As the treasury manager for a sporting goods manufacturer, you are responsible for the firms cash management activities, including the cash collection system. Your firm receives an average of 5,000 remittances per month with an average face value of $10,000. The current collection system consists of customers remitting directly to company headquarters. The average mail delay is 3 days. The typical remittance remains at headquarters for 2 days. You are informed that the average deposit is available in 2 days. Assume that the opportunity investment rate is 5% and that it costs your firm $0.35 to process each check.

a. Compute the monthly total cost for your firm's current cash collection system.

b. Your bank, interested in selling you a lockbox system, indicates that a lockbox system would reduce mail float by 2 days, processing float by 2 day, and availability float by 1 day. If the system charges a variable cost of $.80 per item and monthly fixed cost of S500, should you change to the lockbox system?