Question $5(12$ points$).$ Kate wants to launch a pizzeria. Initially, she needs to invest $$120,000$ in manufacturing equipment and $$50,000$ in net working capital. The project can last for $5$ years. At the end of the project, Kate can recover $100\%$ of the initial investment in net working capital. Kate uses the straight$-$line depreciation method for the manufacturing equipment and assume that the terminal value of the manufacturing equipment is $0.$ When the project goes into operation, she can sell $45,000$ pizzas per year at a price of $$7\mathrm{.}5$ per pizza. It costs about $$4\mathrm{.}5$ to make a pizza. Fixed operating costs such as rent on the production facility are $$20,000$ per year. Taxes are $35\%$ and the required return is $12\%.$ Calculate NPV$,$ IRR, payback, discounted payback, and the profitability index of this project? $$ Revenue Per Year $=($Pizzas Sold Per Year$)$ x $($Price Per Pizza$)$ Revenue Per Year $=45,000$ x $7\mathrm{.}5=$ $$337,500$ Variable Cost Per Year $=($Pizzas Sold Per Year$)$ x $($Variable Cost Per Pizza$)$ Variable Cost Per Year $=45,000$ x $4\mathrm{.}5=$ $$202,500$ Total Operating Cost Per Year $=($Fixed Cost Per Year$)$ x $($Variable Cost Per Year$)$ Total Operating Cost Per Year $=202,500+20,000=$ $$222,500$ EBIT $=$ Revenue $$ Total Operating Cost EBIT $=337,500222,500=$ $$115,000$ Net Income Per Year $=$ EBIT $($EBIT x $0\mathrm{.}35)$ Net Income Per Year $=115,000(115,000$ x $0\mathrm{.}35)=$ $$74,750$