Buckingham Packaging is considering expanding its production capacity by purchasing a new machine, the XC$-750.$ The cost of the XC$-750$ is $$3\mathrm{.}50$ million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $$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 $$12\mathrm{.}5$ 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 $$5$ million this year $($year $0).$ Once the machine is operating next year, the cost of goods for the products produced by the XC$-750$ is expected to be $70\%$ of their sale price. The increased production will require additional inventory on hand of $$2\mathrm{.}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$-750$ has a CCA rate of $46\%$ and no salvage value is expected. The firm expects receivables from the new sales to be $16\%$ of revenues and payables are expected to be $10\%$ of the cost of goods sold. Buckingham's marginal corporate tax rate is $40\%.$

a$.$ Determine the incremental earnings $($using CCA$)$ from the purchase of the XC$-750.$

b$.$ Determine the free cash flow $($including all CCA tax shield effects$)$ from the purchase of the XC$-750$ for the first $10$ years. $($Hint: include the impact in year $11.)$