UC Limited specializes in selling small electrical appliances. A considerable
portion of the company’s sales is on instalment basis. Although most of the
company’s customers make their instalment payments on time, a certain
percentage of their accounts are always overdue and some are never paid at all.
The company’s experience with overdue accounts has been that if a customer
falls two or more instalments behind schedule, then this account is generally
not going to be paid; hence it is the company’s policy of discontinuing credit to
such customers and to write these accounts off as bad debts. At the beginning
of each month, the company reviews each account and classifies them as either
“paid-up,” “current” (being paid on time), “overdue” (one payment past due)
or “bad debt.” To investigate this problem, the analysts at UC Limited have
constructed the transition matrix representing the various states that each
shilling in the accounts receivable can take on at the beginning of two
consecutive months.

Transition Matrix of UC Limited
State of each Sh. at next month
Paid (P1
) Current
(P2
)
Overdue
(P3
)
Bad debt
(P4
)
State of
each
Sh. first
Month
Paid (P1
)
Current
(P2
)
Overdue
(P3
)
Bad debt
(P4
)
1.00
0.30
0.50
0.00
0.00
0.50
0.30
0.00
0.00
0.20
0.10
0.00
0.00
0.00
0.10
1.00

Required:
(i) Interpret P22 and P23. (2 marks)
(ii) “Paid” and “bad debts” states have values of P. Interpret. (3
marks)
(iii) If the original amount of money outstanding was Sh. 100,000, determine
how much UC Limited expect to be paid back if the records indicate
that for every Sh. 100 in payments due Sh. 70 are classified as “current”
and Sh. 30 are classified as “overdue.”
(7 marks)
(Total: 20 marks)
Note: 1.00 0 0 0
Pn = 0.95 0 0 0.05
0.87 0 0 0.13
0 0 0 1.00