How Valuation Ranges Inform a Research View

A valuation range shows which sets of assumptions a quoted price can live with and which it cannot. Run backwards, it stops being a range of prices and becomes a range of required growth rates. For Sarvani Coatings Limited at Rs 486/-, exit ratings from 15 to 35 times require earnings growth between 37.59 and 16.14 per cent a year.

Assembling a discounted cash flow, settling on a discount rate and building a comparable set are set out under valuation method, and they are used below rather than reopened. Why no lone number for what a share is worth is produced anywhere in this material is settled separately, and that stance is relied on here. So are the parts a range is made of: the backward arithmetic that turns a price into an assumption, the gap between what a price requires and what a record supports, the two routes a downside travels, what a ratio quietly compresses, how a view is held without being defended, and why two risks can fail independently of each other. The assembly below turns those parts into one written output, and then stops.

What is a valuation range, and what is it a range of?

A range, here, is not a spread of opinions and it is not a margin for error. A range is a set of assumption sets, each one run through exactly the same arithmetic, reported at its two ends. One input is changed, everything else is left alone, and what comes out at each setting is written down. The record of those settings is the whole object.

Which leaves the question everyone skips, and it decides everything that follows. A range of what? The unit chosen for the range decides what a reader is able to do with it, so the unit is settled before a single number is computed. Prices hand the reader a low figure, a high figure and an irresistible middle. Nobody looks at a spread between two prices and reads it as two assumption sets. Readers take a price spread as a soft target with wings, and they take the centre.

Think of a fruit seller pricing mangoes for the week. If she writes on the board that mangoes will be somewhere between Rs 60/- and Rs 140/- a kilo, every customer hears Rs 100/-. If instead she writes that the price depends on whether the Ratnagiri lorries arrive twice this week or once, she has told them the same thing and none of them can average it. Arriving twice and arriving once do not have a middle. The second board carries more information using fewer numbers, and it holds up even when the reader is skimming.

So the range in this guide is a range of required earnings growth. Required growth is the compound rate a company would have to deliver for the quoted price to work out, under assumptions the reader has stated and holds. The rate is a statement about the price, not about the company, and that direction is what keeps the whole exercise on the right side of the line.

What has to be held completely still before anything is varied?

Before a single figure is computed, what is not moving is written down. Not held in the analyst's head, but set out where a reader can see it and disagree with it.

For Sarvani Coatings Limited the held items are four, and one preference. The quoted price is Rs 486/-, illustrative and standing for one date. The published earnings per shareThe year's profit restated to a per share amount. Restated that way, it can sit beside a price. How the restatement is done is settled under earnings per share. for the most recent completed year is Rs 11.58/-. The share count is 24.00 crore. The horizon is five years. And the required returnThe yearly return an analyst sets as a personal threshold, under which the money is better used elsewhere. A preference chosen, not a quantity anybody measures. is 12 per cent a year, a figure that belongs to the analyst and is stated as such everywhere it appears.

The five held items give one figure that never moves again. Rs 486/- compounded at 12 per cent for five years is Rs 856.50/-. Rs 856.50/- is what the share would have to be worth at the end for the required return to arrive. Every number below is that one figure divided differently.

The single varied input is the exit ratingThe multiple of earnings the shares are assumed to trade at when the horizon ends. Which things a multiple compresses is covered under multiples., moved from 15 times to 35 times, and everything else is frozen precisely so that every point in the result can be attributed to that one move. A range built by loosening three inputs at once is wide, and nobody can say which of the three made it wide. A range built that way looks more thorough and is strictly less useful. The one question a range exists to answer, what is driving the spread, has been made unanswerable.

Ten households in a lane all pay different electricity bills. Establishing what the new air conditioner costs to run means comparing two months in one household with the same people, the same rooms and the same tariff. Comparing ten households at once gives a wider spread and says nothing about air conditioners.

How is the range actually built, step by step?

The arithmetic is short enough to do in full, and doing it in full is the point. Rs 486/- at 12 per cent for five years is Rs 856.50/-. At an assumed rating of 25 times, the earnings per share that supports Rs 856.50/- is Rs 34.26/-. Growing Rs 11.58/- into Rs 34.26/- over five years is a compound annual growth rateThe single yearly rate which, applied five times over, turns the starting figure into the ending one. The rate smooths whatever the path actually was into one repeated step. of 24.23 per cent. Change the rating and only the middle step changes.

