Bruin, Incorporated, has identified the following two mutually exclusive projects:$$

Cash Flow $($A$)$

Year $0=-29,100$

Year $1=14,500$

Year $2=12,400$

Year $3=9,250$

Year $4=5,150$

Cash Flow $($B$)$

Year $0=-29,100$

Year $1=4,350$

Year $2=9,850$

Year $3=15,300$

Year $4=16,900$

$$a$-1.$What is the IRR for each of these projects? $($Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-2.$Using the IRR decision rule, which project should the company accept?$$

Project A

Project B

a$-3.$Is this decision necessarily correct?$$

Yes

No

b$-1.$If the required return is $12$ percent, what is the NPV for each of these projects? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$$ b$-2.$Which project will the company choose if it applies the NPV decision rule?$$

Project A

Project B$$

c$.$At what discount rate would the company be indifferent between these two projects? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$