Problem $27-8$ Lockboxes and Collections

It takes Cookie Cutter Modular Homes, Incorporated, about six days to receive and deposit checks from customers. The company's management is considering a lockbox system to reduce the firm's collection times. It is expected that the lockbox system will reduce receipt and deposit times to three days total. Average daily collections are $$136,000$ and the required rate of return is an EAR of $6$ percent. Assume $365$ days per year.

a$.$ What is the reduction in the outstanding cash balance as a result of implementing the lockbox system? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$

b$.$ What is the daily dollar return that could be earned on these savings? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$-1.$ What is the maximum monthly charge the company should pay for this lockbox system if the payment is due at the end of the month? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$-2.$ What is the maximum monthly charge the company should pay for this lockbox system if the payment is due at the beginning of the month? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$