A company is evaluating a lockbox system proposal. The average number of payments received by the company per day is 1,500 and the average payment amount is $200. The bank proposing the system will charge the company a variable cost of $0.05 per transaction (i.e. payment processed) in addition to a $5,000 annual fee. The bank has estimated that use of the lockbox system will reduce the company's collection time by two days. The annual interest rate is 6%.

(a) Should the proposed lockbox system by accepted?

(b) what is the maximum annual fee the company should pay for this lockbox system?

Please explain with a step-by-step solution including formulas.