I learned in business school that many companies can be analyzed with three variables:

A = Monthly revenue per customer, B = Monthly customer churn, and C = Customer acquisition cost

Here is a quick example to show what I mean:

Verizon charges $50/month for cell service (A). 1.5% of Verizon’s users cancel their cell contract every month (B). Verizon’s sales and marketing costs are a few hundred dollars for every new user (C).

With this info you can figure out Verizon’s “customer lifetime value” ($50 divided by .015 = $3,333).  This is how much money Verizon makes from an average customer over time.  This is offset by “customer acquisition cost” of a few hundred dollars of sales and marketing expense.

As long as the left side of the equation (customer lifetime value) exceeds the right side of the equation (customer acquisition cost) you have a good business on paper.  There are improvements to this formula that account for other factors (gross margin, cost of capital, etc), but VCs make big investments all the time based on 8th grade algebra.

But there is a problem.

Take a look at Zynga, Groupon, and ReachLocal.  For many years these businesses performed well, even well enough to go public, but recently they have hit the skids.  As of their stock prices last Friday, each company is valued at less than the amount of invested capital.  I traced this back and noticed a striking trend: there has never been a successful public company with 5% (or greater) monthly churn.

The problem is that companies with 5% monthly churn must grow their user base by over 5%, every month, forever, just to avoid shrinking.  There are only so many people and companies on the planet, so a business like this eventually fails.  It is not an exact science about when a business like this will fail, but after four or five years there are many more “former” customers than “current” customers.  I imagine it becomes very hard to convince new people to sign up for the service at that point.

It is important to add that not all churn is created equal.  Technically, if you can re-acquire users that churned, then churn doesn’t matter as much.  Verizon does this all the time because people switch back from AT&T.  Diapers.com was particularly successful in doing this as customers had more kids.  Groupon, Zynga, and Reach Local?  Not so much.

This doesn’t mean that high churn businesses can’t be good in the near term.  I only point out that investors in these companies should understand the bet they are making, which is that someone (and probably someone who doesn’t read my blog) will acquire the company before it fails.