Decision Rules in Valuation: Turning a Range Into an Answer

A decision rule is a written statement, fixed before any number is known, of what gets measured, what it is set against, how far apart the two must be before anything happens, what is then done, and when the rule itself is reopened. A valuation ends in a range; a decision needs one act. The rule is the bridge, and one written afterwards is a rationalisation in a rule's clothing.

Start with a water tank on a roof. The shape is easier to feel before it has rupees attached to it. A household in a building with an unreliable supply decides in January that whenever the tank falls below a quarter full, somebody calls the tanker. The January sentence was written when the tank was nearly full and nobody was anxious. In May the tank drops, somebody looks at it, and the call gets made. Nothing was argued about in May.

Now run the same household without the January sentence. The tank drops in May, four people look at the same tank, and one says it is fine because it always looks lower in the afternoon, one says the tanker is expensive this month, one says the supply is due back on Thursday, and one calls. Every one of those four positions is reasonable. The January sentence did not make anybody smarter; it made the May argument unnecessary, and that is the entire function it performs. A valuation decision rule is that sentence, written for a company instead of a tank.

What is a decision rule, and how is it different from having a view?

A decision ruleA written statement, fixed before the number is known, of what is measured, against what, at what threshold, with what action, and when it is looked at again. is a written statement, settled in advance, that converts a measurement into an act. A decision rule has five terms, and it is complete only when all five are written down. A view has none of that structure. A view is a position somebody holds about a company, and it can be an extremely good position, held by somebody who has read everything and thought hard. A view still does not say in advance what would change it or what follows from it, so a view is not a rule.

The distinction is not about quality of thought but about the order of two events. A rule exists before its inputs; a view can be formed at any time, including afterwards, including in the same sitting as the number it responds to. The one property that separates a rule from everything else that looks like a rule is a date: the rule was written down before the number arrived. Strip that away and what remains is a description of a decision already taken, laid out in the grammar of a rule so it reads like a process.

The same thing turns up everywhere in ordinary life under no particular name. A cricket team that decides at the toss what it will do if it loses three wickets in the first ten overs is running a rule. A team that decides at the fall of the third wicket has a view. Both may play the same shot. Only one of them can say afterwards why it played it, and only one of them can be argued with by a person who was not in the dressing room.

Sankalp Industrial Systems Limited, an invented manufacturer, makes industrial valves, precision castings, and the aftermarket parts and service that go with them. Sankalp is listed, with one subsidiary in Sankalp Coatings Private Limited and one associate in Aruna Tooling Private Limited. Sankalp has been valued four different ways elsewhere. Those four values are taken as given, and the work here is on what turns them into one act.

What are the five terms, and what breaks when one is missing?

Five things, and a rule with four of them is not eighty per cent of a rule. A rule with four terms is an argument with some arithmetic attached. Whichever term is missing is the term that will be settled later by whoever is holding the answer at the time.

Term one is the measureThe single figure the rule looks at, defined precisely enough that two people working separately compute the same thing.: the single figure the rule looks at, defined tightly enough that two people working separately land on the same number. Not the value of the company, and not the worth of the business. Both phrases hide at least three choices. The measure names the method, the perimeter and the basis, so there is nothing left to interpret.

Term two is the comparison baseThe figure the measure is set against, the other end of the comparison, and the easiest term to change without anybody noticing.: the figure the measure is set against. The comparison base gets quietly changed more often than any other term, and it has a section of its own below.

Term three is the thresholdHow far apart the measure and the base must be before the rule does anything at all.: how far apart the measure and the base have to be before anything happens. A threshold of nothing is not a threshold. Two figures built by two methods will never coincide to the rupee. If any difference at all counts, the rule fires on every reading.

Term four is the action: what is actually done, stated as something a named person performs on a named date. Not a conclusion. Not an opinion recorded in a file. A verb with somebody attached to it.

Term five is the review triggerThe event or the interval that sends the rule itself back to be looked at again.: the event or the interval that sends the rule itself back to be reconsidered. Without term five the rule is either permanent or reopened whenever somebody feels like reopening it. Nothing about a changing company supports a permanent rule, and reopening at whim is worse.

What does the committee arrive with before it applies anything?

Four answers for the same invented company on the same day, and they do not agree. Each one is an enterprise valueThe value of the operating business itself, before deciding who has a claim on it, so lenders and shareholders are still on the same side of the line.. Each one therefore values the operating business before anybody asks who has a claim on it, and each one can be read as a multiple of the same Year 0 earnings before interest, tax, depreciation and amortisation (EBITDA) of Rs 2,88,00,00,000. A common denominator lets the four sit on one scale without any further adjustment.

