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 operational next$$ year, the extra capacity is expected to generate $$10\mathrm{.}00$ 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{.}06$ 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 $72\%$ of their sale price. The

increased production will also require increased inventory on hand of $$1\mathrm{.}14$ million during the life of the$$ project, including year $0.$

$$ Human$$ Resources: The expansion will require additional sales and administrative personnel at a cost of $$2\mathrm{.}09$ million per year.

$$Accounting: The$$ XC$-750$ will be depreciated via the$$ straight$-$line method over the$10-$year life of the machine. The firm expects receivables from the new sales to be $15\%$ of revenues and payables to be $9\%$ of the cost of goods sold.$$ 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 $10\mathrm{.}4\%,$ compute the NPV of the purchase.

d$.$ While the expected new sales will be $$10\mathrm{.}00$ million per year from the$$ expansion, estimates range from $$8\mathrm{.}10$ million to$$$$11\mathrm{.}90$ million. What is the NPV in the worst$$ 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 $$4\mathrm{.}01$ million. The extra capacity would not be useful in the first two years of$$ operation, but would allow for additional sales in years $3$ through $10.$ What level of additional sales$($above the $$10\mathrm{.}00$ million expected for the$$ XC$-750)$ per year in those years would justify purchasing the larger$$ machine?