Suppose Palmer Properties is considering investing $$3\mathrm{.}5$ million today $($i$.$e$.,$ C$0=-3,500,000)$ on a new project that is expected to last for $8$ years. The project is expected to generate annual cash flows of C$1=-600,000$; C$2=700,000,$ C$3=800,000$ and then $$900,000$ for period C$4$ through C$8.$ If the discount rate is $8\%$ and management$$s payback period cutoff is $5$ years:

$($a$)$ What is the payback period for the project? Show your work

$($b$)$ What is the net present value of the project $?$ Show your work

$($c$)$ What is the internal rate of return on the project $?$ Show your work

$($d$)$ Under which method$($s$)$ above should the company accept the project $($applying the acceptance rules$)?$ Explain