Q$3(20$ points$)$ We are designing a process for the manufacture of $80,000$ tonnes$/$y of ethylbenzene $($EB$).$ The total module cost of the plant has been estimated at $$140m.$

Determine Net Present Value $($NPV$)$ and Discounted Payback Period $($DPBP$)$ and comment on the profitability of this project.

Other information:

$\backslash$table$[[$Land:$,$$$10$m$],[FCI(CT{m}_{cm})$:$,50\%$ at end of year $1,50\%$ at end of year $2],[$Working capital:,$$25$m$],[$Salvage value:,$10\%$ of FCl$],[$Tax Rate:,$25\%],[$Depreciation:$,$MACRS $5-$years$],[$Start$-$up:$,$End of year $2],[$Plant life:,$10$ years after start$-$up$],[$Hurdle Rate:,$10\%],[$EB sales price:,$$2\mathrm{.}15/$kg$],[$Labor cost:$,$$$1\mathrm{.}3$m$/$year$],[$Raw Materials:,$$81$m$/$year$],[$Utilities:$,$$$5\mathrm{.}2$m$/$year$],[$Waste Treatment:,$$0\mathrm{.}8$m$/$year$]]$

$($a$)$ Determine the annual revenue $(R)$ and cost of manufacturing excluding depreciation $($COMd$).$

$($b$)$ Determine cumulative cash position $($CCP$)$ and payback period $($PBP$)$

$($c$)$ Determine net present value $($NPV$)$ and discounted payback period $($DPB$)$ and comment on the profitability of this project, explaining your answer.