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.

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 $3-10.$ 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?Tax rate

Cost of goods as a $\%$ of sales

First year sales value

Sales revenue

Cost of goods sold

Additional personnel

Depreciation

Net operating income

Minus income tax

a$.$ Incremental Earnings

Plus depreciation

Capital Expenditures

Subtract change in NWC

b$.$ Free cash flow

c$.$ Cost of capital

NPV

IRR

MIRR

PI

PB Period

$\backslash$table$[[21\mathrm{.}0\%$d$.$ Sales revenue

NPV

Base case

High revenue

Low revenue

$0$

$[12,000\mathrm{.}00,],[8,000\mathrm{.}00,],[,]$

e$.$

Breakeven sales

Breakeven cost of goods sold

f$.$ Sales revenue

Cost of goods sold

Additional personnel

Depreciation

Net operating income

Minus income tax

Equals Net income

Plus depreciation

Capital Expenditures

Subtract change in NWC

Free cash flow

Cost of capital

NPV

Year $0$

Year $1$

Year $2$

Year $3$

Year $4$

Year $5$

Year $6$

Year $7$

Year $8$

Year $9$

Year $10$

Year $11$

Net Working Capital Calculations:

Increased receivables

Increased payables

Increased inventory

NWC

Breakeven sales with more

expensive machine