A project has the following after$-$tax total $($or net$)$ cash flows.

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Year After$-$tax total $($or net$)$ cash flow$\_$

$1$ $$500,000$

$2600,000$

$3800,000$

$41,000,000$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

The required rate of return on the project is $13$ percent. The initial investment $($or initial cost or initial outlay$)$ of the project is $$1,500,000.$

a$)$ Find the net present value $($NPV$)$ of the project.

b$)$ Find the profitability index $($PI$)$ of the project.

c$)$ Calculate the modified internal rate of return $($MIRR$)$ of the project.