Question

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.

  
From the historical data, the firm has determined the following transition matrix:
  

	New Account	1M Overdue	2M Overdue	3M Overdue	Paid	Bad Debt
New Account	0.0	0.6	0.0	0.0	0.4	0.0
1M Overdue	0.0	0.0	0.5	0.0	0.5	0.0
2M Overdue	0.0	0.0	0.0	0.4	0.6	0.0
3M Overdue	0.0	0.0	0.0	0.0	0.7	0.3
Paid	0.0	0.0	0.0	0.0	1.0	0.0
Bad Debt	0.0	0.0	0.0	0.0	0.0	1.0

  
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. It is assumed that after three months, a debt is either collected or written off as a bad debt. Once a debt is paid up or written off as a bad debt, the account is closed, and no further transitions occur.
  
What is the probability that a one-month-overdue account will eventually become a bad debt?

	A.	0.060
	B.	0.036
	C.	0.120
	D.	0.516
	E.	0.300

Answer 1

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