whole margin. Push input cost per unit up until the gap closes, read the EBITDA that falls out, and compare it with the interest bill. A build is worth having less because it predicts well than because it lets one person change one number and everybody else see exactly what that number did.

A household investor who will never open a spreadsheet still gets something from the same shape. When a company reports a much better margin, the useful question is not whether the margin is impressive. The useful question is which of the two prices moved, and whether the answer is in the report at all. Very often the answer is not there. A report that does not contain it shows how much of the story is being taken on trust.