Question

Billingham Packaging is considering expanding its production capacity by purchasing a new​ machine, the​ XC-750. The cost of the​ XC-750 is $2.72 million.​ Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $48,000 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 $10.2 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 $4.93 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% of their sale price. The increased production will also require increased inventory on hand of $1.1 million during the life of the project. The increased production will require additional inventory of $1.1 ​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 $2.06 million per year. • ​Accounting: The​ XC-750 will be depreciated via the​ straight-line method in years​ 1?10. Receivables are expected to be  14% of revenues and payables to be 10% of the cost of goods sold.​ Billingham?s marginal corporate tax rate is 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 10.3%​, compute the NPV of the purchase.

d. While the expected new sales will be $10.2 million per year from the​ expansion, estimates range from $8.3 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 $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 $10.2 million expected for the​ XC-750) per year in those years would justify purchasing the larger​ machine?

Answer 1

Sales Revenue	$10.2 million
Cost of Goods Sold (COGS)	74%
SGA Expenses	$2.06 million
Capital Expenditure (CE)	$2.72 million
Tax Rate	15%
Cost of Capital	10.3%
Receivables % of sales	14%
Payables % of COGS	10%
Depreciation	CE / 10

(a.)

Years	0	1 to 10
Sales Revenue	-49,30,000.00	1,02,00,000.00
Less: COGS	-36,48,200.00	75,48,000.00
Less: SGA Expenses		20,60,000.00
Less: Depreciation		2,72,000.00
Earnings before Interest & Tax (EBIT)	-12,81,800.00	3,20,000.00
Less: Tax @ 15%	-1,92,270.00	48,000.00
Unlevered Net Income	-10,89,530.00	2,72,000.00

(b.)

Year	0	1	2 to 9	10	11
Inventory	11,00,000.00	11,00,000.00	11,00,000.00	0	0
Add: Receivables	-6,90,200.00	14,28,000.00	14,28,000.00	14,28,000.00
Less: Payables	-3,64,820.00	7,54,800.00	7,54,800.00	7,54,800.00
Net working Capital (NWC)	7,74,620.00	17,73,200.00	17,73,200.00	6,73,200.00
Increase in Net Working Capital	-7,74,620.00	-9,98,580.00	0	11,00,000.00	6,73,200.00

Year	0	1	2 to 9	10	11
Unlevered Net Income	-10,89,530.00	2,72,000.00	2,72,000.00	2,72,000.00	0
Add: Depreciation	0	2,72,000.00	2,72,000.00	2,72,000.00	0
Less: Capital Expenditure	27,20,000.00	0	0	0	0
Add: Change in NWC	-7,74,620.00	-9,98,580.00	0	11,00,000.00	6,73,200.00
Free Cash Flow	-45,84,150.00	-4,54,580.00	5,44,000.00	16,44,000.00	6,73,200.00

(c.) NPV is difference of Present value of all inflows and outflows.

Year	0	1	2	3	4	5	6	7	8	9	10	11	Sum of all PV
Free Cash Flow (FCF)	-45,84,150.00	-4,54,580.00	5,44,000.00	5,44,000.00	5,44,000.00	5,44,000.00	5,44,000.00	5,44,000.00	5,44,000.00	5,44,000.00	16,44,000.00	6,73,200.00
Discounting Factor @ 10.3%	1.0000	0.9066	0.8220	0.7452	0.6756	0.6125	0.5553	0.5035	0.4565	0.4138	0.3752	0.3401
Present Value Of FCF	-45,84,150.00	-4,12,130.55	4,47,144.48	4,05,389.38	3,67,533.43	3,33,212.54	3,02,096.59	2,73,886.30	2,48,310.34	2,25,122.70	6,16,803.30	2,28,988.39	-15,47,793.10

NPV = - $15,47,793.10

(d.) For calculating NPV in best and worst case we have to follow all step for calculating FC in different scenario.

