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{.}69$ million. Unfortunately, installing this machine will

take several months and will partially disrupt production. The firm has just completed a $$49,000$ 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 $$10\mathrm{.}1$ 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 $$4\mathrm{.}97$ 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 $71\%$ of their sale price. The increased production will require additional inventory on hand of $$1\mathrm{.}11$ 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\mathrm{.}02$ million per year.

Accounting: The XC$-750$ will be depreciated via the straight$-$line method over the $10-$year life of the machine. Receivables are expected to be $14\%$ of revenues and payables to be $9\%$ 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 $10\mathrm{.}4\%,$ compute the NPV of the purchase.

d$.$ While the expected new sales will be $$10\mathrm{.}1$ million per year from the expansion, estimates range from $$8$ million to $$12\mathrm{.}2$ 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 $$3\mathrm{.}91$ 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\mathrm{.}1$ million expected for the XC$-750)$ per year in those years would justify purchasing

the larger machine?