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Part $1$

Billingham Packaging is considering expanding its production capacity by purchasing a new$$ machine, the$$ XC$-750.$ The cost of the$$ XC$-750$ is $ $2\mathrm{.}82$ million.$$ Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $ $49$ comma $000$ feasibility study to analyze the decision to buy the$$ XC$-750,$ resulting in the following$$ estimates:

bullet $$Marketing: Once the$$ XC$-750$ is operational 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.

bullet $$Operations: The disruption caused by the installation will decrease sales by $ $4\mathrm{.}96$ million this year. As with$$ Billingham's existing$$ products, the cost of goods for the products produced by the$$ XC$-750$ is expected to be $70\%$ of their sale price. The

increased production will also require increased inventory on hand of $ $1\mathrm{.}08$ million during the life of the$$ project, including year $0.$

bullet Human$$ Resources: The expansion will require additional sales and administrative personnel at a cost of $ $1\mathrm{.}94$ million per year.

bullet $$Accounting: The$$ XC$-750$ will be depreciated via the$$ straight$-$line method over the$10-$year life of the machine. The firm expects receivables from the new sales to be $15\%$ of revenues and payables to be $9\%$ of the cost of goods sold.$$ Billingham's marginal corporate tax rate is $21\%.$

a$.$ Determine the incremental earnings from the purchase of the$$ XC$-750.$

b$.$ Determine the free cash flow from the purchase of the$$ XC$-750.$

c$.$ If the appropriate cost of capital for the expansion is $9\mathrm{.}7\%,$ compute the NPV of the purchase.

d$.$ While the expected new sales will be $ $10\mathrm{.}15$ million per year from the$$ expansion, estimates range from $ $8\mathrm{.}05$ million to$$$ $12\mathrm{.}25$ million. What is the NPV in the worst$$ case? In the best$$ case?

e$.$ What is the$$ break$-$even level of new sales from the$$ expansion? What is the breakeven level for the cost of goods$$ sold?

f$.$ Billingham could instead purchase the$$ XC$-900,$ which offers even greater capacity. The cost of the$$ XC$-900$ is $ $4\mathrm{.}05$ million. The extra capacity would not be useful in the first two years of$$ operation, but would allow for additional sales in years $3$ through $10.$ What level of additional sales$($above the $ $10\mathrm{.}15$ million expected for the$$ XC$-750)$ per year in those years would justify purchasing the larger$$ machine?