Re-Rating: When the Multiple Moves Rather Than the Earnings

A re-rating is a change in the multiple applied to unchanged earnings, so the price moves although the business produced nothing different. The two changes multiply rather than add. The multiple alone takes off 9.8 per cent a year, so earnings compounding at 24.2 per cent a year beside a multiple sliding from 41.9689 times to 25 times over five years gives 12 per cent a year.

Two things sit underneath that. How a multiple gets put together out of a price and a profit line had its own treatment in the valuation work, and it is borrowed rather than reopened. The backward arithmetic that starts at a quoted price and reads out the growth hiding inside it came from the valuation application work, and it arrives already carrying its two reader assumptions. The machinery by which a multiple actually moves is a calendar of things that can prompt a revision elsewhere, set out under revision triggers. The movement itself pulls apart from the earnings movement standing next to it, exactly and without a model.

What is a re-rating, and what is the movement in the other direction?

The plainest version of this is visible from a doorway. A vegetable seller brings the same forty kilos of onions to the same corner every morning. On Monday the going rate is Rs 28/- a kilo. On Thursday, with nothing about her onions changed, the going rate is Rs 34/-. The sack did not improve. The buyers changed their minds about the price of the same sack. Her takings rose by more than a fifth and not one gram of that came from her.

A re-rating is that, applied to a share. The market changes the number of times profit it is willing to pay. The company reports the same profit it was always going to report, and the price of the share moves anyway. The business does not have to do anything different for a re-rating to happen. The mistake of reading a re-rating as the business doing something follows directly from that.

The movement runs both ways, and the other direction has its own name. A de-rating is the same event pointing downwards: the same profit, a smaller number of times it, a lower price. Neither is exotic. Neither is a market failure or a mispricing or anything requiring a special explanation. Multiples in ordinary quoted markets move around all the time, in both directions, on companies whose reported results are perfectly steady. A reader who treats them as rare will explain away every occurrence. Treat both as ordinary weather rather than as events.

Do an earnings change and a multiple change add, or do they multiply?

Everything else follows from one line of arithmetic. A price, on this reading, is a profit line multiplied by a number of times that line. So across a period in which both parts have moved, the price has been multiplied twice: once by whatever earnings did, and once by whatever the multiple did.

Say earnings per shareThe profit a company reported, divided across each share in issue. Settled in the accounting material and used here exactly as published. rise by a quarter and the multiple falls by a tenth. The instinct is to reach for subtraction, call it fifteen per cent up, and move on. The subtraction answer is wrong, and wrong in a direction that flatters. The correct operation is one point two five times nine tenths. The product is one point one two five, or twelve and a half per cent. The two changes compound against each other rather than settling their differences.

A strong earnings year sitting beside a falling multiple can leave the price exactly where it started, so the price on its own tells nothing whatever about which of the two happened. A reader who looks only at what a share did over a year, and reasons backwards to the business, is reading a product and attributing all of it to one of its two factors.

How is a price move that has already happened split?

The split is three steps and it never varies. Take the price change across the period. Take the earnings change across the very same period. Divide the first by the second, and whatever is sitting there afterwards is the multiple change. The three steps are the whole method.

The split is an identityA relationship in arithmetic that holds exactly by construction, so it can never come out slightly wrong. Either it ties or an input was mismatched. rather than an estimate, so it ties to the last decimal every single time. There is no model in it, no assumption, nothing to calibrate and nothing to be approximately right about. If the split leaves something over, the arithmetic has not failed. A price across one window has been compared with earnings across a different one, or a reported figure has been used on one side and an adjusted figure on the other, or a bonus issue moved the per share base underneath the calculation. The residualWhatever is left over once every part already accounted for has been taken out. is a message about the inputs and never about the method.

The split is smaller and harder than it looks. Here it runs once, slowly, on stated figures. Sarvani Coatings Limited, an invented maker of decorative paints and industrial coatings, reported earnings a share of Rs 8.21/- in year two and Rs 11.58/- in year three. The rise is 41.05 per cent across one year. Now hold the price completely still across that same year at the illustrative Rs 486/- and ask what the multiple must have done. At Rs 8.21/- a share the price sat at 59.1961 times. At Rs 11.58/- the same price sits at 41.9689 times. The factor is 0.7090, a fall of 29.1 per cent. A rising numerator under a fixed price leaves the multiple nowhere else to go.

Read the three figures once more, slowly. The discomfort is the point. Earnings rose more than forty per cent and the shareholder received nothing at all. Every rupee of the earnings gain was absorbed by the multiple contracting underneath it. Nobody announced that. No filing recorded it. The reported numbers were doing exactly what a shareholder would have hoped. The loss simply happened, in the arithmetic, alongside them.

What actually makes a multiple move?

Nothing inside the company. The honest answer is worth sitting with. A multiple is not usually discussed that way at all. A multiple is not a fact about a business at all, it is a compressed summary of what a set of people currently assume about growth, durability and risk taken together, so it moves precisely when those assumptions move and at no other time.

Unpack the three. Growth is how fast the assumers think the profit line rises from here. Durability is how long they think it keeps rising before something competes it away. Risk is how much they mind being wrong. Minding shows up as the size of the return they insist on before holding the shares at all. Growth, durability and risk are held in other people's heads, and the three are not disclosed, not audited, not filed and not stable. A multiple is what falls out when a market full of them transacts.

A multiple move is therefore an event about an audience. The relevant question is never what the company did on the day, it is what a set of people decided about durability while nobody was watching. No accounting line anywhere records a re-rating. No amount of statement work will ever detect one, and a research process built entirely out of statement work is structurally blind to half of what moved the price.

