A company plans to purchase equipment for $$500,000$ which will generate after$-$tax cash flows of $$210,000$ in year $1$ and $$200,000$ per year in years $2$&$3.$ This equipment is estimated to have a positive terminal value of $$25,000.$ The company interest rate is $12\%.$ Calculate:

Net present value $($round to the nearest $$)$

Present value index $[$aka "profitability index"$]($round to $3$ decimal places$)$

Payback period $($in years$)$

In addition calculate the internal rate of return.