Customer-Base Valuation in a Contractual Setting: The Perils of Ignoring Heterogeneity

Abstract

The past few years have seen increasing interest in taking the notion of customer lifetime value (CLV) and extending it to value a customer base (with subsequent links to corporate valuation). The application of standard textbook discussions of CLV sees us performing such calculations using a single aggregate retention rate. However, at the cohort level, retention rates typically increase over time. We suggest that these observed dynamics are due, in large part, to a sorting effect in a heterogeneous population. We show that failing to recognize these dynamics yields a downward-biased estimate of the residual value of the customer base. We also explore the implications of failing to account for retention dynamics when computing retention elasticities, and find that the frequently reported estimates underestimate the true effect of increases in underlying retention rates in a heterogeneous world.

Keywords: customer lifetime value, beta-geometric, discrete-Weibull, retention elasticity