$($i$)$ Define Net Present Value $($NPV$)$ and state the NPV rule.

$($ii$)$ Define Internal Rate of Return $($IRR$)$ and state the IRR rule.

$($iii$)$ What is the relationship between IRR and NPV$?$

$($iv$)$ You are looking at investing $$1500000.$ This investment will generate $$400000$ at the end of year $1,$$$600000$ at the end of year $2,$ and $$750000$ at the end of year $3.$ Using $9\%$ as the discount rate, calculate the NPV$.$ Should you accept this investment?

$($v$)$ Determine the IRR for an initial outlay of $$2$ million, and a cash flow of $$250000$ per year into perpetuity.