Question

Consider a department store that classifies the balance of a customer’s bill as fully paid (state 1), bad debt (state 2), 1-30 days in arrears (state 3) and 31-60 days in arrears (state 4). The accounts are checked monthly and the state of each customer is determined. In general, credit is not extended and customers are expected to pay their bills within 30 days. Occasionally, customers pay only portions of their bill. If this occurs when the balance is within 30 days in arrears (state 3), the store views the customer as remaining in state 3. If this occurs when the balance is between 31 and 60 days in arrears, the store views the customer as moving to state 3 (1-30 days in arrears). Customers that are more than 60 days in arrears are put into the bad debt category (state 2), and then bills are sent to a collection agency. After examining data over the past several years, the store has developed the following transition matrix: (b) (c) ?11 ?12 ?13 ?14 1.0 0.0 0.0 0.0 ?= [?21 ?22 ?23 ?24]= [0.0 1.0 0.0 0.0 ] ?31 ?32 ?33 ?34 0.5 0.0 0.25 0.25 ?41 ?42 ?43 ?44 0.5 0.2 0.05 0.25 If the store has £40000 in the 1-30 day category and £50000 in the 31-60 day category, estimate the amount of bad debts the company will experience.

Answer 1

From the given data, the transition matrix is given as

Here an entry xij in matrix represents probability of a customers moving from stage i to stage j.

According to question, company has 20000 pounds in 3rd category and 50000 pounds in 4th category. Assuming that all customers have equal debts, 20% of the customers in 31-60 days category (cat 4) will move to bad debt category (cat 2), while 0% will move from category 3 to category 2. Hence the bad debts of the company can be estimated as

20% OF 50,000 = 10,000