Problem $19-08$ Lockboxes and Collections $[$LO$2]$

It takes Cookie Cutter Modular Homes, Inc., 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 $$163,000,$ and the required rate of return is $7$ percent per year. Assume $365$ days per year.

a$.$ What is the reduction in outstanding cash balances as a result of implementing the lockbox system?

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$.$s $32\mathrm{.}16.)$

$\backslash$table$[[,,],[$a$.,$Outstanding cash balance reduction,$$,489,000],[$b$.,$Daily dollar return,$$,93\mathrm{.}78],[$c$-1.,$Maximum monthly charge,$$,2,813\mathrm{.}42$