Firm's operating as well as cash conversion cycles and decision on speeding up collections

Lunar Calendar Company is analyzing the performance of its cash management department. The firm has inventory which turns 7.2 times per year, an average payment period of 40 days, and an average collection period of 60 days. The firm's total annual outlays are $2,500,000. (Assume a 365-day year.)

(a) Calculate the firm's operating and cash conversion cycles.

(b) Calculate the amount of resources needed to support the firm's cash conversion cycle.

(c) The firm is considering speeding the collection of accounts receivable by using lockboxes. The lockboxes would reduce the average collection period by four days and cost $2,000 in fees. If the firm can earn 9% on its short-term investments, what recommendation would you make to the firm regarding the lockbox system?