$1)$ Kingston Corp. is considering a new machine that requires an initial investment of $$480,000$ installed and has a useful life of $8$ years. The expected annual after$-$tax cash flows for the machine are $$89,000$ for each of the $8$ years and nothing thereafter.

a$.$ Calculate the net present value of the machine if the required rate of return is $11$ percent.

b$.$ Calculate the IRR of this project.

c$.$ Should Kingston accept the project $($assume that it is independent and not subject to any capital rationing constraint$)?$ Explain your answer.