Value is a range, not a number

A single forecast quietly answers a question you have not asked yet: which future is this business heading for? For Halden you do not know. Two builders already order online; whether the rest follow is the biggest open fact about the business. A single base case buries that fact inside one growth rate. Three views drag it into the open, because each view has to say what happened to the builders.

Three views also change the conversation. "Is 12.75 right?" has no useful answer. "What would have to be true for the bear case, and how would I find out?" does. Each view becomes a short list of facts to check, and the checking is where an owner earns an edge. The point is not to average the three. It is to know which story you are in, and to notice early if it changes.

A useful bear case is the plausible bad decade, not the end of the world. Halden's bear view is that owner earnings shrink 3 percent a year for ten years, then hold steady. Shrinking 3 percent ten times in a row leaves about 0.74 million a year by year 10: a quarter less, not zero. It is anchored in a weak point you already found in Owner session 1, builders ordering direct online, and it imagines that trend continuing at a steady pace.

A disaster movie (the showrooms close, the cousin walks out, the business is gone in two years) is a different question. If you think it is likely, Halden fails gate 2, favourable long-term prospects, and goes in the too-hard tray before any valuation. Keep the two apart. The bear case asks "what is it worth if the known weak point keeps hurting". The disaster asks "should I be valuing this at all".

Three tests for a bear case: it names a cause you can observe, it uses a path no worse than the cause can plausibly produce, and a reasonable person who likes the business would still say "yes, that could happen".

The rate does two jobs at once. It charges for time: money in ten years is worth less than money now, even if it is certain to arrive. And it charges for risk: the less sure you are that the cash will come, the more you shrink it. Neither charge is printed anywhere. You choose it, and the choice is as much a part of the valuation as the growth view.

Halden's 10 percent is a judgment for a small private family firm: one region, four suppliers, books only the cousin can read, and a stake you could not easily sell. A large business with audited accounts and steady customers might deserve a lower rate; a riskier one, a higher rate. What you must not do is choose the rate after seeing which value you like. Write the rate and the reason first, then read off the answer. Why money later is worth less, the price of time, is taught in Economics, Foundations session 5 ↗. How professionals derive a rate is beyond these pages; Analyst session 4 shows it as a choice in the arithmetic.

Read it off the grid, nothing else. Hold the rate at 10 percent and change the story: the value moves from 8.18 (bear) to 15.82 (bull), a spread of 7.6 million. Hold the story at base and change the rate from 8 to 12 percent: the value moves from 17.00 to 10.20, a spread of 6.8 million. For Halden, with these particular choices, the story moves the answer slightly more than the rate. The two are close enough that neither can be ignored.

The more important pattern is that they compound. At 8 percent the three stories spread 11.3 million apart; at 12 percent only 5.6. And the bear row barely reacts to the rate (10.08 to 6.91) while the bull row reacts a lot (21.42 to 12.48). The reason is Part 3: the bull view keeps more of its value in the far years, and the rate bites hardest on the far years. Which input matters most is not a fixed fact about valuation; it depends on the business and on the other inputs. Analyst session 6 builds this grid for real filers.

The brass block assumes Halden keeps handing its owners cash, growing slowly, long after year 10. Nobody can forecast year 15 of a tile business. What you can judge is durability: will builders still need advice on which tile suits which floor, will the showrooms still draw them, can a rival or a website take that away? If Halden's advantage lasts, the brass block is roughly right. If it fades, the brass block shrinks, and with it almost half the value.

This is why the bull view gains the most from the far years (51 percent) and the bear view the least (35 percent): hope lives in the far future. It is also why Part 2's bull row reacted most to the rate. A moat, in the language of value investing, is just the reason the brass block might be real. Moats as economics, the strategy of keeping rivals out, are taught in Economics, Foundations session 6 ↗. Here a moat is a valuation input: how long the excess returns last. Analyst session 8 measures how fast they usually fade.

Halden's base value prints as 12.75 million. A spreadsheet would happily print 12,750,000.00. Every one of those extra digits is false. They come from multiplying a guessed growth rate by a chosen discount rate over a future nobody has seen, and nearly half of the total comes from years after year 10. The number has more decimal places than the inputs have certainty.

So treat precision as a signal to look harder, not to relax. When a valuation arrives as one exact figure, ask three questions: which growth story is it, which rate, and what share of it sits beyond the forecast years. If the answers are not on the page, the precision is the model talking, not the business. Rounding Halden's range to 8.2 to 15.8 is not sloppiness; it is the honest number of digits.