Approaches to Forecasting Subscription Revenue

An Introduction of Terms and Equations Used to Predict Long-term Revenue for Subscription Businesses

Sean Larkin
Sep 5, 2018 · 12 min read

In his first blog post for Subscribe Commerce, Tim Dalbey, our CTO, laid out mathematical definitions for how our team determines customer retention, average customer lifespan, and expected customer value and the real value of spending money to increase retention rates.

If you want to dive into the math, which we generally do, there are all sorts of academic papers available online regarding probability models for forecasting subscription revenue. As of yet, there is no single, definitive way to approach these calculations. However, understanding the core concepts of forecasting recurring revenue is critical for subscription-based e-commerce businesses.

As I will demonstrate below, some of the most commonly seen forecasting models present wildly different predictions of future revenue. Since these models are used by business owners for planning marketing spends, purchasing inventory, and ultimately figuring out what they can pay themselves and their teams, every subscription entrepreneur needs to have a thorough understanding of the concepts that underlie these models.

In this blog post, we will cover the following:

  • Defining customer retention, average customer lifespan, and customer lifetime value
  • The difference between cohort retention models and aggregate retention models
  • A comparison of two aggregate retention models for predicting future subscription revenue

Defining Customer Retention, Average Customer Lifespan, and Customer Lifetime Value

Customer retention is the name of the game in subscription e-commerce. With traditional e-commerce, most of your business’ focus is on acquiring new website visitors and converting them into shoppers who buy as much as possible on that first visit. Retaining customers is important, but secondary.

With subscription e-commerce businesses, the model is completely different. You might spend more money acquiring a new customer than you make on the first order you ship them. However, once a customer is signed up for a recurring service or product, they become a predictable source of future revenue, decreasing your marketing costs per transaction, and increasing your profit over time.

There are a couple of definitions and “key performance indicators” (KPIs) that you have to understand when it comes to subscription e-commerce.¹

A “Billing Period”

Though it might be obvious, it’s important to understand that the definitions and calculations below are all based on the idea that you are billing your customers and shipping orders on a consistent schedule and that your billing periods, or cycles, are of a predictable duration (i.e., one month, three months, annual, and so forth). While you might have an initial “trial period” that is of a shorter duration, or customers might switch from a one-month billing cycle to a three-month billing cycle and so forth, for the calculations below, we generally assume consistent billing periods.

Retention vs. Churn

Retention refers to the number of customers your business retains across consecutive billing periods.² As an example, let’s assume your business offers a monthly subscription. If 50 customers sign up for your service in Month A, and 30 of them are still around for Month B, you have retained 30 customers. Your retention rate is therefore 60%, or 30/50, for your second billing (i.e, Month B).

Conversely, churn refers to the number of customers you lose between two billing periods. In the case above, your churn for Month A is 20 customers. Your churn rate for your Month B billing is therefore 40% or 20/50.

Your retention rate plus your churn rate will always equal 100%. So, you can use the equation: R = 1 - C, where R is your retention rate and C is your churn rate.

Voluntary vs. Involuntary Churn

There are two types of churn for a subscription business. Voluntary churn refers to customers that drop off because they are no longer interested in your service and actively cancel their subscription. Involuntary churn refers to customers who are lost either because their billing information has changed and you are unable to connect with them to update that information, or because they were unknowingly signed up for your service, due to credit card fraud.

There are different technical solutions for reducing involuntary churn. “Dunning management systems” can be leveraged to anticipate that customers’ credit cards are about to expire, so that you can proactively request billing information updates. Anti-fraud protections are offered by various e-commerce platforms and third-party integrations.

By identifying and reducing involuntary churn, you can increase your revenue and avoid the costly chargeback fees associated with fraud and unintended billing. Moreover, with involuntary churn taken out of the equation, you can focus your analysis on proactive retention strategies to reduce voluntary churn.

Aggregate Retention vs. Cohort Retention

When looking at your retention from the 10,000 foot level, it’s generally easiest to calculate retention rates based upon the aggregate all of the customers you retain for a given business period, without considering how long they have been a customer.³ From the equation above, if you started the period with X customers and you ended with Y customers, your aggregate retention rate is Y/X.

