with Rutger van Oest
Latent attrition models forecast customer value assuming that the customer can abandon the company, but not the other way around. We extend residual lifetime value (RLV) to accommodate the company’s option to terminate its relationship with low-value customers. Starting from the Beta-Geometric/Beta-Binomial (BG/BB) model, we use dynamic programming to compute RLV when a forward-looking company that is uncertain about the customer can decide in each period whether to continue service or abandon. We define abandonment value as the difference in RLV due to the company’s flexibility in being able to abandon bad customers and relate it to the purchase history of individual customers as well as aggregate customer base characteristics. Using a publicly available data set on donations, we show that abandonment value is substantial, in particular when customers purchase frequently but not recently. Typically, heterogeneity increases option value, and consistent with this we find that abandonment value increases with heterogeneity in purchase probabilities; however, we also find that heterogeneity in drop-out probabilities decreases abandonment value due to sorting effects in the attrition process. Abandonment value is less when the average purchase probability is high, the average drop-out probability is low and the value of purchase is high.
Keywords: customer base analysis; residual lifetime value; option to abandon customers