Optimal time-variable pricing for check-cashing transactions

Credit unions typically have large numbers of low-balance single share account members due to dormant share accounts left after loans are paid off and to significant numbers of check-cashing members. These accounts frequently cost more to maintain than they generate in interest and fee income. This praxis describes a non-linear integer optimization model for determining the optimal time-variable check-cashing fee pricing policy. The model incorporates estimates of labor costs for various member-visit types, which were determined using association rule discovery of combinations of low-level teller transactions. A two-statement Structured Query Language program was used to classify 36 months of transaction history by visit type. The model includes estimation of demand curves for each of the member-visit types as a function of the check-cashing fee charged. The customer lifetime value was estimated for single account and multiple account members to provide an upper bound on the per-member cost of member-visit demand exceeding capacity, and for estimating the maximum lifetime marketing expenditures for cross-selling additional products to single share account members. For the customer lifetime value, first-, second-, and third-order Markov chain and mover-stayer Markov chain models were evaluated at one-, two-, three-, and six-month intervals using the Anderson-Goodman test for verification of the Markov property assumption.; The optimal check-cashing fee is a constant 2% for the Credit Union of Texas data set studied. The Credit Union's actual staffing policies imply a cost of {dollar}10 per member for member-visit demand exceeding capacity. The Markov chain model encounters some school-year related seasonal patterns in rejection of the Markov property assumption; this seasonality may not be present for institutions that do not have a primarily educator-based membership. The upper limit on the customer lifetime value estimate is the perpetuity of the periodic net income for the most profitable state. The Markov chain model customer lifetime value estimate is approximately 60 percent of the upper limit for multiple account members, and 22 percent of the upper limit for single account members, although there are some known inaccuracies in the Credit Union's member level monthly profitability calculations. An analysis of the equation of the mover-stayer lifetime value model makes it clear that retaining members in high-value states is more important to lifetime profitability than improving upward transitions for low-value states. An analysis of the Markov Anderson-Goodman test for a large state-space Markov chain model can be useful in data quality analysis even when the large state-space model is inappropriate for calculation purposes.