Black Red sells $$30$ million of its furniture products to wholesalers on credit terms of $$net $30.$ Currently, the firm$$s average collection period is $70$ days. Black Red is considering offering a $5$ percent discount to customers who pay their bills within $5$ days. The firm expects $50$ percent of its customers to take the discount and its average collection period to decline to $40$ days. Black Red$$s required pretax return on receivables investment is $18$ percent.