Accounts
Receivable
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
State
2 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.
State
6 Account is written off as bad debt.
Suppose
that past data indicate that the following Markov chain describes how
the status
of
an account changes from one month to the next month:
For
example, if an account is two months overdue at the beginning of a
month, there is a 40% chance that at the beginning of next month, the
account will not be paid up (and therefore be three months overdue)
and a 60% chance that the account will be paid up. To simplify our
example, we assume that after three months, a debt is either
collected or written off as a bad debt.
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