108. ZSE Co (June 10 – Modified)
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 which 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.
Required:
A. Calculate the following values:
(i) the expected value of the period 1 closing balance
(ii) the expected value of the period 2 closing balance
(iii) the probability of a negative cash balance at the end of period 2
(iv) the probability of exceeding the overdraft limit at the end of period 2.
Discuss whether the above analysis can assist the company in managing its cash flows.
(i) Period 1 closing balance
Opening balance 
Cash flow 
Closing balance 
Probability 
Expected value 
$000 
$000 
$000 

$000 
(500) 
8,000 
7,500 
0.1 
750 
(500) 
4,000 
3,500 
0.6 
2,100 
(500) 
(2,000) 
(2,500) 
0.3 
(750) 




2,100 
The expected value of the period 1 closing balance is $2,100,000.
(ii) Period 2 closing balance
Period 1 closing balance 
Probability 
Period 2 cash flow 
Probability 
Period 2 closing balance 
Joint probability 
Expected value 
$000 

$000 

$000 

$000 
7,500 
0.1 
7,000 
0.3 
14,500 
0.03 
435 


3,000 
0.5 
10,500 
0.05 
525 


(9,000) 
0.2 
(1,500) 
0.02 
(30) 
3,500 
0.6 
7,000 
0.3 
10,500 
0.18 
1,890 


3,000 
0.5 
6,500 
0.30 
1,950 


(9,000) 
0.2 
(5,500) 
0.12 
(660) 
(2,500) 
0. 3 
7,000 
0.3 
4,500 
0.09 
405 


3,000 
0.5 
500 
0.15 
75 


(9,000) 
0.2 
(11,500) 
0.06 
(690) 






3,900 
The expected value of the period 2 closing balance is $3,900,000.
(iii) The probability of a negative cash balance at the end of period 2
= 0.02 + 0.12 + 0.06 = 20%
(iv) The probability of exceeding the overdraft limit in period 2 is 0.12 + 0.06 = 18%.
Discussion
The expected value analysis has shown that, on an average basis, ZSE Co will have a positive cash balance at the end of period 1 of $2.1 million and a positive cash balance at the end of period 2 of $3.9 million. However, the cash balances that are expected to occur are the specific balances that have been averaged, rather than the average values themselves.
There could be serious consequences for ZSE Co if it exceeds its overdraft limit. For example, the overdraft facility could be withdrawn. There is a 30% chance that the overdraft limit will be exceeded in period 1 and a lower probability, 18%, that the overdraft limit will be exceeded in period 2. To guard against exceeding its overdraft limit in period 1, ZSE Co must find additional finance of $0.5 million ($2.5m – $2.0m). However, to guard against exceeding its overdraft limit in period 2, the company could need up to $9.5 million ($11.5m – $2.0m). Renegotiating the overdraft limit in period 1 would therefore be only a shortterm solution.
One strategy is to find now additional finance of $0.5 million and then to reevaluate the cash flow forecasts at the end of period 1. If the most likely outcome occurs in period 1, the need for additional finance in period 2 to guard against exceeding the overdraft limit is much lower.
The expected value analysis has been useful in illustrating the cash flow risks faced by ZSE Co. Although the cash flow forecasting model has been built with the aid of a firm of financial consultants, the assumptions used in the model must be reviewed before decisions are made based on the forecast cash flows and their associated probabilities.
Expected values are more useful for repeat decisions rather than oneoff activities, as they are based on averages. They illustrate what the average outcome would be if an activity was repeated a large number of times. In fact, each period and its cash flows will occur only once and the expected values of the closing balances are not closing balances that are forecast to arise in practice. In period 1, for example, the expected value closing balance of $2.1 million is not forecast to occur, while a closing balance of $3.5 million is likely to occur.