Question

Pilot plus Pens is deciding when to replace its old machine. The old machine’s current salvage value is $2 million. Its current book value is $1 million. If not sold, the old machine will require maintenance costs of $400,000 at the end of the year, for the next five years. Depreciation on the old machine is $200,000 per year. At the end of five years, the old machine will have salvage value of $200,000 and a book value of $0. A replacement machine costs $3 million now and requires maintenance costs of $500,000 at the end of each year during its economic life of five years. At the end of five years, the new machine will have a salvage value of $500,000. It will be fully depreciated by the straight-line method. In five years, a replacement machine will cost $3,500,000. Pilot will need to purchase this machine regardless of what the choice it makes today. The corporate tax rate is 34% and the appropriate discount rate is 12%. The company is assumed to earn sufficient revenues to generate tax shields from depreciation. Should Pilot Plus replace the old machine now or at the end of five years?

Please write down the specific formula

Answer 1

We shall ignore the purchase of replacement machine after
5 years as that is required for both options and there
is no differentiation between 2 options.
Old Machine Current Book value	1,000,000
Old machine current salvage value	2,000,000
Capital Gain on Old Machine current sale	1,000,000
Tax rate	34%
Tax on Capital Gain on salvage @34%=	340,000
Annual Depreciation on Old Machine	200,000
Book value after 5 years	-
Salvage value after 5 years	200,000
Capital Gain on salvage after 5 yrs	200,000
Tax on Capital Gain on salvage after 5 yrs=	68,000
Annual Maintenance cost	400,000

New Machine :
Cost of New Machine	3,000,000
Useful life in years	5
Annual SL depreciation	600,000
Annual Maintenance cost	500,000
Salvage value after 5 yrs	500,000
Book Value after 5 yrs	-
Capital gain on Salvage	500,000
Tax on Capital Gain @34%	170,000

Annual cost comparison	Depreciation	Maintenance
New Machine anuual expenses	600,000	500,000
Old Machine	200,000	400,000
Incremental Expense	400,000	100,000
Tax saving on Incremental expense @34%	136,000	34,000

	NPV of Replacement
	Initial Investment	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
	New Machine cost	(3,000,000)
	Sale Proceeds from old machine	2,000,000
	Tax on Capital gain of Old m/c sale	(340,000)
a	Total Initial Investment	(1,340,000)
	Cash flow from Operations
	Increase in Maintenance cost		(100,000)	(100,000)	(100,000)	(100,000)	(100,000)
	Tax savings on incremental		34,000	34,000	34,000	34,000	34,000
	Depreciation Tax Savings		136,000	136,000	136,000	136,000	136,000
b	Net Cash flow from operations		70,000	70,000	70,000	70,000	70,000
	Terminal Cash flow
	After Tax Salvage of New Machine						330,000
	Less: Opportunity loss of After Tax salvage of Old m/c						(132,000)
c	Net Termial Cash flow						198,000
d	Total Free cash flow from Replacement=a+b+c	(1,340,000)	70,000	70,000	70,000	70,000	268,000
e	PV factor @12% =1/1.12^n=	1	0.8929	0.7972	0.7118	0.6355	0.5674
f	PV of FCF =d*e=	(1,340,000)	62,503	55,804	49,826	44,485	152,063
g	NPV =Sum of PV of FCFs =	(975,319)

As the NPV of the replacement is negative, Pilot plus should not replace the old machine.