Question

Billingham Packaging is considering expanding its production capacity by purchasing a new​ machine, the​ XC-750. The cost of the​ XC-750 is

$ 2.77$2.77

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

$ 49 comma 000$49,000

feasibility study to analyze the decision to buy the​ XC-750, resulting in the following​ estimates:

bullet•

​Marketing: Once the​ XC-750 is operational next​ year, the extra capacity is expected to generate

$ 10.00$10.00

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

$ 4.91$4.91

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

74 %74%

of their sale price. Theincreased production will also require increased inventory on hand of

$ 1.19$1.19

million during the life of the​ project, including year 0.

bullet•

Human​ Resources: The expansion will require additional sales and administrative personnel at a cost of

$ 1.99$1.99

million per year.

bullet•

​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 %15%

of revenues and payables to be

11 %11%

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

35 %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

9.6 %9.6%​,

compute the NPV of the purchase.d. While the expected new sales will be

$ 10.00$10.00

million per year from the​ expansion, estimates range from

$ 8.05$8.05

million to  

$ 11.95$11.95

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 breakeven 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

$ 3.91$3.91

million. The extra capacity would not be useful in the first two years of​ operation, but would allow for additional sales in years 3 through 10. What level of additional sales​ (above the

$ 10.00$10.00

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

a. Determine the incremental earnings from the purchase of the​ XC-750.

Calculate the incremental earnings from the purchase of the​ XC-750 below​ (with vs. without​ XC?750):  ​(Round to the nearest​ dollar.)

Incremental Effects
Year		0
Sales Revenues	$
Cost of Goods Sold	$
S, G, and A Expenses	$
Depreciation	$
EBIT	$
Taxes at 35%	$
Unlevered Net Income	$

Answer 1

a.Incremental Effects
Year	mlns.
Sales Revenues	10
Cost of Goods Sold	-7.4
S, G, and A Expenses	-1.99
Depreciation	-0.277
EBIT	0.333
Taxes at 35%	-0.11655
Unlevered Net Income	0.21645

b.FCFs			Yr.1-Yr.9
Year 0	Yr.0		FCFs
1.Cost of XC-750	-2.77		Unlevered Net Income	0.21645
Decrease in sales	-4.91		Add back: depn.	0.277
Dec.in COGS(74%*sales)	3.6334		Annual OCF/FCF	0.49345
2.After-tax net sales lost	-0.82979
Inc.in Inv.	-1.19		Yr.10
Inc.Rec.(10*15%)	-1.5		Annual OCF/FCF	0.49345
Inc.inPay.(7.4*11%)	0.814		NWC recov.	1.876
3.NWC introduced	-1.876		FCF	2.36945
Net Yr.0 CFs(1+2+3)	-5.47579

NPV at 9.6% cost of capital

-5.47579+(0.49345*5.85174)+(2.36945*0.39985)

-1.64082

P/A,i=9.6%;n=9 yrs.=5.85174

P/F,i=9.6%;n=yr.9=0.39985

Inputs   (fig.in mlns.)
Incl.Sales	10
COGS(sales*75%)	74%
Year	0	1	2	3	4	5	6	7	8	9	10
1.Cost of XC-750	-2.77
Sales	-4.91	10	10	10	10	10	10	10	10	10	10
COGS	3.6334	-7.4	-7.4	-7.4	-7.4	-7.4	-7.4	-7.4	-7.4	-7.4	-7.4
Sales& admn.		-1.99	-1.99	-1.99	-1.99	-1.99	-1.99	-1.99	-1.99	-1.99	-1.99
Incl. EBT	-1.2766	0.61	0.61	0.61	0.61	0.61	0.61	0.61	0.61	0.61	0.61
Tax at 35%	0.44681	-0.2135	-0.2135	-0.2135	-0.2135	-0.2135	-0.2135	-0.2135	-0.2135	-0.2135	-0.2135
Incl.EAT	-0.82979	0.3965	0.3965	0.3965	0.3965	0.3965	0.3965	0.3965	0.3965	0.3965	0.3965
Add:Dep.tax shld(2.77/10*35%)		0.09695	0.09695	0.09695	0.09695	0.09695	0.09695	0.09695	0.09695	0.09695	0.09695
2.Incl.OCF	-0.82979	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345
(ANSWER:a)
NWC
Inventory	-1.19	-1.19	-1.19	-1.19	-1.19	-1.19	-1.19	-1.19	-1.19	-1.19	-1.19
Receivables(-15%*revenues)		-1.5	-1.5	-1.5	-1.5	-1.5	-1.5	-1.5	-1.5	-1.5	-1.5
Payables(-11%*COGS)		0.814	0.814	0.814	0.814	0.814	0.814	0.814	0.814	0.814	0.814
NWC reqd.	-1.19	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876
Beg. NWC	0	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876
End.NWC	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	-1.876	0
3.Chg. In NWC	-1.876	0	0	0	0	0	0	0	0	0	1.876
FCF (1+2+3)	-5.47579	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	0.49345	2.36945
(ANSWER:b)
PV F at 9.6%(1/1.096^Yr.n)	1	0.91241	0.83249	0.75957	0.69304	0.63234	0.57695	0.52641	0.48030	0.43823	0.39985
PV at 9.7%	-5.47579	0.450228	0.410792	0.37481	0.34198	0.312026	0.284695	0.259758	0.237006	0.216246	0.947419
NPV at 9.7%	-1.64083
(ANSWER:c.)

d.	NPV
Worst (sales $ 8.05 mln.)	-3.62076
Best (sales $ 11.95 mln.)	0.339098
e.
Break-even level of new sales(mlns.)	11.61603
Break-even $ of COGS (% )	70%

f..Forming an equation for the NPV of the base case for XC-750 & the NPV for XC-900

-1.64083=-3.91+((x-(0.74*x)-1.99)*(1-35%)*4.50669)+(3.91/10*35%*6.25159)

solving the above,

sales, x should be minimum $ 9.50992 mlns.

to justify the purchase.

P/A,i=9.6^,n=10 yrs.=6.25159