Two notes on the arithmetic. Both are the sort of thing that quietly corrupts a calculation. First, the 21.45 points is the difference between the unrounded ends, 37.5895 less 16.1422, and it is not obtained by subtracting the two printed figures and hoping. On this occasion the two agree to the second decimal. The agreement is luck rather than method. Second, the per share figure used throughout is the published Rs 11.58/-. Rs 278 crore of profit spread across 24.00 crore shares comes to Rs 11.5833/- a share, and using that instead moves the ends to 37.58 and 16.14. The difference is immaterial here, and it is the kind of gap that becomes material once it is compounded through a longer chain.

Every one of those five rows is a declared choice rather than a measured quantity, and that is stated beside the numbers so that a reader can pick a different span and rebuild it in a minute. Nothing in the record told anyone that 15 and 35 were the right ends. The two ends were chosen because they are wide enough to cover most of what a reader might assume and narrow enough that both ends remain worth printing. A different reader with a different view of where these shares end up rated would draw a different span, and the arithmetic would not object.

Look at the spacing in that drawing before moving on. The spacing is the reason the middle question has a trap in it. Each five times added to the rating buys a smaller reduction in required growth than the five before it. Going from 15 to 20 times takes 7.69 points off the requirement. Going from 30 to 35 times takes only 3.64 points off. The relationship is a division, not a subtraction, so it curves.

What does the record look like drawn on the same scale?

A range with nothing beside it is a decoration. A bare range states what a price would need without stating whether anything like it has ever happened, and a reader can stare at 24.23 per cent all afternoon without learning a thing. The range only becomes a finding at the moment the record is drawn on the same axis, at the same scale, in the same unit.

Four marks go on that axis, and each one needs its period stated beside it. Pairing figures from different periods is how this arithmetic usually goes wrong. Revenue grew 13.9 per cent in the most recent year, being year two to year three. The field these shares sit in grew 11.0 per cent in value over the same single year. The sector volume record runs 2.1, 6.8, minus 1.4, 7.2 and 4.5 per cent across five years, a mean of 3.84 per cent. The mean is a five year figure and a volume figure, and it is drawn as context rather than as a like for like comparison. And profit after tax grew 41.12 per cent, again over one year, year two to year three.

There is a unit problem with three of those four, and hiding it would be worse than naming it. The range is a range of earnings growth. Revenue growth, sector value growth and sector volume growth are not earnings growth. Revenue and the two sector figures only sit on this axis under one stated assumption: that margin holds where it is. Stating that assumption and printing it beside the marks makes the comparison honest. Leaving it out lets the drawing quietly imply something it never established.

The fourth mark, the 41.12 per cent, is the only one natively in the right unit. The profit growth mark is also the only one that clears the whole range. And it is the one mark that cannot be used. The unusable mark is the finding the drawing exists to produce.

Here is why. The 41.12 per cent belongs to a single year in which gross marginWhat is left of revenue once the direct input cost is taken out, shown as a percentage. Every other cost in the business sits below it. rose from 44.0 to 46.0 per cent, a gain of 2.0 points in that one year. Hold the earlier materials ratio of 56.0 per cent against the same revenue of Rs 2,415 crore and gross profit would have been Rs 1,062.60 crore rather than Rs 1,111 crore. Push that Rs 48.40 crore back down the ladder, tax the result at the effective rate the accounts actually show, being Rs 93 crore on Rs 371 crore or 25.0674 per cent, and profit growth for the year comes out near 22.71 per cent instead of 41.12. So roughly eighteen of those forty one points are a level shiftA one off change in a ratio. The shift lifts the base once and then stops. A rate repeats instead, and only a rate can be compounded. rather than a rate.

The period trap is easy to walk into. The 41.12 per cent is a one year number, so the margin gain that belongs beside it is the one year gain of 2.0 points, not the 3.0 point gain measured across two years from 43.0 to 46.0. Repeating the correct one year gain five times brings gross margin to 56.0 per cent. Mistakenly treating the two year 3.0 as an annual rate prints 61.0 per cent, and manufactures five points of margin out of a period mismatch. Either figure is enough to settle the argument, but only one of them is arithmetic.

So what does the picture actually say?

Read it in the order it was built. At every point inside the declared span, including the most generous end, the required growth sits above the growth the record has produced. At 35 times the price still needs 16.14 per cent a year of earnings growth for five years, and the most recent year delivered 13.9 per cent of revenue growth. The three record marks are all below the low end of the range, and the only mark above the high end is the flagged one.

When a record sits below an entire declared range, what has been established is a statement about the price and about the assumptions, and it is never a verdict. The correct sentence is that the quoted price, under a 12 per cent required return, a five year horizon and any exit rating between 15 and 35 times, requires earnings growth this record has not produced without the help of a one off margin gain. The sentence is checkable, it names its assumptions, and it stops.

