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{.}822\mathrm{.}82$

million.$$ Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a

$$$$54$ comma $00054,000$

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\mathrm{.}1510\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{.}964\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

$70\%70\%$

of their sale price. The increased production will require additional inventory on hand of

$$$$1\mathrm{.}801\mathrm{.}80$

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{.}132\mathrm{.}13$

million per year.

bullet$$

$$Accounting: The$$ XC$-750$ will be depreciated via the$$ straight$-$line method over the$10-$year life of the machine. Receivables are expected to be

$16\%16\%$

of revenues and payables to be

$12\%12\%$

of the cost of goods sold.$$ Billingham's marginal corporate tax rate is

$15\%15\%.$

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

$10\mathrm{.}3\%10\mathrm{.}3\%,$

compute the NPV of the purchase.$$

d$.$ While the expected new sales will be

$$$$10\mathrm{.}1510\mathrm{.}15$

million per year from the$$ expansion, estimates range from

$$$$8\mathrm{.}158\mathrm{.}15$

million to

$ $12\mathrm{.}15$$$12\mathrm{.}15$

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{.}204\mathrm{.}20$

million. The extra capacity would not be useful in the first two years of$$ operation, but would allow for additional sales in years

$3$dash$10.$

What level of additional sales$($above the

$$$$10\mathrm{.}1510\mathrm{.}15$

million expected for the$$ XC$-750)$ per year in those years would justify purchasing the larger$$ machine?