Modelling Cashflow and Bad Debt

A trader extends credit to his customers. The credit extended falls into four categories - paid, bad debt, owing - if within a thirty day period - or overdue - if outside the period, up to thirty more days. Any money owing after this period becomes a bad dent. At some point there is £4,500 owing and £2,000 overdue. How much of this will turn into real. paid cash for the business?
The table of transition probabilities is - from experience:

From\To	Paid	Bad Debt	Owing	Overdue
Paid	1	0	0	0
Bad Debt	0	1	0	0
Owing	0.5	0	0.3	0.2
Overdue	0.4	0.3	0.2	0.1

This means for example that there is a probability of 0.5 that a debt owing will be paid before it is overdue.
The transition matrix is  
We can write this as    where

Then  .
This is a matrix of transition probabilities from    to  . .
It is predicted that £5330.55 will be paid and £1169.45 will turn into bad debts.