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ZSE Co is concerned about exceeding its overdraft limit of $2 million in the next two
periods. It has been experiencing considerable volatility in cash flows in recent periods
because of trading difficulties experienced by its customers, who have often settled their
accounts after the agreed credit period of 60 days. ZSE has also experienced an increase in
bad debts due to a small number of customers going into liquidation.
The company has prepared the following forecasts of net cash flows for the next two
periods, together with their associated probabilities, in an attempt to anticipate liquidity
and financing problems. These probabilities have been produced by a computer model that
simulates a number of possible future economic scenarios. The computer model has been
built with the aid of a firm of financial consultants.
Period 1 cash flow Probability Period 2 cash flow Probability
$000 $000
8,000 10% 7,000 30%
4,000 60% 3,000 50%
(2,000) 30% (9,000) 20%
ZSE Co expects to be overdrawn at the start of period 1 by $500,000.
Solution-
a) 1) expected value for period 1= 8000*0.1 + 4000*0.6 + (2000)*30% -500 (overdraft balance in the beginning of period 1)= 2100
2) expected value for period 2= 7000*0.3 + 3000*0.5 + (9000)*0.2 +2100 (balance from period 1) = 3900
now the requirement asked us to calculate EV for both the periods which I understood but it also asked to calculated this:
3) the probability of a negative cash balance at the end of period 2
4) the probability of exceeding the overdraft limit at the end of period 2.
and this is the working of it from the solution-
3)The probability of a negative cash balance at the end of period 2 = 0.02 + 0.12
+ 0.06 = 20%
4) The probability of exceeding the overdraft limit in period 2 is 0.12 + 0.06 =
18%
Sir could you please explain where did they get these values from?If the first year is 7,500 and the second year is 7,000 then the closing balance is 14,500.
The probability of the first year being 7,500 is 0.1 and of the second year being 7,000 is 0.3.
Therefore the probability of both happening is 0.1 x 0.3 = 0.03.If the first year is 7,500 and the second year is 3,000, then the closing balance is 10,500
The probability of the first year being 7,500 is 0.1 and of the second year being 3,000 is 0.5.
Therefore the probability of both happening is 0.1 x 0.5 = 0.05It is the same workings for each of the various possibilities.
Three of the closing balances are negative and so the probability of there being a negative balance is the total of the three probabilities.
The overdraft limit is 2,000 and only two of the closing balances are over 2,000 (5,500 and 11,500), so the probability of exceeding the limit is the total of the two probabilities of getting those balances.
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