Why is a view that needs a re-rating a different kind of claim?

Because it has two halves, and only one of them usually gets any work done on it.

Half one is about the business. Volumes hold, realisationThe revenue a maker collects for each unit it sells, before any cost is taken off it. holds, the cost line behaves, the share of the field is defended. The business half is researchable in the ordinary way. There are filings, there are quarterly numbers, there are competitors reporting alongside, and there is a record that can be read. The work is hard, and it is the kind of hard work an analyst is trained for.

Half two is about people. Half two says that a set of investors who currently pay a certain number of times these earnings will, at some point inside the forecast period, agree to pay more. The second half studies a crowd instead of a business, is almost never actually carried out, and leaves a view leaning on it half unexamined by construction. Ask anyone whose case needs a re-rating what evidence they hold about the second half, and the usual answer is a feeling that the shares are currently under-appreciated. A feeling is not evidence. A feeling is the claim restated.

The exercise, worked all the way through

The exercise below is built on figures that exist only to be taken apart. Every result in it is arithmetic on stated assumptions, and arithmetic on an assumption stays an assumption however many decimals it carries.

The starting point comes from the record. An illustrative price of Rs 486/- on the stated date, against published earnings a share of Rs 11.58/- for year three, the twelve months to 31 March. The multiple is 41.9689 times, shortened to 42.0 times wherever a rounded figure reads better. Then two things the reader supplies rather than observes: a required returnThe yearly return a reader decides in advance that they want from holding a share. A preference somebody chooses, never a quantity anybody measures. of 12 per cent a year, and an assumption that the shares carry 25 times earnings at the end of five years.

Run it forwards. Rs 486/- compounded at 12 per cent for five years reaches Rs 856.50/-. At 25 times, that price needs earnings a share of Rs 34.26/-. Getting from Rs 11.58/- to Rs 34.26/- across five years is a factor of 2.9585. AnnualisedA total change across several years restated as the one steady yearly rate that would reproduce it exactly., the factor is 24.2 per cent a year. All of that was settled in the valuation application work and is imported here, not rebuilt.

Now take the 12 per cent apart.

The split ties, and ties exactly rather than nearly. The identity is doing its work. One caution worth printing: the tie only survives if the multiple is carried at the full 41.9689 times that Rs 486/- against Rs 11.58/- produces. Feed the display figure of 42.0 times into the same arithmetic and the five year product comes out at 1.761037 against a required 1.762342, so the reader is left hunting a residual that only ever existed because a rounded number was allowed to become an input.

And now the thing nobody says out loud when this arithmetic is first run. The reader who casually assumed 25 times in five years, against 41.9689 times today, assumed that 40.4 per cent would come off the multiple, and almost certainly never described it to themselves in those words. They thought they were being conservative. They were building a substantial de-rating into the machinery and then asking the earnings line to carry the entire load. The load is exactly why the required 24.2 per cent came out so demanding.

Run it the other way to prove the arithmetic is not a one direction story. Take the worked case for this company: volume growing 6.0 per cent and realisation growing 3.0 per cent across one year. Volume and realisation compound rather than add, so the revenue pace is 1.0918, or 9.18 per cent and not 9.0. Put the revenue pace beside the same slide to 25 times. The annual price change is 1.0918 multiplied by 0.902, or 0.984, a fall of 1.57 per cent a year. Both results are arithmetic on stated assumptions, and changing an assumption changes the result with it.

What does a de-rating feel like from inside?

A de-rating feels like being right and losing money. The combination is the most disorienting in this work.

Follow the second case for five years. Earnings a share compound at 9.18 per cent, so Rs 11.58/- becomes Rs 17.96/-, a rise of 55.1 per cent. Every one of the three variables the worked view depended on behaves. The multiple slid from 41.9689 times to 25 underneath the whole thing, so the price finishes at Rs 449.12/-, down 7.6 per cent from Rs 486/-. Nothing broke. Nobody lied. Gross marginRevenue less what the goods cost to make, shown as a share of revenue. Settled in the accounting material. held where it was supposed to. The audience simply revalued what it was looking at.

The view was not wrong about the business and it was incomplete about the multiple, and those are two entirely different failures that teach two entirely different lessons. Being wrong about the business means the research was bad: the variables were misjudged, the evidence was misread, the competitive picture was wrong. Being incomplete about the multiple means the research was fine as far as it went and simply did not go as far as the claim did. The correction for the first is better analysis. The correction for the second is stating the multiple assumption out loud so somebody can argue with it. Confusing the two costs a year spent fixing something that was never broken.

Why is the exit multiple in the analyst's own arithmetic the same object?

Here is the part that almost nobody points out, and it changes how the earlier arithmetic reads.

The multiple assumed at the end of the analyst's own period is the very same object as the multiple that re-rates, so assuming 25 times in five years against 41.9689 times today is an assumption of a de-rating whether or not the person making it noticed. There is no separate category of number here. The exit multiple is not an input, a convention, a house standard or a modelling choice. A forecast about what a set of people will assume five years from now sits quietly in a spreadsheet cell, wearing the costume of a technical parameter.

Writing it in those words changes what happens next. An exit multiple of 25 times invites no discussion at all. An explicit statement that 40.4 per cent will come off the multiple over five years invites an immediate and useful argument: why would it, on what evidence, and compared with what? Naming the assumption converts an invisible input into a claim that can be attacked. Attack is the only way an assumption ever gets tested.

The crossing is the whole lesson. Below about 27.05 times the combined bar sits under zero even though earnings never stop growing, and above it the bar turns positive. The exit multiple typed in decides the sign of the answer. An input most readers treat as a technicality is quietly deciding the direction of the entire result. Here is that in a row of settings.