Model Assumptions: Naming Them Before Defending Them

A model assumption is a number chosen rather than observed, and a forecast is built almost entirely out of them. Naming each one, saying whose it is, and measuring how far the answer travels when it moves is the whole of assumption discipline. An assumption defended before it has been named is being protected rather than tested.

The reverse arithmetic that runs backwards from a share price to the earnings growth that price contains is worked out under valuation, and it is used below as a ready-made instrument rather than derived again. The published three year record of Sarvani Coatings Limited, an invented paints and coatings maker, supplies every observation the assumptions below sit beside. The four parts of an investment thesis are set out separately. The question here is not what a view is, but what the numbers underneath a view are made of.

What actually separates an observation from an assumption?

Begin with something concrete. A household electricity bill last month came to Rs 3,480/-. The bill is an observation. The bill is printed on paper, the meter reading is on it, and anybody in the household can walk to the drawer and check it. Now next month's budget is written and Rs 3,480/- goes into the electricity row. The number has not changed by a single paisa. The number now points somewhere else. Last month's bill points backwards at something that happened. Next month's row points forwards at something that has not happened yet, and it sits there because somebody decided to put it there, not because anybody measured it.

The direction a number points is the entire distinction, and it survives being scaled up to a listed issuer without any modification. An observation is a figure already sitting in the published record, and its defining property is that a second person with the same record lands on the same figure. An assumption is a number somebody selected. The selection may be superb. The number chosen may be the most defensible one available anywhere. The choice is still a choice, and the person who made it is answerable for it in a way that nobody is answerable for a printed figure.

Now the awkward part, and it catches careful readers rather than careless ones. A published figure becomes an assumption the moment it is carried forward, so Sarvani Coatings Limited's gross marginRevenue less the cost of materials, expressed as a share of revenue. How the two lines are recognised and measured is settled in the accounting material. of 46.0 per cent is an observation about year three and an assumption about year four, and nothing about the number itself changes when its status does. Recomputed, it is Rs 1,111 crore of gross profit on Rs 2,415 crore of revenue, which is 46.0 per cent, checkable by anyone. Typing that same 46.0 into the year four row of a spreadsheet makes a claim about a year that has not happened yet. The cell looks identical. The obligation attached to it is completely different.

The honest question about any cell in a model is therefore never what is this number. The honest question is where did this number come from, and it has exactly two possible answers: the record, or a person.

Whose assumption is it, the analyst's or the market's?

Ownership gets skipped more reliably than anything else, and skipping it changes the reading of the output more than any other single omission. Consider the reverse arithmetic on Sarvani Coatings Limited, built in the valuation material and applied here. The arithmetic takes a share price and a published per share profit, and hands back the annual earnings growth the price appears to contain. The instrument looks, at first glance, like a machine for reading the market's mind.

Look at what actually goes in. The share price of Rs 486/-, illustrative and stated as at the close of year three, comes from the record. The earnings per shareProfit after tax divided by the number of shares in issue. The figure is published by the issuer; how it is computed and what dilutes it is settled in the accounting material. of Rs 11.58/- comes from the record. Price and earnings per share are both observations, and they give a multiple of 42.0 times. Then two more numbers go in, and neither of them came from the record, from the market or from the company. The required returnThe annual return a reader decides they want from an investment before doing any arithmetic. The wanted return is a preference, not a measurement, and different readers state different ones. of 12 per cent a year is a number the reader picked. The exit multipleThe multiple of earnings a reader assumes the shares will carry at the end of the holding period. Where such a multiple might come from is settled in the valuation material. of 25 times is a number the reader picked for what the shares would carry in five years. Both belong to the reader.

The output is therefore not a statement about what other people expect. The output states what the reader's own two picks imply once they are set beside a price, and calling it a market expectation is a misattribution with a name and a cost. The name is simple enough: the authorship of two of the reader's own numbers has been quietly transferred onto a crowd that never chose them. The cost arrives later, when somebody challenges the figure and the defence offered is what the market thinks rather than the two numbers actually picked.

