Question

Duke Corporation is analyzing two machines to determine which one it should purchase. Whichever machine is purchased will be replaced at the end of its useful life. The company requires a 12 percent rate of return and uses straight-line depreciation to a zero book value over the life of the machine. Machine A has a cost of $405,000, annual operating costs of $21,000, and a 3-year life. Machine B costs $276,000, has annual operating costs of $33,000, and a 2-year life. The firm currently pays no taxes. Which machine should be purchased and why?

		Machine A; because it will save the company about $6,687 a year
		Machine A; because it will save the company about $8,251 a year
		Machine B; because it will save the company about $5,947 a year
		Machine B; because it will save the company about $7,380 a year
		Machine A; because it will save the company about $7,506 a year

Answer 1

Machine A

Time line		0	1	2	3
Cost of new machine		-405000
=Initial Investment outlay		-405000
						100.00%
Sales			0	0	0
Profits	Sales-variable cost		0	0	0
Operating cost			-21000	-21000	-21000
-Depreciation	Cost of equipment/no. of years		-135000	-135000	-135000	0	=Salvage Value
=Pretax cash flows			-156000	-156000	-156000
-taxes	=(Pretax cash flows)*(1-tax)		-156000	-156000	-156000
+Depreciation			135000	135000	135000
=after tax operating cash flow			-21000	-21000	-21000
+Tax shield on salvage book value	=Salvage value * tax rate				0
=Terminal year after tax cash flows					0
Total Cash flow for the period		-405000	-21000	-21000	-21000
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928
Discounted CF=	Cashflow/discount factor	-405000	-18750	-16741.07	-14947.39
NPV=	Sum of discounted CF=	-455438.46

Year or period		0	1	2	3
EAC			-189621.3	-189621.3	-189621.3
Discount factor=	(1+discount rate)^corresponding period		1.12	1.2544	1.404928
Discounted CF=	Cashflow/discount factor		-169304.8	-151165	-134968.7
NPV=	-455438.46
EAC is equivalent yearly CF with same NPV =	-189621.3385

Machine B

Time line		0	1	2
Cost of new machine		-276000
=Initial Investment outlay		-276000
					100.00%
Sales			0	0
Profits	Sales-variable cost		0	0
Operating cost			-33000	-33000
-Depreciation	Cost of equipment/no. of years		-138000	-138000	0	=Salvage Value
=Pretax cash flows			-171000	-171000
-taxes	=(Pretax cash flows)*(1-tax)		-171000	-171000
+Depreciation			138000	138000
=after tax operating cash flow			-33000	-33000
+Tax shield on salvage book value	=Salvage value * tax rate			0
=Terminal year after tax cash flows				0
Total Cash flow for the period		-276000	-33000	-33000
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544
Discounted CF=	Cashflow/discount factor	-276000	-29464.29	-26307.4
NPV=	Sum of discounted CF=	-331771.68

EAC	-196308.6771
Year or period		0	1	2
EAC			-196308.7	-196308.7
Discount factor=	(1+discount rate)^corresponding period		1.12	1.2544
Discounted CF=	Cashflow/discount factor		-175275.6	-156496.1
NPV=	-331771.68
EAC is equivalent yearly CF with same NPV =	-196308.6771

Machine A EAC-Machine B EAC =-189621.3385+196308.6771

=

6687.34