The standalone discounted cash flow gives Rs 21,28,13,79,094, or 7.39 times that EBITDA. The trading comparables, being the peer median applied to the same EBITDA, give Rs 22,46,40,00,000 at 7.80 times. A financial buyer's entry price gives Rs 24,48,00,00,000 at 8.50 times. The precedent transactions, being the median of completed deals, give Rs 27,36,00,00,000 at 9.50 times. The range therefore runs from Rs 21,28,13,79,094 to Rs 27,36,00,00,000, a spread of Rs 6,07,86,20,906, and the traded enterprise value of Rs 22,40,00,00,000 sits inside it.

One line each on why they differ. The full argument belongs with each of the four methods and is set out there. The discounted cash flow is the lowest because it is a standalone valueWhat a business is worth to itself as it stands, with no control, no synergy and no change of funding built into it. with no control, no synergy and no change of funding in it. The trading comparables carry what the market currently pays for a minority stake in similar businesses. A financial buyer funds a large part of the price with debt and deducts the interest against tax, so the buyout entry sits higher. The lift is leverage rather than a better opinion of the business. The precedent set is the highest because every price in it was paid by a buyer taking control.

Year 0 EBITDA of Rs 2,88,00,00,000 is the common denominator under every multiple in that table, and each multiple is that company's enterprise value divided by it. The 2.11 turns on the spread line is the same subtraction expressed in multiples rather than rupees. Every figure is rounded for display and every percentage is computed on the unrounded value. One or two of the percentages will not reproduce exactly when the printed columns are subtracted.

Which single figure does the rule actually measure?

The valuation review committee, an invented body that reviews valuations for Sankalp, fixed term one before any of the four existed. Its measure is the enterprise value produced by the standalone discounted cash flow, computed on the company's own 12.00 per cent weighted average cost of capital, with no control premium, no synergy and no change to the funding mix. The measure comes out at Rs 21,28,13,79,094.

Read that definition again and notice how much work it does. The definition names the method, so the peer median and the precedent median are excluded. The definition names the rate, so nobody can move the answer by re-estimating the cost of capital in the same sitting. The definition names what is left out, so a control premium cannot be quietly added. A measure is well written when a second analyst, handed only that sentence and the underlying accounts, produces the same figure without asking a question.

Compare that with the phrase most people would actually use in a meeting: the value of the company. The phrase does not say which of the four methods, does not say enterprise or equity, does not say standalone or with control, and does not say at which cost of capital. Four unstated choices, and at least a few crore of movement sitting inside each one. The measure is the term that looks trivially easy and is not.

Why is the comparison base the term that gets quietly changed?

Because it is the only term that can be swapped for something equally defensible without changing a single figure anywhere else, and swapping it changes the sign of the answer. Term two is worth slowing down for more than the other four.

The committee's term two is the traded enterprise valueThe same enterprise value measure computed from the observed share price and the balance sheet, rather than from a model., computed the same way on the same day, at Rs 22,40,00,00,000. Set the measure against that base and the base sits Rs 1,11,86,20,906 above it, being 5.26 per cent of the measure. One sentence, one sign, one number.

Now hold that same Rs 22,40,00,00,000 completely still and move only the base. Against the precedent figure of Rs 27,36,00,00,000 the same traded figure sits Rs 4,96,00,00,000 below, being 18.13 per cent. Nothing about the invented company changed between those two sentences, nothing about the day changed, and nothing about the arithmetic is wrong in either one; only the base moved, and the reading went from above to eighteen per cent below.

The everyday version is a shopkeeper's price. A bag of rice at Rs 82/- is above what the wholesale market charged this morning and below what the shop across the road charges, and both statements are true at the same moment about the same bag. Everybody knows a price is only high or low relative to something that has to be named, so nobody is confused by the rice. Valuation works the same way and is far easier to get away with. The bases have technical names and each one has a method behind it.

More than two candidates exist, and the surplus turns the choice of base from interesting into dangerous. Seven figures here could each be called a base with a straight face, and the table below sets the same Rs 22,40,00,00,000 against every one of them. Down the last column the sign changes once and the size changes by a factor of sixty.

Every percentage in that table is the gap divided by the base and not by the measure. Dividing by the other figure changes the number, so the rule has to state that convention as well. Whoever picks a row after seeing the traded figure has chosen the outcome while appearing to apply a process. The base is where the answer was hiding all along, so a rule that does not name its base is not a rule.

Are the average and the midpoint of the four a base?

The average and the midpoint are figures, they are computable, and neither of them is a valuation. Both are enormously tempting and both look neutral, and a rule that reaches for either is usually reaching for something that will not embarrass anybody.

