Bird's Eye Treehouses, Incorporated, a Kentucky company, has determined that a

majority of its customers are located in the Pennsylvania area. It therefore is considering

using a lockbox system offered by a bank located in Pittsburgh. The bank has estimated

that use of the system will reduce collection time by $1\mathrm{.}5$ days. Assume $365$ days a year.

Average number of payments per day

Average value of payment

Variable lockbox fee $($per transaction$)$

Annual interest rate on money market securities

a$.$ What is the NPV of the new lockbox system? $($Do not round intermediate

calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ Suppose in addition to the variable charge that there is an annual fixed charge of

$$3,000$ to be paid at the end of each year. What is the NPV now? $($A negative answer

should be indicated by a minus sign. Do not round intermediate calculations and

round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$