Question

One year ago, your company purchased a machine used in manufacturing for $120,000. You have learned that a new machine is available that offers many advantages; you can purchase it for $160,000 today. It will be depreciated on a straight-line basis over ten years, after which it has no salvage value. You expect that the new machine will contribute EBITDA (earnings before interest, taxes, depreciation, and amortization) of $40,000 per year for the next ten years. The current machine is expected to produce EBITDA of $22,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, after which it will have no salvage value, so depreciation expense for the current machine is $10,909 per year. All other expenses of the two machines are identical. The market value today of the current machine is $50,000. Your company's tax rate is 38%, and the opportunity cost of capital for this type of equipment is 11%. The NPV of the replacement is? Is it profitable to replace the year-old machine?

Answer 1

Old Machine Cost	120,000
Useful Life in years	11
Annual depreciation	10,909
Current book value (after 1 year)=120000-10909=	109,091
Current Market Value	50,000
Capital Loss on sale	59,091
Tax Rate	38%
Tax Savings from Capital Loss =59091*38%=	22,455
New Machine cost	160,000
Useful Life in years	10
Annual SL depreciation	16,000
Annual Incremental Depreciation over old m/c	5,091
Annual Tax shield on incremental depreciation@38%=	1,935
EBITDA difference
Annual EBITDA from New Machine	40,000
Annual EBITDA from Old Machine	22,000
Annual Incremental EBITDA from New Machine	18,000
Tax on Annual Incremental EBITDA @38%	6,840
After Tax Annual Incremental Income from New Machine	11,160

	NPV of Repalcement	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10
	New Machine cost	(160,000)
	Sale Proceeds of Old machine	50,000
	Tax Savings from Capital Loss on old machine sale=	22,455
a	Net Initial Investment	(87,545)
	Cash flow from Operations
	After Tax incremental Operating income		11,160	11,160	11,160	11,160	11,160	11,160	11,160	11,160	11,160	11,160
	Incremental Depreciation Tax shield		1,935	1,935	1,935	1,935	1,935	1,935	1,935	1,935	1,935	1,935
b	Operating cash flow		13,095	13,095	13,095	13,095	13,095	13,095	13,095	13,095	13,095	13,095
c	Free Cash flow from Project =a+b=	(87,545)	13,095	13,095	13,095	13,095	13,095	13,095	13,095	13,095	13,095	13,095
d	PV Factor @11% =1/1.11^n=	1	0.9009	0.8116	0.7312	0.6587	0.5935	0.5346	0.4817	0.4339	0.3909	0.3522
e	PV of Free Cash flows=c*d=	(87,545)	11,797	10,628	9,575	8,625	7,772	7,000	6,308	5,682	5,119	4,612
f	NPV of Replacement=Sum of PV of free cash flows=	(10,429)
	As the NPV of the replacement is negative, the year-old machine should not be replaced.