However, the reality is that a customer’s likelihood of renewing their subscription isn’t the same across all billing periods. We generally see a high churn rate between a customer’s first and second billing. In other words, when folks sign up and try your service, and lot of them cancel their subscription after they receive that first delivery. In contrast, satisfied long-term customers tend to stick around for the long haul. There’s a significantly higher likelihood that a customer who’s been billed 10 times already for your service is going to be retained for an 11th billing, compared to the likelihood that a customer who’s only been billed once will be retained for a second billing.

(In probability speak, we’d say that month-over-month retention distribution curves are not uniform, and that they tend to have a “fat tail.”)

A cohort is defined as a group of customers who share certain characteristics, such as behavior or a common sign-up period. When we calculate the likelihood of customers being retained each month in reference to their start date, we are practicing cohort retention analytics. While cohort retention calculations require more data and are slightly more involved than aggregate retention calculations, they are more actionable when it comes to making certain decisions, such as how you should spend your marketing budget on retention. For example, since we know that customers who’ve been subscribed for 6–12 months are less likely to drop off then customers who’ve been subscribed for just 1–2 months, we don’t need to send as much money on re-marketing to the former group of long-term customers.

(If you are interested in cohort analysis, check out this related post on cohort segmentation.)

Average Customer Lifespan

Average customer lifespan (ACL) (also referred to as Customer Average Lifespan, or CAL) refers to the average number of billing cycles, or periods, that a customer is retained by a subscription service.⁴ This can be calculated historically by adding up the number of months each customer has been retained and dividing by the total number of customers.

ACL can also be calculated predictively by using various probability models based upon retention rates. We will cover a couple of these models later in this post.

Customer Lifetime Value (LTV)

Customer lifetime value (LTV) refers to the aggregate value of all billings of single customer. Sometimes LTV is calculated based upon the total revenue received from a customer, other times is is calculated based upon the total profit generated by the customer. The latter calculation, based upon profit, is a more valuable performance indicator, as it takes into consideration your product’s price markup, your initial marketing spend on customer acquisition, and the costs to continually market to a customer over time.

Average customer lifetime value (ALTV) is calculated historically by adding up the value of all billings for each customer that has churned, and then dividing by the total number of customers that have churned. The problem with this calculation, obviously, is that it doesn’t factor in the value of customers who haven’t churned — which presumably includes your best, longest-term customers.

Expected customer lifetime value (ELTV) is quick estimator for the net value of a customer to your company that can be written on the back of a napkin. ELTV can be calculated by multiplying ACL by the average net profit earned per order or billing, minus acquisition costs.

Here’s the thing though: as you’ll note later on in this post, the assumptions that go into these simple calculations make them inappropriate for building accurate financial models. And in subscription e-commerce — given the vertical’s notorious sensitivity to minor fluctuations in key indexes — that could spell a lot of trouble down the road.⁵

Cohort Retention Models vs. Aggregate Retention Models

As mentioned above, cohort retention refers to the retention of specific groups of customers who share characteristics — the most obvious being the period, usually the month, in which they started their subscription.

Many of the aggregate retention models suggest that there is the same probability that a customer will be retained from one period to the next, regardless of how many periods they have been a subscriber or what their experience with the subscription has been over time. That’s just not the case, and cohort retention models attempt to account for this.

Below is a simple cohort retention distribution, based upon a wonderful blog post by Eric Stromberg.

Presumably, this distribution curve could be created by looking at a subscription business’ historical data and plotting out the average cohort retention month over month. Or, it could be predicted, based upon one of a number of probability models.

Based upon this curve, you can create a spreadsheet table that calculates the number of customers you can expect to retain over time:

(Note: In the example above, a fictional acquisition marketing spend has been included, showing that the size of each incoming customer cohort is likely to grow as the business grows. The number of new customers acquired each month with that marketing spend is not important at this time. To learn more about Cohort Retention models, I would highly recommend that you read Eric Stromberg’s article.

A Comparison of Two Aggregate Retention Probability Models

While aggregate retention models lack some of the subtleties of cohort retention models, they are incredibly useful for back-of-the-envelop forecasting. In short, aggregate retention models allow you to calculate an average retention rate, based upon an average customer lifespan. That average retention rate can then be multiplied by a subscription business’ total customer count to predict how many customers it will have in the future.

