ABC Ins. has the following mutually exclusive projects.

Year Project A Project B

$0-$$$20,000-$$$25,000$

$1$ $$15,000$ $$15,000$

$2$ $$10,000$ $$11,000$

$3$ $$5,000$ $$20,000$

$($a$)$ Suppose the company$$s payback period cutoff is two years. Which of these two projects should be chosen?

$($b$)$ Suppose the company uses the NPV rule to rank these to projects. Which project should be chosen if the discount rate is $12$ percent?