answer this in great detail. be specific becasue the software is picky

Please answer showing work in detail.

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

a$-1.$ If the required return for both projects is $12$ percent, what is the profitability index for both projects?

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 the firm accept?

b$-1.$ What is the NPV for both projects?

Note: A negative answer should be indicated by a minus sign. 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 NPV decision rule, which project should it choose?