A very common aggregate retention probability model is:

Knowing that:

You can do a little algebra to rewrite this function as:

Using this function, the distribution curve below shows the percentage customers of a single cohort that will be retained over time.

So, if your historical customer data suggests that your average customer lifespan is 8 months (which is what the industry generally considers the customer lifespan of a healthy subscription business), you can calculate your retention rate as 87.5%:

With this retention rate in hand, you can now estimate how many customers you will retain from one billing period to the next, regardless of the customers’ cohort (or the month they first signed up).

Using the same new customer acquisition example data that I presented for the cohort retention model, this aggregate retention model would suggest the following:

As you can see, the total number of customers expected at the end of 12 months with this model is 23,550, compared the 20,803 expected with the cohort retention model.

Subscribe Commerce’s Aggregate Retention Probability Model

Instead of using “ACL = 1/Churn” as a retention probability model, we often use the following binomial distribution:

Essentially, this function is based on the fact that there are only two possibilities, a customer is either retained or churned by the end of a given billing period. There are only two possible states, represented by the 0.5 in the equation.

If the average customer lifespan is 2 periods, then the function above can be solved as:

Or

Or

This should make sense intuitively. If our retention rate is 50%, then we know we’ll lose half our customers in the second month.

Like finding the probability of flipping “heads” on a coin multiple times in a row, our retention rate is multiplied by itself for however many periods make up the average customer lifespan.

Using some advanced algebra, the aggregate retention probability model can be re-written as:

Using this function, the following distribution curve shows the percentage of customers of a single cohort that will be retained over time.

Plugging in the same new customer acquisition example data that I presented for the two previous retention models, this aggregate retention model would suggest the following:

When compared to the previous aggregate retention model, this model provides us with a stronger outlook of 25,321 customers at the end of the year, compared to just 23,550 with the previous model. We are comfortable with this more positive outlook because of the strength of the binomial distribution theory.

In Conclusion

Regardless of the function, or distribution curve, you use to represent your customer retention rates, it’s critical to your subscription business’ success that you are forecasting future revenues based upon retention and average customer lifespan. There are many real-world factors that can affect retention. So, in managing your business, it’s important that you are consistently monitoring a wide range of key performance indicators across your marketing, sales, and customer service practices.

In future posts, we will continue to discuss these KPIs. In the meantime, give us a shout if you’d like to work with us to model the financial outlook of your subscription e-commerce business.

Footnotes:

  1. The definition of terms presented in this document is meant to translate the precise, mathematical definitions laid out in Tim Dalbey’s post to the more common vernacular you’ll hear when talking with business owners and strategists about subscription-based e-commerce. We recommend that those who are serious about accurately forecasting subscription revenue read and digest Tim’s more technical definitions.
  2. You may choose to make reference to the pertinent math defining retention rates in Tim’s post.
  3. While subtle, it’s important to understand the difference between the term customer period and business period. A “customer period” is a billing period relative to the age of a specific customer. For example, if a customer has been billed three times, they are in their third customer period. A “business period” simply refers to a period for which a business has been selling subscriptions. For example, a business that’s just completed its fourth billing cycle is in its fourth business period. In a company’s fourth business period, they might be billing customers in their first, second, third, or fourth customer period, depending upon when those customers first subscribed.
  4. Average Customer Lifespan (ACV) should be referred to as Average Customer Period. ACV is the more common term, though it is less precise and can lead to misinterpretation.
  5. We’ll discuss how Subscribe Commerce calculates expected customer value and corresponding cost functions as an input to our recurring-billing financial models in later posts, but for now, feel free to take a look at the functions described in the paper as mentioned earlier.

Subscribe Commerce

As a leading digital agency focused exclusively on subscription e-commerce, we help companies adopt subscription e-commerce strategies and tools that enhance brands, streamline customer journeys, and create predictable revenue streams. Learn more: htttps://subscribecommerce.com.

Sean Larkin

Written by

CEO of Subscribe Commerce, a digital agency focused exclusively on helping brands adopt subscription e-commerce. https://subscribecommerce.com

Subscribe Commerce

As a leading digital agency focused exclusively on subscription e-commerce, we help companies adopt subscription e-commerce strategies and tools that enhance brands, streamline customer journeys, and create predictable revenue streams. Learn more: htttps://subscribecommerce.com.

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