## Calculating the Value of Churn Reduction, Part 1: The Correct Calculation Of Customer Lifetime Value

Much has been said about the value of retention and acquisition, and there are many different theories – unfortunately, much of this can be confusing and misleading. We are going to explain how to calculate these important metrics of a SaaS company correctly. First, we have to start with customer lifetime value (CLV) – many people often use simplified versions of CLV that can be very far off. In this article series I will explain the importance of cash discounting and its application in SaaS metrics. This is a slightly complicated subject (for those of us who never studied finance), but fortunately two professors, Sunil Gupta of Harvard and Donald R. Lehman of Columbia, have already derived a relatively simple equation that does it for you! The first three articles in this series will convince you why and teach you how. Later in the series we will go over the valuation of acquisition campaigns and the value of customer retention. But we can’t get to those until we get a really good understanding of CLV.

where:

If you know exactly what those three terms mean and you know how to convert them to a consistent time period, you may want to just skip to the article by Gupta & Lehman! My discussion here is for people who are either new to SaaS metrics or want to see the least math possible but still get the important points. In this post, and those that come after it, we will explain exactly what those terms mean, and explain enough to know why that is the best formula for CLV, but we will introduce the bare minimum of mathematical equations.

For the mathematically-minded, this equation is derived from an exponential decay model of customer lifetime. For the non-mathematical, the intuition is that if a customer has a 1 in 10 chance of cancelling each month, you expect they will stay about 10 months. Make sense? Sure! Note that if your churn rate is monthly, your expected lifetime is also in months, and if your churn rate is annual then the expected lifetime is in years. We’ll have more to say about this in a little bit. So if this is the expected lifetime, does that mean that the customer lifetime value is just monthly recurring revenue (MRR) times the lifetime, or CLV=MRR/churn? No! Although you see this equation used in some SaaS metrics articles (we won’t link any names) this is wrong and will overstate the value of a customer. It is wrong in two respects: it doesn’t include the cost of acquiring and maintaining the customers, and it doesn’t discount or devalue the cash that will be paid by customers in the future. Without accounting for these you will overestimate the value of a customer and make bad decisions about acquiring and retaining them. We actually won’t use the equation above directly, but it’s important to get an idea for how expected lifetime value comes into play and how you calculate it. So that equation is meant to give you some intuition more than anything else. Next we will explain discounting future cash flows in some detail. Here is a short preview of what to expect:

In the last section we introduced the Customer Lifetime Value (CLV) formula of Gupta & Lehman, and we began to explain it starting with the expected lifetime of a customer. So was that it? The lifetime value of a customer is expected length of the customer’s subscription times the profit you make on them each month. That is:

So if the churn rate is 10%, the CLV is 10 times the recurring margin, if the churn rate is 5% the CLV is 20 times the margin, and if the churn is 1% then the CLV is 100 times the margin. This approximation to CLV is widely used, but it has some serious flaws and as we will see it can significantly overstate CLV…

## Main Result

The best formula for CLV was created by Sunil Gupta and Donald Lehman and first published in their seminal paper, “Customers As Assets [PDF]“, (Journal of Interactive Marketing, 2003, 17.1 pages 9-24). It is:where:

- M is the margin on the customer(s), i.e.recurring revenue (RR) minus Cost of Goods Sold (COGS)
- r is the retention rate
- i is the interest rate for discounting project investments

*consistent*. Consistency of the time period is the main “gotcha” when using the formula, and we will explain how to do it right.If you know exactly what those three terms mean and you know how to convert them to a consistent time period, you may want to just skip to the article by Gupta & Lehman! My discussion here is for people who are either new to SaaS metrics or want to see the least math possible but still get the important points. In this post, and those that come after it, we will explain exactly what those terms mean, and explain enough to know why that is the best formula for CLV, but we will introduce the bare minimum of mathematical equations.

## Expected Lifetime of a Customer

CLV means the value today of a customer, including the money you expect that they will pay you in the future. The first thing you need to know is how likely the customer is to last as a subscriber. For that you use the churn rate and this equation:For the mathematically-minded, this equation is derived from an exponential decay model of customer lifetime. For the non-mathematical, the intuition is that if a customer has a 1 in 10 chance of cancelling each month, you expect they will stay about 10 months. Make sense? Sure! Note that if your churn rate is monthly, your expected lifetime is also in months, and if your churn rate is annual then the expected lifetime is in years. We’ll have more to say about this in a little bit. So if this is the expected lifetime, does that mean that the customer lifetime value is just monthly recurring revenue (MRR) times the lifetime, or CLV=MRR/churn? No! Although you see this equation used in some SaaS metrics articles (we won’t link any names) this is wrong and will overstate the value of a customer. It is wrong in two respects: it doesn’t include the cost of acquiring and maintaining the customers, and it doesn’t discount or devalue the cash that will be paid by customers in the future. Without accounting for these you will overestimate the value of a customer and make bad decisions about acquiring and retaining them. We actually won’t use the equation above directly, but it’s important to get an idea for how expected lifetime value comes into play and how you calculate it. So that equation is meant to give you some intuition more than anything else. Next we will explain discounting future cash flows in some detail. Here is a short preview of what to expect:

**Calculating the Value of Churn Reduction, Part 2: Discounting Future Cash**

In the last section we introduced the Customer Lifetime Value (CLV) formula of Gupta & Lehman, and we began to explain it starting with the expected lifetime of a customer. So was that it? The lifetime value of a customer is expected length of the customer’s subscription times the profit you make on them each month. That is:
So if the churn rate is 10%, the CLV is 10 times the recurring margin, if the churn rate is 5% the CLV is 20 times the margin, and if the churn is 1% then the CLV is 100 times the margin. This approximation to CLV is widely used, but it has some serious flaws and as we will see it can significantly overstate CLV…

**To be continued…**