Many businesses track repeat transactions on a discrete-time basis. These include: (1) companies with transactions that occur at regular intervals (such as subscription renewals), (2) firms that frequently associate transactions with specific events (e.g., a direct marketer that records whether or not customers respond to a particular catalog), and (3) organizations that simply use discrete reporting periods even though the transactions can occur at any time. Furthermore, many of these businesses operate in a noncontractual setting, so they have a difficult time differentiating between those customers who have ended their relationship with the firm versus those who are in the midst of a long hiatus between transactions. Our goal is to develop a model to predict future purchase patterns for a customer base that can be described by these structural characteristics. Our "beta-geometric/beta-binomial" (BG/BB) model allows for heterogeneity in each of the underlying behavioral processes (customers' purchase propensities while active, and time until each customer becomes permanently inactive), and yields relatively simple closed-form expressions for future expectations conditional on past observed behavior. We apply the model to a previously published dataset consisting of cruise-line transactions for a cohort of 6094 customers over a period of five years, and demonstrate the valuable insights that arise from our forward-looking modelling framework.