Billingham Packaging is considering expanding its production capacity by purchasing a new machine, the XC-750. The cost of the XC-750 is \($2.68\) million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a \($45,000\) 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

\($10.15\) 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 \($5.01\) million this year. Once the machine is operating next year, 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 \($1.12\) 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 \($1.97\) 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 10% of the cost of goods sold. Billingham’s marginal corporate tax rate is 35%.

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 9.9%, compute the NPV of the purchase.

d. While the expected new sales will be \($10.15\) million per year from the expansion, estimates range from \($8.20\) million to \($12.1\) 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?

f. Billingham could instead purchase the XC-900, which offers even greater capacity. The cost of the XC-900 is \($3.93\) 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 \($10.15\) million expected for the XC-750) per year in those years would justify purchasing the larger machine?