if Sales is $8.3 million

Years	0	1 to 10
Sales Revenue	-49,30,000.00	83,00,000.00
Less: COGS (74%)	-36,48,200.00	61,42,000.00
Less: SGA Expenses		20,60,000.00
Less: Depreciation		2,72,000.00
Earnings before Interest & Tax (EBIT)	-12,81,800.00	-1,74,000.00
Less: Tax @ 15%	-1,92,270.00	-26,100.00
Unlevered Net Income	-10,89,530.00	-1,47,900.00
Year	0	1	2 to 9	10	11
Inventory	11,00,000.00	11,00,000.00	11,00,000.00	-	-
Add: Receivables	-6,90,200.00	11,62,000.00	11,62,000.00	11,62,000.00
Less: Payables	-3,64,820.00	6,14,200.00	6,14,200.00	6,14,200.00
Net working Capital	7,74,620.00	16,47,800.00	16,47,800.00	5,47,800.00
Increase in Net Working Capital	-7,74,620.00	-8,73,180.00	-	11,00,000.00	5,47,800.00
Year	0	1	2 to 9	10	11
Unlevered Net Income	-10,89,530.00	-1,47,900.00	-1,47,900.00	-1,47,900.00	-
Add: Depreciation	-	2,72,000.00	2,72,000.00	2,72,000.00	-
Less: Capital Expenditure	27,20,000.00	-	-	-	-
Add: Change in NWC	-7,74,620.00	-8,73,180.00	-	11,00,000.00	5,47,800.00
Free Cash Flow	-45,84,150.00	-7,49,080.00	1,24,100.00	12,24,100.00	5,47,800.00
Year	0	1	2	3	4	5	6	7	8	9	10	11	Sum of all PV
Free Cash Flow (FCF)	-45,84,150.00	-7,49,080.00	1,24,100.00	1,24,100.00	1,24,100.00	1,24,100.00	1,24,100.00	1,24,100.00	1,24,100.00	1,24,100.00	12,24,100.00	5,47,800.00
Discounting Factor @ 10.3%	1.0000	0.9066	0.8220	0.7452	0.6756	0.6125	0.5553	0.5035	0.4565	0.4138	0.3752	0.3401
Present Value Of FCF	-45,84,150.00	-6,79,129.65	1,02,004.83	92,479.45	83,843.56	76,014.11	68,915.78	62,480.31	56,645.80	51,356.12	4,59,263.33	1,86,333.69	-40,23,942.65

if sales is $12.1 million

Years	0	1 to 10
Sales Revenue	-49,30,000.00	1,21,00,000.00
Less: COGS	-36,48,200.00	89,54,000.00
Less: SGA Expenses		20,60,000.00
Less: Depreciation		2,72,000.00
Earnings before Interest & Tax (EBIT)	-12,81,800.00	8,14,000.00
Less: Tax @ 15%	-1,92,270.00	1,22,100.00
Unlevered Net Income	-10,89,530.00	6,91,900.00
Year	0	1	2 to 9	10	11
Inventory	11,00,000.00	11,00,000.00	11,00,000.00	-	-
Add: Receivables	-6,90,200.00	16,94,000.00	16,94,000.00	16,94,000.00
Less: Payables	-3,64,820.00	8,95,400.00	8,95,400.00	8,95,400.00
Net working Capital	7,74,620.00	18,98,600.00	18,98,600.00	7,98,600.00
Increase in Net Working Capital	-7,74,620.00	-11,23,980.00	-	11,00,000.00	7,98,600.00
Year	0	1	2 to 9	10	11
Unlevered Net Income	-10,89,530.00	6,91,900.00	6,91,900.00	6,91,900.00	-
Add: Depreciation	-	2,72,000.00	2,72,000.00	2,72,000.00	-
Less: Capital Expenditure	27,20,000.00	-	-	-	-
Add: Change in NWC	-7,74,620.00	-11,23,980.00	-	11,00,000.00	7,98,600.00
Free Cash Flow	-45,84,150.00	-1,60,080.00	9,63,900.00	20,63,900.00	7,98,600.00
Year	0	1	2	3	4	5	6	7	8	9	10	11	Sum of all PV
Free Cash Flow (FCF)	-45,84,150.00	-1,60,080.00	9,63,900.00	9,63,900.00	9,63,900.00	9,63,900.00	9,63,900.00	9,63,900.00	9,63,900.00	9,63,900.00	20,63,900.00	7,98,600.00
Discounting Factor @ 10.3%	1.0000	0.9066	0.8220	0.7452	0.6756	0.6125	0.5553	0.5035	0.4565	0.4138	0.3752	0.3401
Present Value Of FCF	-45,84,150.00	-1,45,131.46	7,92,284.13	7,18,299.30	6,51,223.30	5,90,410.97	5,35,277.40	4,85,292.29	4,39,974.88	3,98,889.28	7,74,343.27	2,71,643.09	9,28,356.45

if Sales is $8.3 million, then NPV is - $40,23,942.65

if sales is $12.1 million, then NPV is $9,28,356.45