There is a household version of exactly this. A buyer looks at a flat quoted at Rs 90,00,000/-, decides on a 9 per cent annual return, decides it will fetch a certain rent, and arrives at a rate at which the rent has to rise for the price to make sense. The buyer then tells a friend that the market is assuming rents rise that fast. The market assumed nothing of the kind. The buyer assumed a return and a rent, and the arithmetic did the rest. Two of the three inputs came out of the buyer's own head, and the sentence spoken attributed all three to somebody else.

Which assumptions are load bearing, and which are just sitting there?

An assumption is load bearing when the answer moves materially as it moves, and decorative when it does not. The distinction sounds obvious written down. Inside a spreadsheet with sixty input cells it is anything but obvious. The cells all look the same, they are all coloured the same, and a reviewer walking down them spends the same attention on each.

Here is the test run on Sarvani Coatings Limited's year three ladder, and notice that the base is stated before any figure is produced. Move each line by one per cent of its own published value, hold everything else exactly where the record put it, tax the difference at the rate the record implies, and divide by the shares in issue. Every row below is that one operation, repeated seven times.

The top two rows carry about three quarters of the whole response between them. The bottom two together shift profit after tax a share by less than two paise. The other fifty six inputs can be maintained perfectly for a week and change nothing at all, so a model with sixty inputs usually has four that matter, and finding which four is the work. This is not an argument for building a shorter model. The argument is for knowing, before anybody asks, which handful of cells are worth defending in a room and which ones a challenger can be allowed to move.

The shape below is the point rather than any single bar. Sensitivity in a real forecast is almost never spread evenly. Sensitivity piles up on two or three lines and then falls away to nothing, and a reviewer who does not know where the pile is will spend an afternoon on depreciation.

How is one tested without rebuilding the model?

Nothing needs rebuilding. One assumption moves on its own, by an amount stated out loud before the move, and the change in the output is read off. The move and the reading are the entire method, and the whole integrity lives in the stated amount.

Nudging a variable by whatever amount makes the point is precisely how a model is made to say what its builder already wanted it to say. So the size of the move has to be stated and defensible before the move is made. Two per cent is a stated move. A quarter of a point is a stated move. Whatever it takes is not a move, it is a conclusion working backwards, and the giveaway is that the number moved is always the one that produces the desired answer and never the one next to it.

Done properly on the reverse arithmetic, it goes one pick at a time, each move announced first. Holding the exit multiple at 25 times and lowering the required return from 12 per cent to 10 per cent: the growth the price contains falls from about 24.2 per cent to about 22.0 per cent. Putting the required return back to 12 per cent and raising the exit multiple from 25 times to 30: it falls to about 19.8 per cent. Neither of those two moves involved Sarvani Coatings Limited in any way. Nobody visited a plant, nobody read a quarterly filing, nobody learned anything about paint. The headline moved by 2.2 points and then by 4.4 points because a reader changed their mind about what they wanted.

Set that against how much company news it would take to shift the same headline by four points, and the ranking of what deserves scrutiny in a research note reverses. The two lines most worth challenging in that arithmetic are the two the analyst wrote themselves.

Which assumptions hide because nobody ever writes them down?

The dangerous assumptions are almost never the ones in the input tab with a coloured background and a label. The labelled inputs have been argued about. The dangerous ones are structural: they were made by the shape of the model rather than by a number typed into it, and nobody made them on purpose, so nobody wrote them down and nobody can attack them.

Four of them turn up in nearly every forecast. The base year the forecast starts from fixes what counts as normal. The length of the forecast period decides how much of the answer sits in the final year. Holding the share count constant quietly rules out both issuance and buyback. And the one that does the most damage: a cost held as a share of revenue and a cost held as an amount per unit sold are entirely different assumptions that look identical on the screen.

