Customer Lifetime Value

As a two-side marketplace provider, merchants lifetime value is crucial to Ritual’s success. Traditionally, customer lifetime value is calculated by the formula below:

However, there are two limitations about this approach.

  • Attrition rate varies term by term.
  • Profit margin are different.

In order to improve incorporate the two limitations, a more dedicated approach was used here. Assume our vision for a merchant’s lifetime value is 1 year.

And two variables were considered independently here.

  • M(y): the profit margin generated by a merchant in the yth month.
  • L(y): the fraction of merchants whose lifetime was exactly y months.

From the L(y) value we inferred the following:

  • A(y): Fraction of merchants who left prior to their yth month.
  • R(y): Fraction of customers still with with in their yth month.

In this problem, we adapted a relatively new approach since we knew the merchant churning months by month. For that reason, moving forward is easier than moving backward in retail/subscription based industry at Ritual. In the table below, I showed how to adjust profit margin by churn rate. Based on industry objective, profit margin was not discounted.

Objective:

In order to scientifically bid on merchant related ads, we need to estimate lifetime value for merchant by 1, 2 and 3 years as well as by metro and zone types. Data was fetched from the Look we set up. And a sample plot is shown here. Merchants are grouped by their activation months on Ritual. Y-axis is the aggregated ritual fee we collected.

Methodologies:

In order to calculate merchant lifetime value, we need to consider the following two factors:

  1. How much money on average does a merchant generate month by month?
  2. What’s the possibility a merchant churn in that month?

Obviously, these questions are difficult to answer without cohort (by acquisition time or by acquisition location) since cohort provided a stable number of merchants. And this approach provides us the insight about flexible churn rate since churn rate is calculated term by term.

Regarding the two terms,

  • Average ritual fee is calculated term by term by total ritual fee collected divided by active number of merchants in that month.
  • Churn rate is calculated term by term by this formula.

After multiplying the two terms and doing a rolling sum, we know the 6/12/24 months lifetime value. To elaborate this idea, I created some toy data below.

Example: Suppose we acquired 100 merchants in Toronto at the 1st month of 2018. These 100 merchants are called as a cohort. The following tables illustrate how the cohort based LTV is calculated.

Week Number of Merchants Churn Rate Ritual Fee in This Period Ritual Fee Per Merchant Churn Adjusted Ritual Fee per Merchant
1 100 N/A $10,000 $100 $100
2 100 0% $10,000 $100 $100
3 98 2% $10,000 $102 =102*(1-0.02) = $100
4 95 3.1% $10,000 $105 $105*(1-0.031)=102
5 90 5.3% $10,000 $111 $105
... ... ... ... ... ...
12 60 5% (assume) $10,000 $167 $159
Total 100+100+100+102+105+.....+159

Based on this table, we know this cohort has 60 merchants “survived” after 12 months with the average 1 year(12 months) LTV of $ 1,000 (supposed). And the table below shows how to calculate merchant average LTV in each metro. The data below means we have 10 active merchants in cohort 1 at their 12 months, 20 active merchants in their 20 months, etc. The metro one-year ltv is weighted by the number of active merchants in that month for each cohort.

Cohort Number of Merchants Average 1 Year LTV Weighted LTV
1 10 $1,000 0.1*$1,000
2 20 $1,100 0.2*$1,100
3 30 $1,200 0.3*$1,200
4 40 $1,300 0.4*$1,300
Result $1,200

In this example, the average LTV for Toronto area is $1200. All the other cities follow the same rubric to get the numbers.