A company is considering an investment proposal to install a new machine at a cost of Tk$.1,00,000.$ Its life period is $5$ years with a residual value of Tk$.15,000.$ The tax rate is $40$ percent. The estimated cash flows before depreciation and tax are as follows :

$\backslash$table$[[$Year$,$CFBT $($Taka$)],[1,26,000],[2,28,650],[3,30,200],[4,35,100],[5,55,600]]$

Required Rate of Return is estimated at $12\%$

Compute the following :

$($i$)$ Pay Back Period, $($ii$)$ Average Rate of Return, $($iii$)$ Internal Rate of Return, $($iv$)$ Net Present Value, $($v$)$ Discounted Pay Back Period and $($vi$)$ Profitability Index.