Work that last one through on Sarvani Coatings Limited and it stops being abstract at once. The published year three record has the cost of materials at Rs 1,304 crore on Rs 2,415 crore of revenue, or 54.0 per cent. Now forecast year four on the worked thesis case: volume up 6.0 per cent, realisationRevenue per unit sold. Realisation moves when prices change and also when the mix of what is sold changes. A rise in realisation is therefore not the same thing as a price rise. up 3.0 per cent, so revenue of Rs 2,636.70 crore. Holding materials at 54.0 per cent of that gives Rs 1,423.82 crore, gross profit of Rs 1,212.88 crore, and a margin of 46.00 per cent. Holding materials cost per unit instead gives Rs 1,382.24 crore, gross profit of Rs 1,254.46 crore, and a margin of 47.58 per cent.

Same starting record. Same volume assumption. Same revenue. A difference of Rs 41.58 crore in gross profit, 1.58 points of margin, and about Rs 1.30/- a share, produced entirely by which of two identical looking rules the model was built with. And here is the part that has to be said out loud: holding the cost at 54.0 per cent of revenue is not the neutral option. Holding the cost at 54.0 per cent is an active assumption that input cost per unit rises by exactly 3.0 per cent, in perfect step with realisation, every single year. Nobody chose that. The assumption arrived through the shape of the formula, and it will keep arriving until somebody writes it down as a sentence.

Why does an assumption carry the period of the figure it came from?

Every assumption inherits the period of the figure it was built out of. Carrying a rate across periods without saying so is an unnamed assumption of the worst kind. The danger is that it looks like careful work.

Sarvani Coatings Limited makes this concrete and slightly uncomfortable. Its gross margin ran 43.0 per cent, then 44.0 per cent, then 46.0 per cent across the three published years. So the gain is 3.0 points from year one to year three, and it is 2.0 points from year two to year three. Two true statements, two different periods, and they are not interchangeable in any sentence.

The per unit work sits on one of those two periods only. Between year two and year three, volume rose 6.0 per cent, revenue per unit rose about 7.5 per cent, and the cost of materials per unit of output rose about 3.6 per cent. The three numbers close on each other precisely. Take 56.0 per cent, multiply by 1.036 and divide by 1.075, and the result is 54.0 per cent, the published materials share of revenue in year three. The decomposition works, and it works for a two point move across one year.

The 3.0 points cover two years and the per unit figures cover one, so the decomposition cannot explain the 3.0 point headline. Pairing them produces a sentence that sounds more rigorous than either figure alone while being simply wrong. The year one volume growth is not in this record at all, so the two year move cannot be decomposed per unit at all. The decomposition also leaves something out. Input cost per unit did not fall. Materials cost per unit rose about 3.6 per cent. Realisation outran cost, and that is what improved the margin. Costs coming down would be a different story, leading somewhere different.

What goes wrong when an assumption is defended before it is named?

Something quite specific goes wrong, and the failure feels like competence while it is happening.

The order that works is four steps and it is not decorative. The assumption is written down. Then whose it is. Then what would have to happen for it to change. Only then is it argued for. Reversing the last two produces a defence with nothing underneath it. An assumption argued for before it has been written down leaves nothing on paper for a challenger to put a pen through, so it cannot be attacked. An unattackable claim is not a strong claim. It is an untested one.

The reversal plays out in a room like this. Somebody says the gross margin assumption looks aggressive. The analyst answers with three good reasons the company can hold its pricing: the dealer network, the brand spend of Rs 121 crore, the industrial segment. Everyone nods. The meeting moves on, and confidence in the forecast has gone up. But three things remain unestablished: whether the gross margin was an assumption the analyst made or an output the model produced, which line the model actually holds constant, and what fact arriving next quarter would change it. Three questions, none asked, and the note now carries more conviction than before the challenge.

The teacher's version of the rule: an answer that was never written on the sheet cannot be marked. The same thing said in a model review makes the fix embarrassingly cheap. When challenged on something not yet written down, the analyst writes it down first, in one sentence, and then answers. Writing it down costs about forty seconds and converts a conversation into a test.

What does a written assumption actually look like?

Five fields, and the model becomes reviewable the moment all five are filled in. A number. A unit. A period. An owner, meaning whose choice it was. And a trigger, meaning the observation that would force a change.

