$(25$ points$)$ The after$-$tax cash flows for a new process are shown below $($all figures are expressed in $8$ million$).$ Using these figures, calculate the following:

$($a$)$ Payback period $($PBP$)$

$($b$)$ Cumulative cah position $($CCP$)$ and cumulative cash ratio $($CCR$)$

$($c$)$ Rate of return on investment $($ROROI$)$

$($d$)$ Discounted payback period $($DPBP$),$ assuming a $15\%$ discount rate

$($e$)$ Net present value $($NPV$),$ assuming a $15\%$ discount rate

$($f$)$ Discounted cah flow rate of return $($DCFROR$)$

$($g$)$ Is it a profit able process? Explain your answer.

$\backslash$table$[[$Year$,$Investment,$\backslash$table$[[$Depreciation$],[$alowance$]],$Revenue,Expenses,Net profit,$\backslash$table$[[$After$-$tax$],[$cash flow$]]],[0,-10,,,,,-10],[1,-20,,,,,-20],[2,-30,,,,,-30],[3,-20-{10}^a,,,,,-30],[4,,14,45,34,8\mathrm{.}69,22\mathrm{.}69],[5,,22\mathrm{.}4,45,42\mathrm{.}4,2\mathrm{.}054,24\mathrm{.}454],[6,,13\mathrm{.}44,45,33\mathrm{.}44,9\mathrm{.}1324,22\mathrm{.}5724],[7,,8\mathrm{.}064,45,28\mathrm{.}064,13\mathrm{.}3794,21\mathrm{.}4434],[8,,8\mathrm{.}064,45,28\mathrm{.}064,13\mathrm{.}3794,21\mathrm{.}4434],[9,,4\mathrm{.}032,45,24\mathrm{.}032,16\mathrm{.}5647,20\mathrm{.}5967],[10,,0,45,20,19\mathrm{.}75,19\mathrm{.}75],[11,,0,45,20,19\mathrm{.}75,19\mathrm{.}75],[12,,0,45,20,19\mathrm{.}75,19\mathrm{.}75],[13,{20}^6,0,45,20,19\mathrm{.}75,39\mathrm{.}75]]$

${?}^a$ The working capital is $810$ million

${?}^b$ The salvage value is zero

$($Hint: you need to draw the nondiscounted cumulative cash flow diagram for this process first. Use it to answer parts $($a$)-($c$).$ Then, discount the cumulati ve values to year $0$ and draw the discounted cumulative cash flow diagram. Use it to answer questions $($d$)-($f$).)$