Billingham Packaging is considering expanding its production capacity by purchasing a new machine, the XC$-750.$ The cost of the XC$-750$ is $$2\mathrm{.}75$ million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $$50,000$ feasibility study to analyze the decision to buy the XC$-750,$ resulting in the following estimates: $$ Marketing: Once the XC$-750$ is operating next year, the extra capacity is expected to generate $$10$ million per year in additional sales, which will continue for the $10-$year life of the machine. $$ Operations: The disruption caused by the installation will decrease sales by $$5$ million this year. Once the machine is operating next year, the cost of goods for the products produced by the XC$-750$ is expected to be $70\%$ of their sale price. The increased production will require additional inventory on hand of $$1$ million to be added in year $0$ and depleted in year $10.$ Human Resources: The expansion will require additional sales and administrative personnel at a cost of $$2$ million per year. $$ Accounting: The XC$-750$ will be depreciated via the straight$-$line method over the $10-$year life of the machine. The firm expects receivables from the new sales to be $15\%$ of revenues and payables to be $10\%$ of the cost of goods sold. Billingham$$s marginal corporate tax rate is $35\%.$ Based on the information provided, please write a report to answer the following questions: $1.$ Determine the incremental earnings from the purchase of the XC$-750.2.$ Determine the free cash flow from the purchase of the XC$-750.3.$ If the appropriate cost of capital for the expansion is $10\%,$ compute the NPV of the purchase.

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