In the cash balance model from Example 11.6, the timing is such that some receipts are delayed by one or two months, and the payments for materials and labor must be made a month in advance. Change the model so that all receipts are received immediately, and payments made this month for materials and labor are 80% of sales this month (not next month). The period of interest is again January through June. Rerun the simulation, and comment on any differences between your outputs and those from the example.
EXAMPLE 11.6 MAINTAINING A MINIMAL CASH BALANCE AT ENTSON
The Entson Company believes that its monthly sales during the period from November of the current year to July of next year are normally distributed with the means and standard deviations given in Table 11.2. Each month Entson incurs fixed costs of $250,000. In March taxes of $150,000 and in June taxes of $50,000 must be paid. Dividends of $50,000 must also be paid in June. Entson estimates that its receipts in a given month are a weighted sum of sales from the current month, the previous month, and two months ago, with weights 0.2, 0.6, and 0.2. In symbols, if Rt and St represent receipts and sales in month t, then
The materials and labor needed to produce a month’s sales must be purchased one month in advance, and the cost of these averages to 80% of the product’s sales. For example, if sales in February are $1,500,000, then the February materials and labor costs are $1,200,000, but these must be paid in January.
At the beginning of January, Entson has $250,000 in cash. The company wants to ensure that each month’s ending cash balance never falls below $250,000. This means that Entson might have to take out short-term (one-month) loans. For example, if the ending cash balance at the end of March is $200,000, Entson will take out a loan for $50,000, which it will then pay back (with interest) one month later. The interest rate on a short-term loan is 1% per month. At the beginning of each month, Entson earns interest of 0.5% on its cash balance. The company wants to use simulation to estimate the maximum loan it will need to take out to meet its desired minimum cash balance. Entson also wants to analyze how its loans will vary over time, and it wants to estimate the total interest paid on these loans.
Objective To simulate Entson’s cash flows and the loans the company must take out to meet a minimum cash balance.
WHERE DO THE NUMBERS COME FROM? Although there are many monetary inputs in the problem statement, they should all be easily accessible. Of course, Entson chooses the minimum cash balance of $250,000 as a matter of company policy.