Question

You are evaluating two mutually exclusive machines used in your firm's production process. The ABC machine costs $261,000, has a 3-year life, and has pretax operating costs of $60,500 per year. XYZ machine costs $455,000, has a 5-year life, and has pretax operating costs of $32,000 per year. For both machines, use straight-line depreciation to zero over the machine's life and assume a salvage value of $47,000. If your firm's tax rate is 35% and your discount rate is 9%, compute the equivalent annual cost for both machines.

EAC for ABC machine = $

EAC for XYZ machine = $

(Round EAC's to the nearest $ value. Do not enter a '$' symbol. EACs are negative, so use a minus sign to indicate a negative number, as in '-2345.').

Answer 1

Cost of Machine ABC	261,000
Life of Machine ABC	3	years
Operating Cost (pre-tax)	60,500
Salvage Value ABC	47,000

Tax Rate	35%
Discount Rate	9%

The depreciation per year for machine ABC is calculated on a straight line basis as follows
Depreciation ABC (per year) = (Cost of Machine ABC - Salvage Value ABC) / (Life of Machine ABC)
= (261,000-47,000) / 3 = 71,333

To calculate the equivalent annual cost, let us first calculate the cashflow for Machine ABC
A negative value signifies cash outgo, and a positive signifies a cash inflow

Year 0	Cost of Machine ABC		(261,000)
Year 1	Operating Cost X (1-Tax Rate)		(39,325)
	Depreciation Benfit		24,967
Year 2	Operating Cost X (1-Tax Rate)		(39,325)
	Depreciation Benfit		24,967
Year 3	Operating Cost X (1-Tax Rate)		(39,325)
	Depreciation Benfit		24,967
	Salvage Cost		47,000

Depreciation Benefit arises because if one purchases the machine, they can charge the depreciation to the profit & loss account and claim tax benefit. Thus,
Depreciation Benefit = Tax Rate X Depreciation charge per year
=35% X 71,333 = 24,967

Also, operating costs can be set-off against the revenues of the company and thus, we need to consider the post-tax operating costs = Operating Costs X (1 - Tax Rate)

Thus, the cashflow in the case where the machine ABC is purchased is

Year 0	(261,000)
Year 1	(14,358)
Year 2	(14,358)
Year 3	32,642

Thus the Net Present Value (NPV) = 239,498

To calculate the Equivalent Annaulized cost for Machine ABC, we need to use the PMT Function in excel

PMT Rate 99 Nper Pv 239498 Fu o Type o = 0.09 = 3 = 239498 = -94614.82427 Calculates the payment for a loan based on constant payments and a constant interest rate.

EUAC Machine ABC = PMT (rate, no. of years, NPV of Machine ABC cashflow, 0, 0)
EUAC Machine ABC = PMT( 9%, 3, 239498),0,0)
= -94,615

The calculations for Machine XYZ are similar

Cost of Machine ABC	261,000
Life of Machine ABC	3	years
Operating Cost (pre-tax)	60,500
Salvage Value ABC	47,000

Tax Rate	35%
Discount Rate	9%

The depreciation per year for machine XYZ is calculated on a straight line basis as follows
Depreciation XYZ (per year) = (Cost of Machine XYZ - Salvage Value XYZ) / (Life of Machine XYZ)
= (455,000-47,000) / 5 = 81,600

To calculate the equivalent annual cost, let us first calculate the cashflow for Machine ABC
A negative value signifies cash outgo, and a positive signifies a cash inflow

Year 0	Cost of Machine XYZ		(455,000)
Year 1	Operating Cost X (1-Tax Rate)		(20,800)
	Depreciation Benfit		28,560
Year 2	Operating Cost X (1-Tax Rate)		(20,800)
	Depreciation Benfit		28,560
Year 2	Operating Cost X (1-Tax Rate)		(20,800)
	Depreciation Benfit		28,560
Year 3	Operating Cost X (1-Tax Rate)		(20,800)
	Depreciation Benfit		28,560
Year 4	Operating Cost X (1-Tax Rate)		(20,800)
	Depreciation Benfit		28,560
Year 5	Operating Cost X (1-Tax Rate)		(20,800)
	Depreciation Benfit		28,560
	Salvage Cost		47,000

Depreciation Benefit arises because if one purchases the machine, they can charge the depreciation to the profit & loss account and claim tax benefit. Thus,
Depreciation Benefit = Tax Rate X Depreciation charge per year
=35% X 81,600 = 28,560

Also, operating costs can be set-off against the revenues of the company and thus, we need to consider the post-tax operating costs = Operating Costs X (1 - Tax Rate)

Thus, the cashflow in the case where the machine XYZ is purchased is

Year 0	(455,000)
Year 1	7,760
Year 2	7,760
Year 3	7,760
Year 4	7,760
Year 5	54,760

Thus the Net Present Value (NPV) = 239,498

To calculate the Equivalent Annaulized cost for Machine ABC, we need to use the PMT Function in excel

PMT 1 Rate 99 Nper 5 Pv 361715 Fro Type o = 0.09 = 5 = 361715 1 = -92994.19807 Calculates the payment for a loan based on constant payments and a constant interest rate.

EUAC Machine XYZ = PMT (rate, no. of years, NPV of Machine ABC cashflow, 0, 0)
EUAC Machine XYZ = PMT( 9%, 5, 361715,0,0)
= -92,994

To summarize

EUAC Machine ABC = -94,615
EUAC Machine XYZ = -92,994