A Statistical Approach to Customer Lifetime Value - Part 1: An Overview for Subscription Businesses

Congratulations! You just successfully launched your new magazine about the fine intricacies of Beanie Baby Collection and your parents couldn’t be more proud. The magazine is listed on the Apple App Store for $0.99, netting you a cool $0.70/month after Apple’s cut. You invest some money into marketing and gain 100 subscribers, which dwindle to 50 by the end of the year. How much money should you spend on your next customer?

Why is this important?

As your probably know, this puzzle is known as customer lifetime value (CLV) and it’s one of the most common unknowns for marketing managers. If each customer is worth on average $3, then the maximum you can spend to acquire each customer is $3. This type of analysis drives each of the 4 p’s of marketing:

1. Promotion - If I pay $100 for a week-long ad, I better get at least 33 new customers in order to break-even at an acquisition cost of $3/customer to match the $3/customer lifetime value. Correctly estimating the lifetime value will better help allocate marketing dollars and evaluate which opportunities are best pursuing.

2. Price - Price affects two components of the customer lifetime value equation: the revenue per time period and the average number of time periods per customer. While that sounds complicated, it’s quiet intuitive: increasing the price of your product will increase each month’s subscription value, but may turn off some customers and decrease their average lifetime. Balance wisely.

3. Product - Improving your product, like say the quality of writing on the magazine, increases the willingness to pay for your product and decreases the likelihood of unsubscribing. If adding an extra editor will cost you $40,000/year, better make sure that customer lifetime value will increase by that amount.

4. Place - I actually am not sure that customer lifetime affects or is effected by where or how you sell the product. I guess the fee or commission structure affects the revenue per period, so there’s an optimization there. Additionally, you may segment your customers based on where they buy your product, and differing lifetime values for each place.

Hopefully by drilling through the 4 p’s and linking them to CLV, I’ve established the importance of investing capital to discover this number.

How is this calculated?

The current approach for CLV is boring and outdated and is as follows:

At its core, you sum up the discounted cash flows from each period, using the retention rate to forecast what the average customer does. When \(t = 0\), it’s the first period and the customer gives you their first payment of $1. When \(t = 1\), the retention rate of let’s say 50% kicks in, and drops the number of payments in period 1 in half, reflecting half of our customers leaving. As \(t\) approaches infinity, you arrive at your CLV.

Put more simply, a retention rate of 50% means the average customer stays for two periods, providing an average of two payments. Alternatively, a retention rate of 90% means that 10% of your customers churn each period, meaning the average customer stays for 10 periods. The formula for this method is as follows:

This formula comes from the summation of an infinite geometric series. There’s no discounting to this method, but you could integrate it easily.

What’s wrong?

Let’s go back to our original magazine example and think about those 50 customers that left over the course of the year. Perhaps 25 of them left immediately because they were confused about our content. The remaining 25 left evenly over the next 11 months. At a yearly level, our retention is 50%, but the CLV is misleading because the average fails to capture the pattern of churn. Those initial 25 people only paid us once!

Moreover, the remaining customers may actually like us and stay forever! Remember, our retention rate of 50% implies that our initial cohort of 100 will decrease to 50, 25, 12, 6 and then 3 by the end of year 5. In practice, however, churn rates change over time.

What to do?

So what’s a savvy marketer supposed to do? The best first step would be to track a cohort for as long as possible and see what the actual cohort did over their lifetime. Plot on a graph the churn rate overtime and see what the curve looks like. Finally, add up the total payments and divide by the number of subscribers to get a rough idea of your CLV.

Next step? Follow along to my second post on this series to talk about more advanced modeling techniques.

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