Customer Lifetime Value

Session 7 - Customer Lifetime Value

Course Introduction

• Welcome to Marketing Analytics.

• This is Session 7, focusing on Customer Lifetime Value.

• RSM is presented as a force for positive change.

Module Overview

• Module 1: Introduction to course, stats, and R.

• Module 2: Linear regression.

• Module 3: Binary logistic regression.

• Module 4: Consumer preferences with utility functions and estimating preferences.

• Module 6: The grammar of graphics and exploratory data visualization.

• Module 7: Customer lifetime valuation.

• Module 8: Targeted promotions.

• Module 9: Privacy and marketing analytics (Targeting and privacy).

• Module 5: Loading and tidying data, guest lecture by Google.

Agenda

• Problem set 1.

• Customer management.

• Recency, Frequency, and Monetary value (RFM).

• RFM score.

• CLV and RLV.

• Customer equity.

Customer Management Strategies

*Save up to 60% on an extended range of styles and sizes
*Plus, you can save an extra 10% when you spend over 250€
*Get €20 off all orders above €100 with the code: THANKYOU

Customer Segmentation

• Star customers: Ideal segment.

• Vulnerable customers: Profitable but at risk of churn due to lower value delivery; improving their experience can convert them into Star Customers.

• Free riders: Benefit from high service levels but contribute little financially.

• Lost causes: Low profitability and receive little value; efforts should be minimized or redirected.

Customer Management Processes

• Customer acquisition: Attracting new customers.

• Customer retention: Keeping existing customers engaged and satisfied, encouraging repeat purchases and loyalty.

• Customer development: Maximizing customer lifetime value (CLV) by deepening engagement and expanding the relationship.

Customer Lifetime Value (CLV)

• CLV is the present value of all future profits an individual customer generates over their relationship with the firm.

• Customer equity is a firm-level metric summarizing the entire customer base.

• Customer equity is the total CLV across all existing and future customers.

Pillars of CLV Management

• Customer acquisition.

• Customer retention.

• Customer development.

Customer Acquisition Strategies

• Increase market size (e.g., new products).

• Increase marketing investment.

• Increase effectiveness of acquisition programs.

• Offer discounts and incentives.

• Generate positive word of mouth.

Customer Retention Strategies

• Understand the underlying factors for churn.

• Churn: Percentage of customers who leave during a given time period.

• Improve customer experience.

• Differentiate offers from competitors.

• Incentivize lock-in, re-purchase, subscription.

• Reward loyalty.

Modeling Churn with Logistic Regression

• Churn can be modeled using logistic regression, giving the probability that a customer leaves the company.

• This is different from the customer’s retention rate r, which is the percentage of customers that stay with the company.

Example: Retention Rate Calculation

• Given a model for churn, calculate the retention rate for a customer with Age = 20 and Tenure = 100.

Expected Customer Lifetime

• Calculating expected customer lifetime based on retention rate r.

• Which given retention rate equals:

• The expected customer lifetime is almost two years.

Customer Development Techniques

• Share of wallet: Percentage of a consumer’s total expenditures on a product/service that goes to a specific company.

• Cross-selling: Selling other products to an existing customer.

• Up-selling: Selling a premium product to a customer who doesn't already have it.

Share of Wallet

• Share of wallet is the percentage of a customer's total spending in a category captured by a company.

• Difficult to obtain from the firm's perspective because competitor data is unobserved.

Cross-Selling

• Selling additional or complementary products to increase the breadth of purchase.

Up-Selling

• Encouraging the purchase of a higher-end or premium version to increase the value of the purchase.

RFM Dashboard

• Recency: How long has it been since the customer transacted?

• Frequency: How often does the customer transact?

• Monetary value: What value does the customer transact?

• RFM score allows customer segmentation in terms of loyalty.

• Example: a customer scoring 311 has a recent purchase but low frequency and low monetary value.

RFM Analysis: Downsides and Benefits

• Downsides:

  • Descriptive.

  • What about new customers?

  • Rules for 1,2,3 are arbitrary.

  • How much should we spend to recover a customer?

• Benefits:

  • Simple Excel analysis.

  • Fast insights.

  • Understandable by managers.

  • Gives an overview of the entire customer base.

CLV Definition and Relation to RFM

• CLV is the present value of all future streams of profits that an individual customer generates.

• RFM data is not equal to CLV, but is often used as input to a CLV model.

CLV Equation

• CLV is calculated using the formula:

  • CLV = \sum{t=0}^{\infty} \frac{mt r_t}{(1 + i)^t}

  • Where:

    • m_t = profit or contribution margin during time t

    • r_t = retention probability during time t

    • i = constant discount rate

    • t = time (e.g., day or year)

• Emphasizes that value is closer to the present.

• Margin times the probability that a customer will stay.

Simplified CLV Equation

• Under assumptions of constant profit margin m, constant retention rate r, constant discount rate i, and an infinite horizon, the CLV equation can be simplified.

CLV Examples

• Examples of constant and time-varying CLV measures are provided with revenue, margin, and retention rates over days 10, 20, and 30.

Practice Scenarios

• Practice exercises to calculate CLV with given revenue, margin, retention, and discount rates over specified time periods.

