Buckingham Packaging is considering expanding its production capacity by purchasing a new$$ machine, the$$ XC$-750.$ The cost of the$$ XC$-750$ is $ $3\mathrm{.}25$ million.$$ Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $ $50$ comma $000$ feasibility study to analyze the decision to buy the$$ XC$-750,$ resulting in the following$$ estimates:

Marketing$$: Once the$$ XC$-750$ is operating next$$ year, the extra capacity is expected to generate $ $11\mathrm{.}0$ million per year in additional$$ 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 $ $1\mathrm{.}7$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 $35\%$ and no salvage value is expected. The firm expects receivables from the new sales to be $13\%$ of revenues and payables are expected to be$10\%$ of the cost of goods sold.$$ Buckingham's marginal corporate tax rate is $34\%.$

c$.$ If the appropriate cost of capital for the expansion is $13\%,$ compute the NPV of the purchase$($including all CCA tax shield$$ effects$).($Hint: when calculating the NPV$,$ you should calculate the free cash flows excluding CCA tax shields then add the PV CCA tax shields to get the NPV$.)$

d$.$ While the expected new sales will be $$$$11\mathrm{.}0$ million per year from the$$ expansion, estimates range from $ $8$ comma $800$ comma $000$ to$$$ $13$ comma $200$ comma $000.$ What is the NPV in the worst$$ case? In the best$$ case?

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Part $1$

c$.$ If the appropriate cost of capital for the expansion is $13\%,$ compute the NPV of the purchase.

The NPV is $$$

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