Carlson Corp. is considering whether to expand widget production. This would require the purchase of a...

Carlson Corp. is considering whether to expand widget production. This would require the purchase of a new widget-producing machine at a cost of $5,400,000. The machine would produce 450,000 widgets per year during its useful life of three years, and would be depreciated for tax purposes at a rate of $1,800,000 per year. The machine would have a salvage value of $500,000. Expanding widget production would also require the use of a building that could otherwise be leased for $500,000 per year. Working capital would be 12% of the next year’s sales. Widget prices are $20 and are expected to remain stable. The materials and labor required to produce a widget cost $12, and these costs are also expected to remain stable. The income tax rate is 21%. The discount rate is 10% per year.

(a) Compute the incremental free cash flow resulting from the purchase of a widget machine on a year-by-year basis.

(b) What is the NPV of the widget machine?

Expert Solution

(a) Calculation of incremental cash flows

Particulars	Year 0	Year 1	Year 2	Year 3
No. of widgets		450,000	450,000	450,000
Sale price per widget		20	20	20
Variable cost per widget		12	12	12
Sales		9,000,000	9,000,000	9,000,000
Variable costs		(5,400,000)	(5,400,000)	(5,400,000)
Opportunity cost of building		(500,000)	(500,000)	(500,000)
Depreciation		(1,800,000)	(1,800,000)	(1,800,000)
Cash flows before tax		1,300,000	1,300,000	1,300,000
Taxes @ 21%		(273,000)	(273,000)	(273,000)
Cash flows after tax		1,027,000	1,027,000	1,027,000
Add: Depreciation		1,800,000	1,800,000	1,800,000
Gross cash flows		2,827,000	2,827,000	2,827,000
Capital investment	(5,400,000)	-	-	-
Net working capital [9,000,000*12%]	(1,080,000)	-	-	1,080,000
Salvage value after tax [500,000(1-0.21)]				395,000
Incremental cash flows	(6,480,000)	2,827,000	2,827,000	4,302,000

(b) Computation of NPV of widget machine

Particulars	Year 0	Year 1	Year 2	Year 3
Incremental cash flows	(6,480,000)	2,827,000	2,827,000	4,302,000
PVF @ 10%	1.0000	0.9091	0.8264	0.7513
Present value	(6,480,000)	2,570,000	2,336,364	3,232,156
Net present value [Sum of PV]	1,658,520

jeff jeffy answered 2 years ago

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