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Comment by reasonnw | Hacker News Reader

The math doesn't sound realistic to me. He use a percentage for the churn rate but not a percentage for the number of new users, he is comparing an arithmetic progression with a geometric progression. As is well known, a geometric progression always beats an arithmetic progression.

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Typically you are investing into getting new customers, so unless you can get CAC < first month payment[1], you will have a limited marketing budget hence a static number of new users.

[1] One way of achieving infinite marketing budget is to offer discounts for annual prepay, if e.g. you get 25% of customers to pay 10 months upfront (annual plan with 2 months free), you receive 25% * 10 + 75% * 1 = 3,25 monthly payments in month 1. If you get CAC below 3,25 ARPU then you have infinite marketing budget and that can indeed go geometric. But that's a big if, and even then at some point your marketing channels will dry up at some scale, while churn remains the same at scale as businesses keep dying or changing their mind.

The math is pretty realistic for a given starting point. Of course in practice there will be other factors that might compound the churn braking the growth or that might allow a larger marketing budget based on the increasing growth in absolute terms leading to more turnover (I devoted a paragraph to that at the end of the article).

But for the purposes of illustration it is the easiest to keep all the numbers fixed and let only one of them vary.

The Matthew Effect.

The herd behaviour.

Word of mouth.

People like to see an application has a lot of good reviews and users to buy, so your growth is a percentage of your users.

It would be interesting to know when the number of users is increasing as a percentage or as a fixed number depending of the sector. Is there available data for the growth of users by sector/product/industry?

That's what you want: linear costs and geometric profits. It's not sustainable forever, of course, but the longer you can push the flat part of the curve to the right the better. All three flatten. but flattening at 60,000 versus 10,000 is the difference between an article in the local paper and one in the WSJ.

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