$5.($Worth $20$ points$)$ A petroleum company is considering a new project that complements its existing business. The machine required for the project costs $$2$ million. The marketing department predicts that sales related to the project will be $$1\mathrm{.}2$ million per year for the next four years, after which the market will cease to exist. The machine will be depreciated down to zero over its five$-$year economic life using the straight$-$line method. Cost of goods sold and operating expenses related to the project are predicted to be $25\%$ of sales. After four years the machine can be sold for $$150,000.$ The petroleum company also needs to add net working capital of $$100,000$ in Year $0$ when it acquires the machine. The additional net working capital will be recovered in full at the end of the project$$s life as opposed to the machine economic life. The corporation tax rate is $35\%.$ The required rate of return for the petroleum company is $15\%.$ Compute the NPV$.$ Compute the internal rate of return. Compute the profitability index. Should the petroleum company proceed with the project? Your worksheet must follow this format:$\backslash$table$[[,,,,,,],[,,,,,,],[,,,,,,],[$Free Cash Flow,,,,,,$],[,,,,,,]]$