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 12.2. Each month Entson incurs fixed costs of $250,000. Taxes of $150,000 must be paid in March, and taxes of $50,000 must be paid in June. 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 Strepresent 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 dips 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 through 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.