The average of the four is Rs 23,89,63,44,774. The four sum to Rs 95,58,53,79,094, an odd number of rupees, so their average genuinely lands on a half rupee and is printed rounded. The midpoint of the range, being the low end plus the high end halved, is Rs 24,32,06,89,547. The average and the midpoint are Rs 42,43,44,774 apart on the unrounded values, and they differ at all only because the four values are not evenly spaced. The step from the discounted cash flow to the trading comparables is Rs 1,18,26,20,906. The step from there to the buyout entry is Rs 2,01,60,00,000. The step from there to the precedent median is Rs 2,88,00,00,000. The gaps widen further up the scale, so the midpoint of the two ends sits above the average of all four.

A small trap sits in the printed figures. The four numbers averaged were each already rounded, so averaging the printed crore figures gives Rs 2,389.64 crore rather than the correct Rs 2,389.63 crore. Every printed figure is rounded for display and every identity is computed on the unrounded value, and here the difference is visible in the last digit.

The deeper objection is not about rounding. Neither the average nor the midpoint answers a question any of the four methods asked. The discounted cash flow answers what the standalone cash flows are worth at this company's own rate. The trading comparables answer what the market pays today for a minority stake in similar businesses. The buyout entry answers what a leveraged buyer could pay. The precedent set answers what buyers taking control actually paid. The average answers none of those. The average is a fifth number with no method behind it, and it inherits the errors of all four while carrying the assumptions of none.

How far apart is far enough to count?

The committee's term three is a gap of more than ten per cent of the measure in either direction. Ten per cent of Rs 21,28,13,79,094 is Rs 2,12,81,37,909, so the rule does nothing while the base sits anywhere between Rs 19,15,32,41,185 and Rs 23,40,95,17,003.

The gap it actually found was Rs 1,11,86,20,906, being 5.26 per cent. The gap is inside the threshold with Rs 1,00,95,17,003 of room to spare, so the rule returns its first branch. Notice that the rule did not need the gap to be small; it needed the gap to be smaller than a number that was written down before anybody knew what the gap would be.

A threshold has to be stated as a percentage of something, and the something matters. Ten per cent of the measure is Rs 2,12,81,37,909. Ten per cent of the traded base would be Rs 2,24,00,00,000, or Rs 11,18,62,091 wider. On this reading the difference does not change the outcome, but it easily could on another, and a rule that leaves the denominator unstated has left a fourth choice open.

Here is the part that makes the threshold worth a figure of its own. Move the base and keep the same ten per cent, and the set of values the band captures changes completely. Drawn around the discounted cash flow, a ten per cent band reaches from Rs 19,15,32,41,185 to Rs 23,40,95,17,003 and captures three of the five points on the scale. Drawn around the trading comparables it captures four. Drawn around the buyout entry it captures three, but a different three. Drawn around the precedent median it captures one, and it misses the buyout entry by only Rs 14,40,00,000. A near miss that narrow invites somebody to argue the threshold should have been eleven per cent.

What does the rule tell somebody to actually do?

Term four is where most written rules quietly stop being rules. Term four has to name an act, performed by somebody, on a date. Not a conclusion about the company. Not a sentence in a file describing how things look. A verb.

The committee's term four has two branches and both of them are analytical work. Inside the threshold, the work is recorded, the gap is noted with its date, and the matter goes no further this quarter. Outside the threshold, the forecast is reworked with a named second reviewer before anything else happens. Nobody transacts in either branch.

Look at what the second branch does not say. The branch does not say the company is worth more or less than the market thinks. The branch says a second person reworks the forecast. The wording is deliberate. A rule reads that way when the people writing it have accepted that a gap between a model and a price is at least as much a fact about the model as a fact about the price.

Is doing nothing a decision, and does it need its own branch?

Yes, and it is the branch most rules leave out. The null branchThe part of a rule that states what happens when nothing happens, so that inaction is a possible output rather than a failure. states what follows when the arithmetic says nothing much. Leave it out and the rule can only ever produce movement, and the movement then comes from the rule rather than from the evidence.

Think about a doctor's brief. If the instruction says only what to do when a reading is abnormal, a normal reading has no instruction attached to it, and the person holding the chart is left improvising. Add the null branch and the normal reading has an output: note it, date it, see the patient again in six months. Noting and dating a normal reading is a real output, and it is checkable later.

A rule that cannot produce inaction is not a rule but a plan with arithmetic decorating it. Any rule can be tested on that point. The question is what set of numbers would make it do nothing. If no such set exists, or if the person who wrote it has to think for a while, the rule was written to reach somewhere.

