The margin of safety

The margin answers one question: how far can my estimate of value fall before the price I paid is too much? That is a question about the value, so the gap is written as a share of the value. Halden's base view is 12.75 million for the whole; the cousin is asking the equivalent of 10.0 million. The gap is 2.75 million, and 2.75 out of 12.75 is 21.6 percent. Your base estimate can be 21.6 percent too high and you still have not overpaid.

Dividing by the price instead gives 27.5 percent for the same gap, a bigger and more flattering number that answers a different question (how much the price would have to rise to reach your estimate). It is not wrong arithmetic, but it is not the safety question, and the flattering version is the one people reach for when they want to buy. Graham set out the margin of safety in chapter 20 of The Intelligent Investor, which he titled as the central concept of investment (reported: the book was not read at source for these pages). The idea in his words is paraphrased here, not quoted: buy at a price far enough below a conservative estimate of value that errors in the estimate do not ruin you.

Run the same formula against the other two views. Against the bull view, 15.82 million, the margin is 36.8 percent and the price looks generous. Against the bear view, 8.18 million, it is -22.2 percent: the price is above what the business is worth if the two builders who now order online are the start of a trend. One price, three margins, and one of them points the wrong way.

Which one matters depends on what you can live with, not on which view you believe most. If the bear view would be a painful loss you could not shrug off, the bear margin is the one that has to be positive. If you are confident the bear view is far-fetched, you can lean on the base, but that confidence is itself an estimate, and Owner session 6 is about how often confidence like that is too narrow. Another way to read the same price: at 10 percent, with 2 percent growth after year 10, 10.0 million for the whole implies owner earnings shrinking about 1.4 percent a year for ten years (modelled). The price already sits between the bear and the base. Analyst session 5 works that reverse calculation by hand.

Three different things can push the real load past what you expected, and the margin has to absorb all of them.

Estimate error. Your value came from guesses: the spend to stand still, the growth path, the rate. Owner session 2 showed that moving those guesses within honest bounds spreads Halden's value from 6.9 to 21.4 million. Some of that spread is still there when you pay. Bad luck. A supplier fails, a road closes outside a showroom, a recession arrives in year two. None of these was in any view, and none was your fault. Your own mistakes. You misread the books, trusted the wrong person, or let a price you heard earlier pull your estimate towards it. The margin is the one protection that works against all three at once, because it does not need you to know in advance which one will happen.

"It is 40 percent below where it was last year" sounds like a margin of safety and is not one. A fall in price measures a change in other people's opinion; it says nothing about the gap between the price now and the value now. If the business got worse, the value may have fallen further than the price, and the "cheap" price could carry a negative margin.

The neighbour's "about a million" is the same trap from the other side. It is a price for a different business, paid last year, by somebody else. Being at or below it tells you nothing about Halden. A margin always has value on one side of the subtraction, and the value is yours: estimated from the business, written down as a range, before you looked at any price. Why a past or quoted price is not information about value is the whole of Owner session 5.

A one-third margin against Halden's base of 12.75 million puts your ceiling at 8.50 million for the whole, 0.85 million for 10 percent. Notice where that lands: just above the bear view of 8.18. Measured against the base, a one-third margin happens to leave you almost safe against the bear as well. That is not a coincidence you can rely on; it is a property of how wide this particular range is.

Turn the principle into questions. How wide was your range? Halden's runs from 8.2 to 15.8 million at one discount rate, and wider across rates; a wide range asks for a wide margin. How much of the value depends on the far future? In Owner session 2, nearly half of Halden's base value came from beyond year 10, and the far years are the least knowable. How much do you trust the numbers you were given? Halden's books are kept in a way only the cousin understands. Each "not sure" pushes the margin up. A business you understand very well, with steady owners' cash and books you can read, can carry a smaller one.

Once you have set a ceiling, the cousin's price either sits below it or above it. At 1.00 million for 10 percent, it sits above your 0.85. You can offer your ceiling, explain why, and accept that she may say no. You can ask for what would change your estimate, such as books you can read or evidence that the online ordering is not spreading, and recompute. Or you can walk away.

Walking away costs nothing that you owned. The too-hard tray from Owner session 1 can hold this offer too. The mistake to avoid is the quiet one: moving your ceiling up to meet her price because you have already imagined owning the slice. A ceiling set before the conversation is worth more than one set during it, which is why the build-along writes it down first.