You are the manager of a local shipping$/$logistics facility, and your boss has two possible projects to improve efficiency in the loading dock. Your company uses an internal annual rate of return of $6\%($or $0\mathrm{.}06).$ Evaluate the two potential projects as shown below. One project has immediate savings in years $1$ through $5.$ The second project has no savings in the first year, but has greater savings for years $2$ through $5.$

$1)$ find the net present value $($NPV$)$ of each project, and $2)$ make a recommendation to your boss about which project appears better. Show all of your calculations and "work".

Project A:

Project cost $($today$,$ at time zero$)=$ $$15,000$

Annual savings $($or revenues$)$ of $$4000$ per year, for five years $($years $1,2,3,4,$ and $5)$

Project B:

Project cost $($today$,$ at time zero$)=$ $$20,000$

Annual savings $($or revenues$)$ in year $1=$ $$0$

Annual savings $($or revenues$)$ of $$7000$ for the next four years $($years $2,3,4,$ and $5)$

Remember to show all of your calculations and "work" $.$