### Pitfalls in calculating CLV – why using an “average retention rate” can lead to grossly inaccurate CLV numbers

Customer Lifetime Value (CLV), the total profit a business will make from a new customer, is a valuable metric. It puts a theoretical cap on what a firm is willing to spend to acquire a new customer.

CLV is predictive – it’s a projection of what a new customer *will* spend over time. As a result, there are “good” and “bad” CLV numbers – the closer the prediction is to what actually happens, the better.

Unfortunately, some common techniques used to calculate CLV produce results so inaccurate they’re basically meaningless. In this post, we’ll explain why one common pitfall – using an “average retention rate” – can lead to CLV predictions with margins of error over 50%.

The most common CLV formula taught in textbooks is:

Here, *m* represents the monthly payment, *r *the month-over-month retention rate, *d* the discount rate, and *t* is the time period. The formula is basically a proxy for, “on average, customers stick around for X months and pay Y per month when they’re here.” There are too many problems with this equation for a single post, but for now we’ll focus on the retention rate, *r*. Retention is usually the most significant driver for CLV, but when we try to make a calculation, we have to decide – what value should we choose for *r*?

### The common mistake – use an average retention rate

Figuring out the “average retention rate” is a common, but logically flawed, first step. For example, one might look at the overall customer base and count how many people leave, or churn, in a typical month. This type of thinking can have a *disastrous* impact on CLV accuracy.

The issue is that blending customers into an “average” significantly distorts reality. If you gain two customers – one with a retention rate of 100% and another with a retention rate of 0% – you can imagine how the situation would play out. The first customer would pay forever, and the second would leave right away. However, if you first average the two retention rates together, you’ll have two customers with a 50% retention rate. Both will be gone within a few months. Order of operations is critical.

### How average retention rates can undervalue CLV by over 50%

Imagine we have two groups of customers who sign up for our business – 100 customers in Group Awesome, where customers have a month-over-month retention rate of 90%, and 100 customers in Group Sad, whose customers have a 10% monthly retention rate. In this sample business, customers pay us $10 per month until they leave.

If we follow the “average retention rate” school of thought, every customer has a month-over-month retention rate of 50% (the average of the 90% group and the 10% group). To calculate expected revenue per customer, we need to simulate how this group of customers will drop over time. Each month a customer is “alive,” we’ll earn $10.

Rather than looking to total lifetime revenue, for the purposes of this example we can simplify things and focus on what customers will spend over a year. Paying $10 per month while they’re active, this group of 200 customers will spend a total of $3,984.38, or $19.92 per customer. The number is low for a $10/month business because very few customers stick around for long.

Next, as an alternative, we’ll let both groups run their own course instead of taking the average retention rate. As we look at the same type of graph, we start to see the why this is so important. The 100 Group Sad customers will be almost entirely gone after a month, but many of the 100 Group Awesome customers will continue to pay for quite a while.

The total revenue from the same 200 customers paying $10 while they’re active is now $8,285.70, or $41.83 per customer.

Using the average retention rate undervalues the 1-year value by over 52%.

We can extend this line of thought into a more complicated (and perhaps realistic) scenario. Let’s assume we have three groups of 100 customers who join our business: Group Awesome (95% month-over-month retention), Group OK (75% monthly retention), and Group Sad (55% monthly retention). Again, we’ll compare using the average retention rate for all 300 customers – in this case 75% – to playing each group out on its own.

The 300 customers will spend $11,619, or $38.73 per customer.

The 300 customers will spend $15,278, or $50.93 per person.

Once again, the “average retention rate” approach undervalues the 1-year value by over 23%.

The reason this impact is so profound is that, when we calculate CLV, retention rates are compounding. There’s a big mathematical difference in taking the average *before* compounding *r* compared with taking the average CLV *after* compounding each individual’s unique *r*.

### Summing it Up

For CLV to be meaningful, it must be accurate. Unless your business happens to have customers who are all identical, the techniques we use to calculate CLV need to respect that different customers have different retention rates. The discussion should be one that describes these differences – not one that focusses on aggregate attrition.

The retention rate is just one place where things can go awry when calculating CLV. We’ll touch on more common pitfalls in some upcoming posts.

I find your fonts kind of difficult to read. I don’t know if it’s the anti aliasing or what, but it seems very jagged and inconsistent in intensity/darkness

I concur

Thanks for the feedback! We’re working on this.

I took a class on this stuff, but I would love a refresher on how to do the math behind multiple different retention groups. Care to share?

We’ll be posting related articles in the future — you can subscribe to our feed in your favorite RSS reader for more content like this.

So it sounds like the answer is (assuming you can’t distinguish between Awesome, OK, and Sad) is to use the hazard function formula for calculating the PV of cashflows instead of retention rates. Or course, as you say, this only solves one of many problems associated with classic approaches.

I look forward to more blog posts like this.

That’s right. The problem with the traditional formula assumes a constant hazard function. Where as in virtually every situation, there is negative duration dependence (decreasing hazard). So that customers who have been with the company longer, are less likely to churn.

I’m taking a deep dive on CLV and this issue comes up. Could either of you point me in the right direction to find more info on how to calculate and use hazard function to come up with PV of cashflows? Much thanks.

Great post Aaron. Just discovered this. How would you reflect hazard function in the classic equation instead of a retention rate? To my simple mind, the intent of the two seems the same — so long as the retention rate is captured properly, it should be OK?

The hazard function and retention rate are inverse, however when people talk about ‘retention rate’ it is implicitly assumed that the ‘retention rate’ is constant. If you adjust the formula to account for increasing retention rate over time, you should be fine.

Thank you for this. Btw, I would include in that equation the original one-time acquisition cost of each customer. “Margin” (m) covers Revenue – COGS per customer. But each customer has additional acquisition costs associated with him, which are not covered in generic COGS. Isn’t this your understanding?

I actually like the font (no kidding). What is it?

Bob

Thanks! It’s called Botanika.

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I’m assuming you are calculating this in Excel. Can you write out the excel formula for your last example that would total $15,278 over your 3 segments. Or better yet, post your spreadsheet. Thanks.

I got $15,278.08 using these numbers. Not sure if you’ll be able to see in image though.

Good example of a problem caused by “aggregation bias”. Shows up all over the place e.g, marketing science, econometrics, ecology

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