Push the span further and the crossing point becomes findable. A crossing point is more useful than an open ended statement that the range never reaches the record. Repeat last year exactly, 13.9 per cent with margin held, and earnings per share of Rs 11.58/- becomes about Rs 22.20/- in five years. The same 12 per cent is then met at a rating near 38.58 times. The shares are quoted today at 41.97 times the published earnings. So the price is consistent with another five years exactly like the last one, provided the rating at the end has not fallen by more than about 8.07 per cent from where it sits now.

The condition reads as mild until the thing it is a condition on comes into view. The condition puts almost the whole question onto whether these shares are still rated near forty times in five years. The rating question asks how a market chooses to price a business rather than anything the business does. The arithmetic has not answered the question. The arithmetic has relocated it, and relocating it is the useful work. A question about a rating can be argued about openly, and a vague sense that a price looks demanding cannot.

How wide should a range be before it stops informing anything?

Width is the question everyone waves away, and it has a clean answer. Widen a range far enough and it contains every outcome anybody could name. Nothing is excluded, so nothing has been learned, and the honesty is fake honesty: a range running from 5 to 60 per cent takes no position that could ever be wrong. Narrow it far enough and what remains is a single figure with whiskers drawn on it, pretending to a precision the inputs never had.

A range is informative exactly when at least one of its ends is inconsistent with the record. An end that fails is the only part of a range that carries information. The test is a low bar deliberately. A range is not asked to be right. A range is asked to be capable of being wrong.

The range built above passes that test twice over. Both ends sit above what the record delivered. Passing twice is a stronger result than the test requires, and it is worth saying plainly rather than dressing up: the reason both ends fail is partly that the span from 15 to 35 times was a declared choice, and a reader who thinks these shares end up rated at 45 times would build a span that does not fail at its high end. Which is exactly why the span is printed beside the result. A declared span with its numbers on show can be argued with. A span presented as though the record produced it cannot.

What does all of this actually allow to be written down?

The finished output takes this form. Five parts, in this order, set down on a single notebook sheet.

One, the range and the unit it is in: required compound earnings growth of 16.14 to 37.59 per cent a year over five years. Two, the assumption that was varied and the span it was varied across: the rating assumed at the end, from 15 to 35 times, a span this reader declared rather than derived. Three, everything held, printed: a quoted price of Rs 486/- at one date, published earnings of Rs 11.58/-, 24.00 crore shares, a five year horizon, a 12 per cent required return that is this reader's preference. Four, the record on the same scale with periods named: revenue growth of 13.9 per cent over one year, sector value growth of 11.0 per cent over one year, a five year sector volume mean of 3.84 per cent, and profit growth of 41.12 per cent over one year flagged because roughly eighteen of its points are a one off margin gain. Five, the crossing point and the evidence that would move it: repeating 13.9 per cent for five years needs a rating near 38.58 times against 41.97 today, and the two things that would change this reading are a disclosure separating price from mix in the revenue line, and a share of the field computed on the same base each year.

The written statement above is the finished output, and it replaces the single figure rather than delaying it. The statement is longer for a reason. Every clause in it is either an assumption somebody chose, a figure from the record with its period attached, or arithmetic joining the two. There is nothing in it a reader has to take on trust, and nothing in it that stops being true when the price moves tomorrow. The price is one of the printed inputs rather than a hidden one.

Where does the reading stop, and why exactly there?

The reading stops at the written statement. Not one clause later.

The next thing anybody wants to say is whether 16.14 per cent a year is achievable, or whether a rating near forty times is likely to hold. Both are natural questions and neither is arithmetic. Answering them converts a finding about a price into a view about a company, and that conversion needs three things the arithmetic does not have: the reader's money, the reader's horizon, and the reader's judgement about a business whose margin question the published accounts do not settle.

Stopping here is the completed work rather than an unfinished draft, and the sequence closes on that sentence deliberately. Everything before it was built so that the handover is clean: the assumptions are named and attributed to the analyst who holds them, the record is drawn with its periods stated, the arithmetic joining them is short enough to check, and the point where somebody has to decide is marked rather than blurred. The assumption crosses that line, and the conclusion does not.

The secular trendThe underlying long run rate in a series once the ups and downs of the cycle are averaged out. Separating it from the cycle is covered in the sector material. of 3.84 per cent in sector volumes is a good last reminder of why. The 3.84 per cent sits so far below every point in the range that the arithmetic looks damning, and yet volumes are not revenue, revenue is not earnings, and five years of averages are not a forecast. An account that ended by declaring what all that means about these shares would have thrown away everything that made the working worth reading.