# What is cohort analysis: example of a subscription model

When we talk about customer retention, we are looking to measure how many of them are buying products or services from a company after a number of periods since their first purchase.

For instance, if we "acquired" 100 new customers in 2020, we will have retained 80% of them in 2021 if 80 of them have purchased again the following year. The churn or the attrition will be 20% of customers we had in 2020 but did not purchase again.

The period can be defined by the business according to its business model, and generally matches the billing frequency (for subscription models), or the main interval between purchases (often a year in the leisure travel industry).

The cohort analysis methodology aims at measuring the percentage of retained customers and the statistical revenue per customer after 5, 10, and generally any number of periods since their first transaction. A cohort means "all the customers acquired during a given period".

Statistical is an important term here as we are not following individual customers but understanding how a given population and its contribution to the business evolves over time. It is a very useful tool to understand the build up of the customer lifetime value.

We will take the example of a simple subscription model where customers generates £1 per month in profit for a service, to understand how the cash-flow of the business varies based on two key metrics: the churn rate and the cost per acquisition

### Churn rate and customer lifetime value

We have launched a business which provides the customers with advice, inspiration, photo, ... on a daily basis.

We charge £1 per month for the service, with negligible variable costs.

We have been operating for a little more than a year and have established that, after a year, we have retained 80% of our initial customers.

We are also monitoring our paying customers and see that for any cohort, we are retaining more than 98% of our customers month over month (80% YoY retention correspond to 98.2%  month over month)

The red curve shows that, month after month, we are receiving less revenue from our "cohort" as we are regularly losing customers. However, after 36 months, we are still expecting about 50p (we only have lost 50% of our customers over this period), and about 25p after 6 years.

Over a 6 years period, each of our initial customers will have contributed on average £40.00 margin to the business. If we stretched the curve to 10 years, we would get close to the £54 maximum lifetime value.

Let's see how the churn rate influences the curves, and the implication for the business.

Higher churn rates mean that the average revenue per month falls much faster: after just 18 months, the revenue per customer hits 50p for a churn rate of 40 when it takes 3 years for a churn rate of 20%.

As a result, the lifetime value with a churn rate of 40% is less than £24 and less than £35 for a churn rate of 30%. This has consequences on the time it will take for the business to absorb the cost of acquisition per customer. It also conditions how much the business can afford to pay for a new customer.

For instance, with a churn rate of 40%, it will take 42 months to break even on a £20 CPA of , and a £25 CPA will never be compensated in full as the customer lifetime value falls short of this amount.

By contrast, a 20% churn means that it will take "just" 25 months before a business can start generating profit from a customer with a £20 CPA. The lifetime value is also £54 vs £23 for a churn rate of 40%, leaving a lifetime profit expectancy of £34 vs a mere £3.

Over time, businesses will high retention rate will enjoy much healthier financials than businesses with high attrition.

The two following tables show the time required to break-even and the lifetime value of the profit (after 6 years)  by customer based on different assumptions on churn rate and CPA. We are still assuming a £1 profit per active customer and per month.

### Financial scale up model using cohort analysis

We have now a good understanding on how the lifetime value for a customer depends on the margin per transaction, the churn rate, and the initial cost of acquisition.

Let's suppose that we have established all three elements in the model, and we want to secure some incremental cash from lenders or investors to finance the growth of the business.

Using this model and making another simple assumption provides vital clues on the financial needs of the business as it scales up.

The simple assumption consists in considering a constant investment profile for the business, period over period: for instance, the business will invest £10,000 to acquire 500 new customers every month: same investment, same CPA and same churn rate. The following chart if for a CPA of £20 and a churn rate of 20%.

During the first couple of years, you need to trust the mathematics to keep your confidence (and so do your investors !), as the business seems to be digging an ever increasing financial hole.

When you look closer though, the curve seems to be flattening as we progress in time: is there hope at the end of the funnel?

Patience seems to be paying and from the period 25 onwards, the cumulated revenue of the previous cohorts exceeds the cost per acquisition for each new one, generating a net positive contribution. If every cohort is identical, the point in time when the net cash-flow becomes positive coincides with the break-even point within a cohort, and the total cash requirement can also be estimated mathematically.

As we build the business plan, we can model the sensivity of the cash-flow to both the churn and CPA.

The power of retention plays out very strongly in the mid-long term as the existing customer base becomes predominant over newly acquired customers.

In this example, the difference between a 20% churn rate and a 40% churn rate translate into moving into net positive cash-flow in 4 years as opposed to 13 years. As the churn rate worsens further, the lifetime profit becomes lower than the cost of acquisition meaning that the curve will never turn around towards a recovery.

### How to manage cost per acquisition and churn rate strategically

As acquisition is generally a loss-making activity on the initial transaction, understanding the time to breakeven in a subscription model, or the number of transactions in an ecommerce business is essential, and necessarily leads to understand the evolution of the customer value over time.

Cohort analysis is a very powerful tool to understand the financials of a company, monitor the evolution of the average revenue per customer over its lifetime, and set appropriate targets in terms of cost per acquisition.

Understanding that the financial model revolves around the 3 key metrics: margin by transaction, cost per acquisition and churn rate helps structure the marketing and communication activities to carefully monitor and improve each of them.

Whilst the model looks simple, I have actually seen it applied very successfully in a start-up, managed according to a rigorous mathematical approach to forecasting.