Bird's Eye Treehouses, Incorporated, a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. Therefore, it 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.

Average number of payments per day $760$

Average value of payment $ $710$

Variable lockbox fee $($per transaction$)$ $ $\mathrm{.}10$

Effective annual rate on money market securities $3\mathrm{.}8\%$

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