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 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.

Operations: The disruption caused by the installation will decrease sales by $$5$ 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$ 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$ million per year.

Accounting: The XC$-750$ will be depreciated via the straight$-$line method over the ten$-$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 $21\%.$

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 $10\%,$ compute the NPV$,$ IRR,

MIRR, PI$,$ and payback period of the purchase.

d$)$ While the expected new sales will be $$10$ million per year from the expansion, estimates range from $$8$ million to $$12$ 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 $$4$ million. The extra capacity would not be useful in the first

two years of operation but would allow for additional sales in years $310.$ 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?

$***$ Please show all work on excel