D AVIDSON'S D EPARTMENT S TORE
As a result of intense competition and an economic recession , Davidson's Department Store in Atlanta was forced to pay particularly close attention to its cash flow. Because of the poor economy, a number of Davidson's customers were not paying their bills upon receipt, delaying payment for several months, and frequently not paying at all. In general, the Davidson's policy for accounts receivable was to allow a customer to be 2 months late on his or her bill before turning it over to a collection agency. However, it was not quite as simple as that.
Davidson's has approximately 10,000 open accounts at any time. The age of the account is determined by the oldest dollar owed. This means that a customer can have a balance for items bought in two different months, with the overall account being listed as old as the earliest month of purchase. For example, suppose a customer has a balance of $100 at the end of January, $80 of which is for items bought in January and $20 for items bought in November. This means the account is 2 months old at the end of January because the oldest amount on account is from November. If the customer subsequently pays $20 on the bill in February, this cancels the November purchase. Then if the customer makes $100 worth of purchases in February, the account is $180, and it is 1 month old (since the oldest purchases were from January).
Carla Reata, Davidson's comptroller, analyzed the accounts receivable data for the store for an extended period. She summarized these data and developed some probabilities for the payment (or nonpayment) of bills. She determined that for current bills (in their first month of billing), there is an .86 probability that the bills will be paid in the month and a .14 probability that they will be carried over to the next month and be 1 month late. If a bill is already 1 month late, there is a .22 probability that the oldest portion of the bill will be paid so that it will remain 1 month old, a .40 probability that the entire bill will be carried over so that it is 2 months old, and a .32 probability that the bill will be paid in the month. For bills 2 months old, there is a probability of .54 that the oldest portion will be paid so that the bill remains 1 month old, a .16 probability that the next -oldest portion of the bill will be paid so that it remains 2 months old, a .18 probability that the bill will be paid in the month, and a .12 probability that the bill will be listed as a bad debt and turned over to a collection agency. If a bill is paid or listed as a bad debt, it will no longer move to any other billing status.
Under normal circumstances (i.e., not a holiday season ), the store averages $1,350,000 in outstanding bills during an average month; $750,000 of this amount is current, $400,000 is 1 month old, and $200,000 is 2 months old. The vice president of finance for the store wants Carla to determine how much of this amount will eventually be paid or end up as bad debts in a typical month. She also wants Carla to tell her if an average cash reserve of $60,000 per month is enough to cover the expected bad debts that will occur each month. Perform this analysis for Carla.