Kim Mitchell, the new credit manager of the Vinson Corporation, was alarmed to find that Vinson sells on credit terms of net $90$ days while industry$-$wide credit terms have recently been lowered to net $30$ days. On annual credit sales of $$2\mathrm{.}5$ million, Vinson currently averages $95$ days of sales in accounts receivable. Mitchell estimates that tightening the credit terms to $30$ days would reduce annual sales to $$2375,000,$ but accounts receivable would drop to $35$ days of sales and the savings on investment in them should more than overcome any loss in profit. Assume that Vinson$$s variable cost ratio is $85\%,$ taxes are $40\%,$ and the interest rate on funds invested in receivables is $18\%.$