Most people who keep an assumption list keep the first three and skip the last two. The last two are what turn a list into an instrument. Without an owner, nobody knows whether they are challenging the company, the market or the analyst. Without a trigger, there is no way to be wrong on schedule: the assumption simply persists, quietly, until the answer it produced looks silly.

Read the last row again. The last row is the structural assumption from earlier, and it has an owner that is not a person. An ordinary assumption list never carries such an entry. Writing it as a sentence is the only thing that surfaces it at all, and that is why it is worth the most.

What two of the reader's own numbers do to the headline

Now put the whole method on one worked instance and keep the observations and the assumptions visibly apart at every step.

The observations first. An illustrative share price of Rs 486/-, stated as at the close of year three. Published earnings per share of Rs 11.58/-. Price and earnings per share give a multiple of 42.0 times, and how that figure was reached is worth pausing on. Profit after tax was Rs 278 crore. The record prints no share count, but 24.00 crore shares is the count that reproduces both published per share figures. Rs 1,486 crore of net worth over 24.00 crore shares rounds to the published Rs 61.92/- of book value. Rs 278 crore over the same count gives Rs 11.5833/-, and that rounds to the published Rs 11.58/-. Run the multiple on either version, the published Rs 11.58/- or the exact Rs 11.5833/-, and it is 42.0 times to one decimal. Rounded inputs frequently do not agree, so the agreement is worth checking rather than assuming. When they do not agree, the absolutes are the right ones.

Now the two assumptions, both the reader's. A required return of 12 per cent a year. Shares valued at 25 times earnings at the end of year five. Rs 486/- grown at 12 per cent for five years is Rs 856.50/-. Divided by 25 that means the earnings per share in year five has to be Rs 34.26/-. Getting from Rs 11.58/- to Rs 34.26/- over five years takes about 24.2 per cent a year in earnings growth. The 24.2 per cent is the implied growthThe earnings growth a share price contains once a reader has stated a required return and an exit multiple. How the arithmetic is derived is settled in the valuation material., and it is the sentence people repeat.

Then move one pick at a time, announcing each move first. Hold the exit at 25 times and take the required return down to 10 per cent: about 22.0 per cent. Put the required return back to 12 per cent and take the exit multiple to 30 times: about 19.8 per cent. Neither move involved Sarvani Coatings Limited. The sentence the price appears to assume roughly 24 per cent growth is true only with both of the reader's picks attached to it, and repeating it without them converts the reader's own arithmetic into a claim about other people.

Now the load bearing test on the model itself, with the base stated before the figure. On year three revenue of Rs 2,415 crore, shifting the gross margin line by a single point changes gross profit by Rs 24.15 crore. The effective tax rateTax charged divided by profit before tax. Where the rate itself comes from is a matter for the tax law and the accounting material. in the record is Rs 93 crore on Rs 371 crore, which is 25.07 per cent rather than the 25.1 per cent that gets printed, so the after tax figure is about Rs 18.10 crore. Divided by 24.00 crore shares, one point of gross margin is worth about Rs 0.75/- a share. The rounded 25.1 per cent instead gives Rs 18.09 crore. The difference is small here and not always, so the absolutes are the right place to start.

The base is part of the assumption rather than context for it, so it belongs in the statement explicitly. The Rs 0.75/- is computed on year three revenue. The same point computed on a forecast year with more revenue in it gives a larger figure, and quoting the two against each other as though they measured the same thing is one of the quieter ways a sensitivity table becomes misleading.

Where did every figure here come from, and where did none of them come from?

Every rupee, percentage and share count in this guide belongs to Sarvani Coatings Limited, a maker of paints and coatings. The price of Rs 486/- carries an as-of stamp of the year three close. The 12 per cent a year the reader wants, and the 25 times the shares are put on at the end, are picks the reader made rather than figures anybody estimated. Where a figure could have been reconstructed from a rounded percentage, it was computed from the published absolutes instead: the effective rate is Rs 93 crore over Rs 371 crore, and the share count is stated and then checked forward against both published per share figures rather than back-solved from either.