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. Based on the following information, should the lockbox system be adopted? Assume $365$ days per year.

Average number of payments per day $825$

Average value of payment $ $745$

Variable lockbox fee $($per transaction$)$ $ $\mathrm{.}15$

Annual interest rate on money market securities $5\mathrm{.}5\%$

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 $$5,000$ 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$.,32\mathrm{.}16.)$