Customer Lifetime Value

Defining Targeting and LTV Models

• Customer targeting typically involves three models:

  • Propensity model
  • Time-to-event model
  • Lifetime value model
• These models can be used individually or together
• A propensity model estimates the probability of a customer doing some event
• A time-to-event model estimates the number of days until a customer does some event
• A lifetime value model estimates the value of a customer

• The events in a propensity or time-to-event model include:

  • A candidate responding to an email campaign
  • A customer puchasing a specific product
  • A customer expanding to a new prorduct
  • A customer purchasing additional units of a prduct
  • A customer changing shopping habits
  • A customer churning
• All three of these models can help determine the impact of this event

Illustrating CLV with Churn Predictions

• A great use-case for churn forecasting is within CLV estimations
• Again, CLV estimates predict how much a customer is worth to us over their entire lifetime

• This information is crucial for evaluating the ROI of:

  • Customer acquisition
  • Customer retention
  • Customer maximization

• At a high level, CLV can be defined as the following:

  • Where, $CAC$ refers to customer acquisition costs
  • And, $RR$ refers to recurring revenue (or purchases)
  • And, $COGS$ refers to cost of goods sold

$$CLV = -CAC + \sum_{\text{lifetime}} RR - COGS$$

• Typically, we can consider the $CAC$ to be fixed, so we may be more interested in learning a customer's future lifetime value:

$$FLV = \sum_{\text{lifetime}} RR - COGS$$

Estimating Lifetime Value

• Estimating the expected future lifetime of a customer is a requirement for estimating the expected sum of a customer's RR
• Specifically, the expected future lifetime $L$ of a customer is solely dependent on their churn rate for a given period:

$$l = \frac{1}{\text{churn}}$$

• Next, we must estimate the expected revenue $r$ for the customer
• Specifically, this can be estimated as the average revenue for the customer in a given period:

$$r = \sum_{i=1}^{n} RR_{i}$$

• Then, the expected sum of a customer's RR becomes the following:

$$\sum_{future} RR = r \times l$$

• For example, we may define a churn period as a single month

  • Suppose a customer's churn rate is 12% per month
  • And, the expected lifetime is $l = \frac{1}{0.12} = 8.3$ months
  • If their expected revenue is $r = \$ 10$ per month, then the $\sum_{lifetime} RR = 10 \times 8.3$
  • In other words, the expected recurring revenue over the customer's lifetime is $\$ 83$

Using Segmentation in CLV Estimation

• Classification and propensity models created for an entire customer population usually have limited accuracy
• Since, propensities can be determined by many different factors
• For example, a customer in one segment may churn due to low product quality
• Whereas, a different customer in another segment may churn due to high prices
• Thus, including segments will create more accurate and targeted classification (or propensity) models

• Consequently, the model repository can maintain specialized models for different combinations of:

  • Business objective
  • Brands
  • Product classification
  • Customer segments

References

• Textbook for Fighting Churn with Data
• Textbook about Algorithmic Marketing
• Course about Predicting Customer Lifetime Value