The accounts receivable situation of a firm is often modeled as an absorbing Mar

Question

The accounts receivable situation of a firm is often modeled as an absorbing Markov chain. Suppose a firm assumes that an account is uncollectable if the account is more than three months overdue. Then at the beginning of each month, each account may be classified into one of the following states:

State 1: New account

State2: Payment on account is one month overdue

State 3: Payment on account is two months overdue

State 4: Payment on account is three months overdue.

State 5: Account has been paid

State6: Account is written of as bad debt

In this case 60% of all new accounts are one month overdue, 50% of the one month overdue accounts are paid the same month, but 50% are two months overdue. 60% of the two months overdue accounts are paid the same month, however the rest will go 3 months overdue. 70% of the three months overdue accounts are paid that same month, however 30% are written of as bad debt.

What is the probability that a new account will eventually be collected?

What is the probability that a one-month-overdue account will eventually become a bad debt?

If the firm’s sales average $100,000 per month, how much money will go uncollected?

Explanation / Answer

1)

Required probability =P(Immediate collection ) + P( Collection in one month overdue) + P( Collection in twomonth overdue) +P( Collection in threemonth overdue) =

0.4 + 0.6*0.5 + 0.6*0.5*0.6 + 0.6*0.5*0.4*0.7 = 0.964

3)

Hence, firm's average uncollected probability = 0.0396. For sales of 100000 dollars per month, 39600 would remain uncollected.

2) P( Bad debt for a one-month over due account ) = P(Going into 2month)*P((Going into 3month)* P(Bad debt) = 0.5*0.4*0.3 = 0.012

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