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# Customer Lifetime Value for Subscription Products

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Estimating Customer Lifetime Value allows you to say how much you can spend on customer acquisition and retention. This is especially important for subscription-based products like games, online services, information marketing, loyalty programes etc. In this article we will use a classical approach to estimate CLV with a simple equation and customer cohort analysis. There are more accurate probabilistic models available and I will look into them in following posts. If you are just starting with CLV calculation for your business, I strongly recommend going for the simple solution first and then becoming sophisticated as necessary.

The classical equation for CLV uses a discounted sum of monthly income multiplied by the probability of survival to a given month:

$$CLV = \sum^T_{t=0} m \frac{r_t}{(1+d)^t}$$

Where:

• $$m$$ – monthly cash flow (subscription fee).
• $$r_t$$ – retention rate for month t (probability of being a customer for t consecutive months).
• $$d$$ – discount rate to calculate the current value of future money.

To further simplify our model we assume that customers always subscribe for the full month, i.e. all payments (even for new customers) are made on the 1st day of the month.

To calculate retention rate for the t-th month, we use a simple cohort analysis. Prepare your customer base so that for each customer you know the month when she joined and for how many months she stayed a subscriber. Next, decide how far back into the past you want to go with your analysis. Let us assume you have decided to use past 2 years of data from Jan 2013 till Dec 2014 . Create a square table with one row and column per month of historical data. Next, add 1 to each cell where row indicates when the customer has subscribed and column indicates in which months she had an active subscription. If a customer has joined in Apr 2013 and remained a subscriber for 3 months, we should add 1 to cells in row Apr 2013 and columns: Apr 2013, May 2013, Jun 2013.

If you do this for all of your customers, you will end up with an upper-triangular table of customer counts similar to this one:

You read this table as follows: “100 customers joined in Jan 2013, of which 63 extended their subscription to Feb 2013. From the 100 customers that joined in Jan 2013, 47 continued their subscription to Mar 2013…”. If you sum numbers in columns you will get the total number of active subscriptions in a given month. This is a very basic example of a cohort analysis.

From the above cohort table, we can now easily calculate the retention rate from month 1-to-2, 1-to-3 etc. For example, retention rate from 1-to-2 is 63%, from 1-to-3 is 47%, from 1-to-4 is 38% and so on.

The only one piece of the equation left to untangle is the discount rate. UK government published a good article explaining discount rate and net present value. In the UK, a recommended discount rate for calculations is 3.5% per annum. We will divide it by 12 to get discount rate per month.

Plugging all of the above into a simple spreadsheet, we can easily do the calculation for any set of parameters:

A randomly picked customer has a Customer Lifetime Value of £406 in a 1 year time frame. This is the amount we can spend on customer acquisition and loyalty programs to break even. You can find the above spreadsheet here.

### One response to “Customer Lifetime Value for Subscription Products”

1. […] as far as what constitutes a customer life time value (CLV). Often it’s defined as the projected potential value of a customer in a time horizon going into the future. Current value of a customer based on a time horizon into the past is some […]