Three models, one price: why you triangulate

One model is one opinion

A valuation model does not discover value. It takes your assumptions and does arithmetic on them, very neatly, to two decimal places.

That neatness is the danger. A growth model asked for a ten-year growth rate will accept 9% and return a value; it will equally accept 15% and return a value two thirds larger. Nothing in the output marks which input was a judgement call. The number comes out looking like a measurement.

So the real question is not "what is this worth?" but "how much does the answer move when my assumptions move?" One model cannot answer that. Three models built on different inputs can, because an assumption that is badly wrong will usually break them unevenly.

Where the word comes from

A satellite navigation device does not know where you are. It knows its distance from several satellites, and your position is the one point consistent with all of those distances at once. One satellite puts you somewhere on a sphere. Two narrow it to a circle. Three fix a point.

Valuation works the same way, with one difference worth being honest about: the distances are estimated, not measured. So you never get a point — you get a region. A tight region means the three models are telling a consistent story about the same business. A loose region means they are not, and you should find out why before you trust any of them.

Three models, three tenses

The three are not three ways of doing the same calculation. Each asks a structurally different question, which is precisely why they are worth running together.

• • The present-tense model asks what the business is worth if it never grows again — a floor, built on a figure you can almost read off the statements.
• • The future-tense model asks what the business is worth if it keeps compounding — the most generous of the three, and the one that depends most on a judgement.
• • The cumulative model asks how many years of cash flow it takes to get your money back — the one that converts a ratio into a span of time you have intuition about.

Notice that their inputs barely overlap. The first runs on current earning power, the second on an estimated growth rate, the third on cash flow and time. An assumption error that flatters one of them has no particular reason to flatter the other two.

Reading three numbers

Two sets of results, same first model. The difference between them is the entire point of the exercise.

In case A the three sit inside a band about 15% wide. Three different methods, three different inputs, one region — that is a usable answer, and the convention is to take the highest of them as your entry price, because all three already nodded.

In case B, the present-tense model says 140 and the other two say roughly 90. That is not a precision problem to be split down the middle. It is a message: the business throws off real cash today, and both of the forward-looking methods decline to project it. Find out which of them is wrong before you use any number at all.

Three reasons they diverge

1. The growth assumption is doing too much work. If the future-tense number is far above the other two, check what rate you entered and where it came from. A rate borrowed from the single best three-year window will produce exactly this pattern.
2. Cash flow and reported earnings disagree. If the cumulative number is the outlier, the cash statement and the income statement are telling different stories. That is a question about the accounts, not about the valuation.
3. The business is cyclical. Near a peak, current earning power is flattering and every forward method looks conservative; near a trough, the reverse. On a genuinely cyclical business all three models are measuring where the cycle happens to be standing.

In all three cases the divergence has done its job. It did not give you a price; it told you which part of your analysis is not finished.