Financial Planning Model. For a number of years, Brugge Company of Brussels, Belgium, has had difficulty in budgeting its monthly income statement and cash flows. As an outside consultant, you have been hired by the controller to develop a rudimentary financial planning model that will lead to a budgeted monthly income statement and cash receipts and cash disbursements schedules. Upon investigation, you find the following relationships:

(a) Sales revenue is growing at 0.5 percent per month.

(b) Sixty percent of each month's sales are for cash; the remaining 40 percent are credit sales.

(c) Credit sales are collected at 50 percent in the month of sale, 45 percent in the month after the sale, and 5 percent in the second month after the sale.

(d) Cost of goods sold averages 75 percent of sales.

(e) Purchases in units each month equal the forecast sales units for the next month.

(f) Seventy percent of purchases are paid in the month of purchase, with half of these qualifying for a 2 percent cash discount. The remaining 30 percent is paid in the following month.
(g) The monthly operating expenses are 1 percent of monthly sales revenue plus fixed costs in Belgian francs of BF20,000, of which BF2,000 is depreciation. These expenses are paid in the month incurred.
(h) Income taxes are ignored on a monthly basis.
Required Prepare a series of equations, based on the foregoing relationships, that will allow the company to budget net income and cash flow. Define independent and dependent variables by symbols or abbreviations. Use subscripts to indicate time periods, such as \({ }_{t}\) for the current month, \({ }_{t-1}\) for the prior month, and \({ }_{t+1}\) for the next month.