How long excess returns last

The two-stage DCF from Analyst session 4 has three dials that are really one claim about durability. The growth years, n: how long the business can reinvest at returns above its cost of capital. The growth rate in those years, g: how much it can reinvest at those returns. The fade: how fast growth drops to the terminal rate afterwards. In our function the fade is a cliff, from 5 percent to 2.5 percent in one step, which is a simplification you should say out loud when you show the number.

So "this business has a wide moat" translates into the model as "n is long, and the fade is slow". "No moat" translates as "n is short, and anything it earns above the rate is gone soon". A pitch that says wide moat and then uses the same ten years as every other company has not put its claim into its number.

Growth costs money: to grow, a business reinvests. If the reinvestment earns exactly the cost of capital, every dollar put in is worth a dollar, and growth adds nothing. Analyst session 3's constructed Brightwell Pumps showed it: at a 9 percent cost of capital and 3 percent growth, its value was 160.0 with a 15 percent return on capital, 133.3 at 9 percent (the same as no growth at all) and 100.0 at 6 percent, where growth destroyed value. See Analyst session 3: Return on invested capital.

That is why the growth years and the moat are the same dial. Long growth years in a model only add value if the business earns above its cost of capital during them. Damodaran's rule that reinvestment equals growth divided by return on capital makes the link explicit. Our dcf() does not charge for reinvestment separately: it grows owner earnings at g, so it quietly assumes the reinvestment earns well. Every long n is a claim that the moat holds for those years.

Two readings are wrong. "High returns are always competed away" is wrong: after ten years the top group still earned well above the bottom group. "A great business stays great" is wrong too: half the advantage went in a decade, on average. The base rate sits between them, and it is the starting point for any n you choose. An analyst who picks fifteen years of above-average returns should be able to say why this business beats a base rate in which half the gap closes in ten.

The finding is about groups, not any one company. Some top-quintile companies held their position; some fell to the middle or below. The base rate does not tell you which a particular business will be. It tells you how much evidence you need before you assume it is one of the durable ones.

The Base Rate Book makes a point that surprises people: regression toward the mean does not need competition as its cause. Any one year's return is part lasting advantage and part luck, a good harvest, a competitor's stumble, a currency swing. Sort companies by this year's return and the top group is full of companies that had both. Next year the advantage tends to stay and the luck does not repeat, so the group drifts toward the middle even if no rival lifted a finger.

That changes how you read a single great year. The more luck there is in a measure, the faster it regresses, and the less one good year should lengthen your n. The same book found earnings growth rates "not very persistent", which is the same mechanism showing up in a noisier number. A run of returns over many years, through a bad patch, is better evidence of a moat than any single year at the top.

Three things shrink the reward for a longer advantage period. The gap between growth and the rate is small. Growing at 5 percent and discounting at 9 percent, each year's extra cash is worth less today than the year before, so years 11 to 15 arrive heavily discounted. The terminal already assumes growth. After the growth years the model still grows at 2.5 percent forever; a longer n only swaps 2.5 percent for 5 percent in a few distant years. Distance compounds. A dollar in year 15 at 9 percent is worth far less today than a dollar in year 5.

That is why people overestimate what a moat is worth in a model at these inputs. Change the inputs and the answer changes: a business that could grow much faster than its discount rate would gain far more from extra years, which is exactly when a long n most needs evidence. At 5 percent and 9 percent, the honest summary is: doubling the advantage period from five years to ten adds 7.41, adding five more adds 6.15. The moat matters, but it is not the input that moves this valuation most; Analyst session 6 showed the discount rate and the growth rate swing it further.

Buffett's 1977 letter, read at source, lists four things Berkshire wants in a business it buys shares in, judged the way it would judge buying the whole company: one it can understand, with "favorable long-term prospects", run by honest and competent people, available at a very attractive price. The second criterion is the qualitative form of tonight's input. It does not say how many years. It says the analyst must have a reason to believe the economics will still be good a long way out.

Translate it into the model and it becomes a question you answer in writing before you set n: what would have to be true for this business to keep earning above its cost of capital for ten more years, and what evidence do I have that it is? Nothing on this page measures any filer's actual moat. The P&G figures show what the model does with an assumption; the assumption is still yours, and the build-along makes you write it down.