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

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

$0$$ $75,000$$ $33,000$

$128,50010,500$

$235,00022,500$

$341,00016,500$

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?

a$-1.$ Project I:

a$-1.$ Project II:

a$-2.$

b$-1.$ Project I:

b$-1.$ Project II:

b$-2.$