Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $268,500, has a three-year life, and has pretax operating costs of $46,100 per year. The Techron II costs $367,500, has a five-year life, and has pretax operating costs of $49,100 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $25,500. Assume the tax rate is 35 percent and the discount rate is 10 percent.

   

Requirement 1:

Compute the EAC for both the machines. (Do not include the dollar signs ($). Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

The After-tax salvage Value

After-tax salvage value = Salvage Value x (1 – Tax Rate)

= $25,500 x (1 – 0.35)

= $25,500 x 0.65

= $16,575

Equivalent Annual Cost (EAC) for Techron I

Operating Cash Flow (OCF)

Operating Cash Flow (OCF) = Pretax Cost Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= [−$46,100(1 − 0.35)] + [($268,500 / 3 Years) x 0.35]

= -$29,965 + $31,352

= $1,360

Net Present Value

Year	Annual cash flows ($)	Present Value Factor (PVF) at 10.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	1,360	0.9090909	1,236.36
2	1,360	0.8264463	1,123.97
3	17,935 [1,360 + 16,575]	0.7513148	13,474.83
TOTAL	2.4868520	15,835.16

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $15,835.16 - $268,500

= -$252,664.84

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 10%, 3 Years]

= -$252,664.84 / 2.4868520

= -$101,600.27 (Negative)

Equivalent Annual Cost (EAC) for Techron II

Operating Cash Flow (OCF)

Operating Cash Flow (OCF) = Pretax Cost Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= [−$49,100(1 − 0.35)] + [($367,500 / 5 Years) x 0.35]

= -$31,915 + $25,725

= -$6,190

Net Present Value

Year	Annual cash flows ($)	Present Value Factor (PVF) at 10.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	(6,190)	0.9090909	(5,627.27)
2	(6,190)	0.8264463	(5,115.70)
3	(6,190)	0.7513148	(4,650.64)
4	(6,190)	0.6830135	(4,227.85)
5	10,385 [-6,190 + 16,575]	0.6209213	6,448.27
TOTAL	3.7907868	(13,173.20)

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$13,173.20 - $367,500

= -$380,673.20

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 10%, 5 Years]

= -$380,673.20 / 3.7907868

= -$100,420.63 (Negative)

DECISION

We should prefer the “Techron II” since it has the lower Equivalent Annual Cost (EAC) of -$100,420.63 as compared with the Equivalent Annual Cost (EAC) of Techron II.

Equivalent Annual Cost (EAC) for Techron I will be -$101,600.27 (Negative)

Equivalent Annual Cost (EAC) for Techron II will be -$100,420.63 (Negative)

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.