Every valuation method takes uncertain inputs and multiplies them together, so the output is a band rather than a figure. The habit worth building is refusing to collapse it.
9 min read · Level 3
There is a reasonable objection to everything above, which is that ranges are how analysts avoid being wrong: produce a band wide enough and you can never be caught out, and a decision still has to be made at a single price. That objection has force, and the answer to it is not to collapse the range but to commit to a point inside it in advance, in writing, with the reason. What makes a point estimate dangerous is not its singularity - it is that nobody ever records which assumptions produced it, so when the asset disappoints there is nothing to learn from. A range with a stated buying price is falsifiable in a way that a bare number never is: you can go back, find the assumption that broke, and be better at the next one. The uncomfortable implication is that the value of doing a valuation lies mostly in the record it leaves, and rather less in the number it produces.
Valuation is the attempt to say what something is worth, as distinct from what it currently costs. The two are different questions and only one of them is knowable: the price is a fact that anyone can read, and the value is an estimate that a person has to build.
Every method for building it shares a shape. You take something the business produces - earnings, cash, rent - and combine it with a judgement about how long it continues, how fast it grows, and what return you require for taking the risk. Each of those inputs is uncertain. Multiplied together, the uncertainties do not cancel; they compound.
So the honest output of a valuation is two numbers with a space between them. A single figure is not a more precise answer to the same question. It is an answer to a different and easier question, which is what number would make the decision feel settled.
Because the size of the range is itself the most useful thing the exercise produces. A band you could drive a bus through tells you the asset's worth depends almost entirely on assumptions you cannot check, which is a genuine finding about the asset rather than a failure of the analysis.
And because a single number invites the one behaviour that reliably loses money: paying near the top of it. A range makes the question concrete - where in this band am I buying? - and that question has an answer you can act on. A point estimate hides it completely, which is exactly why point estimates are so popular.
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A small business generates roughly a million dollars a year that its owner can take out.
Suppose the honest uncertainty on that figure is ten percent either way: somewhere between 900,000 and 1,100,000. And suppose businesses of this kind change hands at somewhere between eight and fourteen times that number - a spread that is entirely ordinary, and depends on the buyer, the year and how dependent the business is on its owner.
The low corner is 900,000 times 8, which is 7,200,000. The high corner is 1,100,000 times 14, which is 15,400,000.
The top of that band is 15,400,000 divided by 7,200,000, or 2.14 times the bottom. Two inputs, each individually reasonable, and the answer more than doubles across the range.
The central estimate is 1,000,000 times 11, which is 11,000,000. Now watch what a single number costs. Buying at the top corner, 15,400,000, means paying 4,400,000 more than the central estimate - 40% of it - and everything has to go right merely to break even against your own best guess. Buying at 9,000,000 is 18.2% below the central estimate and 25% above the bottom corner: it leaves room for the estimate to be wrong in the direction estimates usually turn out to be wrong.
None of that analysis required a better model. It required not throwing the range away.
The first mistake is confusing precision with accuracy. A valuation that concludes 11,283,400 is not more careful than one that concludes 'somewhere between seven and fifteen million'; it is less honest, because the extra digits were produced by arithmetic rather than by knowledge.
The second is treating price as evidence of value. The price is what a different person concluded, under different circumstances, possibly under pressure to act. It is information about them, not about the asset.
The third is anchoring the range on the number you first heard. An asking price, a previous round, a headline figure - each of these quietly becomes the centre the band is built around, and the work then consists of justifying it rather than testing it.
The fourth is producing a range and then ignoring it at the moment of decision, which is the commonest failure of all. A band that has no effect on the price you are willing to pay was a writing exercise.
For each input, write the lowest and highest figure you would defend to somebody who disagreed with you. Doing this before you see an answer is the whole safeguard, because afterwards the bounds narrow to whatever supports the conclusion you have already reached.
Run the low inputs together and the high inputs together. The width between them is the finding. A band whose top is more than twice its bottom means the asset's worth is a matter of opinion, and you should decide whether that is a business you want to own.
Move each input on its own and see how much the answer shifts. Usually one dominates. That input is where the analysis should have been spent, and it is frequently not the one that took the longest to research.
Write the number, and write what it would take for that price to turn out to be too much. A range that has not been converted into a maximum you will actually pay has not yet done any work.
At the start of any valuation, and again at the end, when the temptation to report a single figure is strongest.
A range is not a licence to avoid concluding. 'Somewhere between four and forty million' is not humility, it is an admission that you do not understand the asset well enough to hold a view - and the correct response to that is to stop, not to buy the middle of it.
A shape that shows up repeatedly when a valuation is revisited after the fact is that the range was genuinely wide when it was first built, and considerably narrower by the time the decision was taken. No single revision was unreasonable - a growth assumption raised after a good quarter, a discount rate trimmed after the business felt more familiar, a comparable dropped because it turned out to be a poor match. The cumulative effect is a band that has quietly moved until it contains the asking price, at which point the valuation is no longer testing the decision but ratifying it.
Date your assumptions and keep the first version. A range that has been revised is fine; a range that has been revised without a record is a number you chose.
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