There is a second reason the null branch matters, and it is about the record rather than the logic. A rule that fires on every reading generates no information. A reading that mattered can never be told apart from a reading that did not. A rule that returns nothing most quarters and something occasionally has identified which quarters were unusual, and that is worth having on its own.

When is the rule itself looked at again?

Term five names what reopens the rule, and it names it in advance for exactly the same reason terms one to four are fixed in advance. The committee's version says the rule is looked at again if the company changes its funding mix, if the peer set changes by more than one member, or after four quarters, whichever comes first.

Each of those three is an event that would make one of the earlier terms wrong rather than merely inconvenient. A change in the funding mix moves the cost of capital, and the measure is computed at that rate. A change in the peer set moves the trading comparables, one of the figures the committee looks at. Four quarters is the backstop. A rule nobody has thought about for a year cannot then survive on inertia.

Almost every informal process runs the alternative instead, and reopens the rule whenever it seems sensible to reopen it. A review called when it seems sensible is a review called when somebody dislikes the answer, and that is the same defect as choosing the base afterwards, arriving through a different door. If the rule can be reopened at will, it binds only while it agrees, and a rule that binds only while it agrees binds nothing at all.

How is a decision rule different from a hurdle rate?

A hurdle rate and a decision rule are not the same size of object, and treating them as though they are is one of the most common ways a process ends up with four of its five terms unwritten. A hurdle rateA single required rate of return, used as a threshold inside a larger rule. One term, not the whole rule. is one number. The number fixes term three and nothing else.

Hand two analysts the same hurdle and the same company and they can honestly reach opposite conclusions. Everything except the threshold is still undecided between them. One measures a standalone value and one measures a value with a control premium in it. One compares against the traded figure and one compares against the precedent median. One concludes that a report should be written and one concludes that a meeting should be held. Nothing in the hurdle adjudicated any of that.

A hurdle is one term of five. A process that has agreed a hurdle and nothing else has agreed considerably less than it thinks it has. The useful move, when a hurdle is offered as though it settled the matter, is to ask the other four questions out loud. Which figure, computed how. Against what. Leading to what act, by whom. Reopened when. The four questions take about a minute and they are almost never all answerable.

What does the rule say when the range contains the figure it compares against?

Whatever the rule said in advance. The range itself will never say. A range that contains the comparison figure is the straddleWhere the range contains the comparison figure, so the same range supports opposite readings with equal honesty. case, and the straddle is the ordinary case rather than the exception.

The traded enterprise value of Rs 22,40,00,00,000 sits inside the range of Rs 21,28,13,79,094 to Rs 27,36,00,00,000. The statement is true and completely empty. Every point inside a range is inside it. Sitting inside a range is not a finding, and it rules out precisely nothing. The same position is compatible with the reading that the traded figure is above one method and with the reading that it is well below another, exactly as the earlier table showed.

So a straddle is not a problem to be solved by looking harder at the range. A straddle is a problem solved earlier or not solved at all. Once four answers are on the table every one of them is available and each supports a different sentence, so the rule has to have named one base before the range existed.

Who holds the rule, and what does the record of it look like?

Somebody has to be able to produce the rule as a document, and the document has to carry a date and an author. A rule nobody can produce is indistinguishable afterwards from a decision that was made first and described later, whatever anybody remembers about it.

The record has four parts and none of them is optional. Who wrote it. When. The wording of the five terms at that moment. Every change since, with a date and a reason for each. The change log is the part people skip and the part that carries most of the evidential weight. A rule with no history cannot be audited even if every version of it was written in good faith.

The everyday version is a rent agreement. A verbal understanding between a landlord and a tenant about when the rent rises can be perfectly honest and still useless in a dispute. There is nothing to read. The written rule is not primarily a thinking aid. A written rule lets a person who was not in the room reconstruct why a particular act followed a particular number.

What is a decision rule not?

A decision rule is not a forecast. Nothing in the five terms claims to know what happens next, and a rule can be perfectly well written and still return a branch that turns out badly. Judging a rule by whether the outcome was pleasant is judging it on the one thing it never claimed.

A decision rule is not a substitute for the valuation work either. A rule applied to a badly built measure produces a confident act off a poor number, and the discipline of writing five terms does nothing to improve the fourth decimal of a cash flow forecast. The rule sits after the modelling and it is orthogonal to it.

And it is not a source of authority. The committee's ten per cent is a number that committee chose, and it stands here as that committee's choice rather than as a level anybody should adopt. A rule belongs to the committee that wrote it and binds nobody else, and the four values restated above establish nothing about Sankalp Industrial Systems Limited beyond the fact that the traded figure sits inside them.