Bufetico
Nine numbers from a company you know. This is the cash Amazon had left over each year after paying for everything the business needed, in billions, from 2017 to 2025:
6.4, 17.3, 21.7, 25.9, then two years below zero, minus 14.7 and minus 16.9, then 32.2, 32.9 and 7.7.
The simplest way to measure growth, and the one I started with, is to take a first number and a last one and work out the yearly rate that connects them. Start in 2020, at 25.9, and end at the 7.7 of 2025, and you get minus 21.6%.
Feed that into a model and it does what you asked. It projects a company shrinking by a fifth every year, for as far out as the model looks. Follow that through to a price per share and Amazon comes out at a small fraction of what it was trading for. The stock was near $200 at the time.
The math was right. The question was wrong.
Minus 21.6% really is the rate that connects 25.9 to 7.7. The problem is that it looks at two numbers and throws away everything in between, and that only works if the last one is a normal year.
For Amazon it wasn’t. The cash fell in 2025 because Amazon spent it on new capacity, data centers this time. The business hadn’t shrunk by 76%. It had decided to build.
And the series says so, if you read the whole of it. In 2021 and 2022 the cash went negative while Amazon was building warehouses, and two years later it was back above 32. A first-to-last calculation can’t see any of that. It sees a small number at the end and assumes that’s the direction.
The same numbers, measured another way
Now measure it another way. Work out the change from each year to the next, then take the middle one of those changes. That middle value is the median.
Do that across the whole series, skipping the pairs where a negative year makes a percentage meaningless, and Amazon comes back at +19.7%.
Same numbers, two answers. First-to-last asks where the company ended up compared with where it started. The median asks what a normal year looks like here. If you’re trying to picture the years ahead, the median is the one that helps. A normal year tells you more than one strange year that happens to sit at the end.
Why the median beats the average
An average would also beat first-to-last, but it has a problem of its own: one freak year drags it. Let’s say a company grew 12%, 14%, 11%, and then 400% because it bought a competitor. The average of that is a number that never happened and won’t happen again.
The median doesn’t care how big that 400% is. It only cares that it sits at one end of the list. That’s why it holds up across thirty thousand companies, where checking them one at a time isn’t an option.
Where this breaks
The median is slow. A company that really is in decline, three straight years of falling cash and no investment story behind it, still shows a decent number for a while, because the median waits for most of the years to turn before it moves.
So the growth number can’t be the only thing you look at. You also have to look at the shape of the series. A run of falling cash should knock a company out whatever its median says. The number says what a normal year looks like. The shape says if normal still holds. A model that only runs the first test will keep passing companies on the way down.
Which method sits under your tool
Almost every free valuation tool measures growth first-to-last, and I understand why. It’s one line of arithmetic and it looks pretty precise. It also had Amazon shrinking while Amazon was building data centers.
If you use any tool that projects growth, find out which method sits underneath it. It changes the answer more than anything else you’ll decide.