Residual Lifetime Valuation (RLV)

• RLV is the residual value of the customer from a specific point in time (tau).

• If the unit of time is days, then if tau = 12, we start summing the CLV at day 12.

RLV Examples

• Examples of RLV calculations are shown with revenue, margin, retention, and discount rates given a specific tau value.

Practical Use and Problems with CLV/RLV

• CLV or RLV calculation may not always be possible due to missing data.

• Online missing data can occur because:

  • Customers are identified with cookies for each online visit.

  • Mobile and desktop activity cannot be identified as one customer.

• This is why online firms encourage users to log in or create an account.

Core Idea of CLV Models

• All CLV models are based on:

  • Discounting customer value or revenue at time t to the present.

  • Multiplying by the retention probability at time t.

  • Summing over all future time periods.

Components of Customer Lifetime Value Models

• Shows graphical representations of:

  • Expected margin from customer if active at time t.

  • Marginal probability customer survives to time t.

  • TVM discount factor at time t.

  • Net present value of expected margin at time t.

• CLV is equal to the total area of the shaded region.

CLV as a Special Case of RLV

• CLV is a special case of residual lifetime value.

• Residual lifetime value indicates how much value remains given what we’ve observed so far, starting from a specific time (tau).

Contractual vs. Non-Contractual Settings

• Contractual: We know exactly when a customer becomes inactive (e.g., telecom, SaaS, gyms, streaming services).

  • Can estimate survival easily.

• Non-contractual: We don’t observe whether customers are inactive (e.g., retail, e-commerce, hospitality, banking).

  • Customers may be dormant or churned, but we can’t tell for sure.

  • Need to make more assumptions.

BG/BB Model Overview

• Introduces the Beta-Geometric/Beta-Bernoulli (BG/BB) model.

• One sub-model reflects RF (Recency and Frequency of transactions), and the other captures M (Monetary value of each transaction).

BG/BB Model - Transaction Probability

• Each customer starts as active and can potentially transact in each period.

• A customer buys at time t with probability p.

• Not all customers have the same p, each has their own, following a Beta distribution.

BG/BB Model - Inactivity Probability

• The probability of becoming inactive is denoted as \theta (theta).

• Each customer has their own \theta, modeled as a random variable.

• Once inactive, a customer never returns to being active.

BG/BB Model - Recap

• Recap: probabilities to transact p and to become inactive \theta.

• Parameters of distributions are estimated instead of estimating p and \theta directly.

  • \alpha and \beta are estimated for p (transacting probability).

  • \gamma and \delta are estimated for \theta (inactivity probability).

Customer Purchase Probability (p) Interpretation

• If we model p with a Beta distribution and obtain \alpha = 0.96 and \beta = 2.88:

  • The average transaction probability of a customer is \frac{\alpha}{(\alpha+\beta)} = 0.25.

Customer Churn Probability (θ) Interpretation

• If we model \theta with a Beta distribution and obtain \gamma = 1.2 and \delta = 13.86:

  • The average dropout probability of a customer is \frac{\gamma}{(\gamma+\delta)} = 0.079.

BG/BB Model - Monetary Value

• A customer has x transactions, and the amount spent on each transaction is denoted as v1, …, vx.

• Each transaction is assumed to be Gamma distributed, introducing parameters \kappa (kappa) and
  u (nu).

BG/BB Model - Kappa and Nu

• \kappa is the same for each customer and determines the overall shape of the revenue per transaction distribution.

• Each customer has their own \nu, determining the average level of spending and the degree of variability over many transactions.

• Customers’ values of \nu follow a gamma distribution with parameters \lambda (lambda) and \\mu (mu).

Estimation in R

• Using RFM data as input:

  • x = number of transactions since we first acquired the customer.

  • t.x = the period during which the most recent observed transaction took place.

  • m.x = the average monetary value of each transaction.

  • n.cal = the number of periods for which we have data on the customer.

Parameter Estimation in R

• The command bgbb.EstimateParameters() is used to estimate the parameters of the beta distributions.

  • \alpha and \beta describe the purchase probability distribution.

  • \gamma and \\delta describe the churn probability distribution.

Interpretation of Results in R

• The plot is interpreted as follows:

  • \frac{\alpha}{(\alpha+\beta)} = 0.25

  • \frac{\gamma}{(\gamma+\delta)} = 0.08

• Now the model can be used to make predictions.

Monetary Value Parameter Estimation in R

• Focusing on monetary value, the spend.EstimateParameters() function obtains:

  • \kappa (kappa) = 8.95

  • \lambda (lambda) = 10.32

  • \\mu (mu) = 9.13

Distribution from Lambda and Mu

• Sample ν distribution from kappa and nu.

• Now each customer has such a distribution.

Prediction in R

• How much do we expect new customers to spend on their next transaction?

• We use the spend.expected.value() function.

• It uses the information in the estimated distributions.

CLV Calculation in R

• To obtain CLV:

  • We need the discounted expected number of transactions (dert) for this customer over the expected remainder of their time as an active customer.

  • For a newly acquired customer, we have the weekly discount rate.

• The dert and expected value give us the CLV.

Practical Application

• How much should we spend on new customers?

• Preferably smaller than 69 euros.

• We can do this for any customer!