Billingham Packaging is considering expanding its production capacity by purchasing a new machine, the XC$-750.$ The cost of the XC$-750$ is $$2\mathrm{.}68$ million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $$45,000$ 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\mathrm{.}15$ 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\mathrm{.}01$ 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 $71\%$ of their sale price. The increased production will require additional inventory on hand of $$1\mathrm{.}12$ million to be added in year $0$ and depleted in year $10.$

$$ Human Resources: The expansion will require additional sales and administrative personnel at a cost of $$1\mathrm{.}97$ 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 $35\%.$

b$.(2$ points$)$ Determine the free cash flow from the purchase of the XC$-750.$ Note that you need determine the required net working capital first.