# “*1/churn”* is the wrong calculation of LTV for young companies

For SaaS companies, tracking the Expected Lifetime Value of a Customer (LTV) is one of the most critical key performance indicators (KPIs) that they can track, because it has massive implications on the unit economics, and therefore viability, of their businesses.

For both transactional, and recurring revenues (subscription) businesses the ratio between Customer Acquisition Cost (CAC — how much you pay to get the customer in the door), and the LTV of that customer (how much money they will deliver to you) → the CAC:LTV ratio, is the turning point that defines if they have a good business or not.

In simple terms, if it costs you $1 to get a customer in the door and they pay you $100 of Gross Margin over their life, that is probably a good business; but if it costs you $100 to get a customer in the door, and they only give you $1 of Gross Margin over their life as a customer, you should probably shut that business down.

So, if the CAC:LTV ratio is the turning point on which the viability of a business can be decided, it’s pretty critical that each of those numbers are calculated correctly.

The calculation of LTV is seemingly straight forward. You work out your churn rate (e.g what percentage of your customers leave every period), and then just do *1/churn%*. E.g. if 10% of your customers leave each year, then *1/10% = 10 years* is the average customer lifetime. Straight forward!

**Well, unfortunately not.**

The *1/churn%* calculation only makes sense for large cohorts, and here’s why: It is a probabilistic calculation, so for small cohorts with few customers, the actual average customer lifetime could vary greatly from *1/churn%*. To see this in action see this example of a small, 10 customer cohort, with 10% churn per month.

*Note: There is a full excel file with all the examples for download at the bottom of the page.*

What you’ll see here is that, as expected, the *1/churn%* calculation with a 10% churn rate results in a 10 month customer lifetime; but a 10% churn rate also implies 1 customer leaves each month, and if that’s the case then all 10 customers will be gone within 10 months.

That means the average customer lifetime is **actually 5.5 months, not 10 months**. In other words, because the Cohort is small, the actuals deviate significantly from the idealized calculation. So in this case, the idealized calculation would have led you significantly astray (by ~45%!)

# The Particle:Wave Duality of Customers

To get super geeky about this, the technical difference here is whether or not you think of customers as particles(unitary, indivisible, non-probabilistic), or waves (flowing, divisible, probabilistic.) And depending on the number of customers you have in a cohort, the math to deal with them shifts from particle math (non-probabilistic), to wave math (probabilistic) → it’s the particle:wave duality of customers!

Practically, what this means is that at small *n,* a 10% churn likely means you are losing a rough fixed NUMBER of customers per period in churn (in this example, 1 per period); whereas at large *n* you are losing a fixed PERCENTAGE of the customer base at each point in time. And the implication is that there are actually different equations for each of the customer lifetimes depending on the size of the cohort:

*Large N: Customer Lifetime = 1 / Churn%*

*Small N: Customer Lifetime = ((1 / Churn %) + 1 )/ 2*

This might be easiest to see in graph form. If you graph the shape of the percentage of a cohort’s customers that remain in the cohort over time, then the average customer life is the first integral of that curve, or visually, it’s the area under the curve.

**Here, (a) is the Large N curve:**

*Customers Remaining = yChurn Rate = crPeriod = x*

*Cohort Curve: y = (1 — cr)^x*

*Customer Life = area under the curve = 1 / cr*

**(b) is the Small N curve:**

*Customers Remaining = yChurn Rate = crPeriod = x*

*Cohort Curve: y = 1 — (x * cr)*

*Customer Life = area under the curve = ((1 / Churn %) + 1 )/ 2*

Don’t believe me? I built a simulator that does bottom-up simulation of what each customer in a cohort will do (stay vs. churn) in each period, and then ran the simulation a few hundred times.

Here it is for large cohorts (1,000 customers). You will see that the simulated behavior matches the idealized *1/churn%* curve almost exactly:

And here it is for a small cohort (10 customers). You will see that the simulated behavior matches the *small n* cohort line closely. In this case the *large n* calculation would have been very wrong (~40% wrong) when calculating customer lifetime:

# Why should we care?

So this seems all rather academic, but why the hell should we care?

Well this has massive implications for companies when they are at the early stage and trying to work out if their business model is viable.

Just using the example above, if you were to use the standard customer lifetime calculation, but a small cohort, your estimate of customer lifetime would have been off by over 40%. That is a massive difference. And if you’re spending significant dollars to get that customer through the door, that could easily be the difference between you surviving as a business or going bankrupt.

# The Shape of Things To Come

But what’s even more important to realize is that these two formulae are only two potential shapes of your customer cohort curve.

The real tough problem for early stage companies is that they are trying to extrapolate from a small amount of data (only a few cohorts), over a small amount of time (often only a few months or years) and trying to work out what their customers will do over the next 3 to 10 years, all while not knowing if they will be acquiring similar customers, or if their types and quality of customer will change as they grow. That is a LOT of unknowns to be extrapolating.

In other words, if you are just at the end of your first year, you might run your calculations and see that you have a 10% churn rate. But what will your customers do next year? There isn’t a single correct answer. In fact, there are almost infinite scenarios for how your customers will behave given this 10% data point that you have. The four most common scenarios would be:

(a) My customers will behave like the idealized large cohort *(1/churn%)*(b) My customers will behave like the idealized small cohort (

*((1 / Churn %) + 1 )/ 2)*

(c) My bad customers initially leave, but then the remaining customers stick around ~forever

(d) My customers hit a wall (my cohorts collapse)

It’s essentially impossible to know which curve your customers will follow when you are early in the life of your company. Only time will tell.

# The Bottom Line

The bottom line is that at the early stages of a company, the calculation of customer life, and therefore LTV should be viewed as both art and science. **Hard-and-fast rules like 1/churn% are just as likely to be wrong as they are to be right.**

The most prudent thing for you as the entrepreneur to do is to think of your potential customer lifetime as a range, from the best case (your customers have a horizontal asymptote), to the worst (your customers hit a wall).

Essentially, you should be thinking of your customers as living somewhere in the shaded are in the graph below:

As you get more information about how your customers behave through time you can tighten that range, but it will never cease to be a range. **No real-world customers will ever conform perfectly to the 1/churn% rule, and you have to be ever cognizant of that fact.**

Hence, in the interests of intellectual honesty, and not bankrupting your company, you should always talk about customer life, and hence LTV, as a range, not a hard and fast number. Further, you should ensure that you are spending sustainably according to your understanding of that range, how wide it is, and how wide it could be; rather than simply spending according to the value spat out by the hard-nosed, but often wrong *1/churn%* calculation.

But most importantly — you should never stop being intellectually curious about how your customer cohorts are actually performing in the real world. They aren’t just numbers in a spreadsheet, there are real people behind those numbers, and people are irrational and unpredictable. People don’t conform to idealized equations. So you should never stop trying to fill in the gaps in your knowledge about their behavior in order to have the best possible estimate of what your LTV range could be.

**And always remember — LTV is a range, not a number, and you should plan for both ends of the range accordingly.**

Excel model and bottom up simulator available here.