The Michner Corporation is trying to choose between the following two mutually exclusive design projects:

Year Cash Flow $($I$)$ Cash Flow $($II$)$

$0$$ $78,000$$ $36,000$

$130,00012,000$

$238,00025,500$

$344,00019,500$

a$-1.$ If the required return is $13$ percent, what is the profitability index for each project?

Note: Do not round intermediate calculations and round your answers to $3$ decimal places, e$.$g$.,32\mathrm{.}161.$

a$-2.$ If the company applies the profitability index decision rule, which project should it take?

b$-1.$ If the required return is $13$ percent, what is the NPV for each project?

Note: Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$-2.$ If the company applies the net present value decision rule, which project should it take?