Billingham Packaging is considering expanding its production capacity by purchasing a new$$ machine, the$$ XC$-750.$ The cost of the$$ XC$-750$ is $ $2\mathrm{.}74$ million.$$ Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $ $45$ 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 operating next$$ year, the extra capacity is expected to generate $ $10$ million per year in additional$$ sales, which will continue for the$$ ten$-$year life of the machine.

bullet $$Operations: The disruption caused by the installation will decrease sales by $ $4\mathrm{.}91$ million this year. As with$$ 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 $ $1\mathrm{.}01$ million during the life of the project. The increased production will require additional inventory of $ $1\mathrm{.}01$million$,$ to be added in year $0$ and depleted in year $10.$

bullet Human$$ Resources: The expansion will require additional sales and administrative personnel at a cost of $ $2\mathrm{.}01$ million per year.

bullet $$Accounting: The$$ XC$-750$ will be depreciated via the$$ straight$-$line method in years$1-10.$ Receivables are expected to be$15\%$ of revenues and payables to be $10\%$ of the cost of goods sold.$$ Billingham's marginal corporate tax rate is $15\%.$

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 $10\mathrm{.}1\%,$ compute the NPV of the purchase.

d$.$ While the expected new sales will be $ $10$ million per year from the$$ expansion, estimates range from $ $8\mathrm{.}05$ million to $ $11\mathrm{.}95$ million. What is the NPV in the worst$$ case? In the best$$ case?

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

f$.$ Billingham could instead purchase the$$ XC$-900,$ which offers even greater capacity. The cost of the$$ XC$-900$ is $ $4\mathrm{.}09$ million. The extra capacity would not be useful in the first two years of$$ operation, but would allow for additional sales in years$3-10.$ What level of additional sales$($above the $ $10$ million expected for the$$ XC$-750)$ per year in those years would justify purchasing the larger$$ machine?