Question

You are evaluating two different silicon wafer milling machines. The Techron I costs $282,000, has a 3-year life, and has pretax operating costs of $77,000 per year. The Techron II costs $490,000, has a 5-year life, and has pretax operating costs of $44,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $54,000. If your tax rate is 23 percent and your discount rate is 10 percent, compute the EAC for both machines. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Which machine do you prefer?

Techron I Techron II

Answer 1

The After-tax salvage Value

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

= $54,000 x (1 – 0.23)

= $54,000 x 0.77

= $41,580

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)

= [−$77,000(1 − 0.23)] + [($282,000 / 3 Years) x 0.23]

= [-$77,000 x 0.77] + [$94,000 x 0.23]

= -$59,290 + $21,620

= -$37,670

Net Present Value

Period	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of Cash Flow ($)
1	-37,670	0.9090909	-34,245.45
2	-37,670	0.8264463	-31,132.23
3	3,910 [-37,670 + 41,580]	0.7513148	2,937.64
TOTAL		2.4868520	-62,440.05

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

= -$62,440.05 - $282,000

= -$344,440.05

Equivalent Annual Cost (EAC)

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

= -$344,440.05 / 2.4868520

= -$1,38,504.44 (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)

= [−$44,000(1 − 0.23)] + [($490,000 / 5 Years) x 0.23]

= [-$44,000 x 0.77] + [$98,000 x 0.23]

= -$33,880 + $22,540

= -$11,340

Net Present Value

Period	Annual Cash Flow ($)	Present Value factor at 10%	Present Value of Cash Flow ($)
1	-11,340	0.9090909	-10,309.09
2	-11,340	0.8264463	-9,371.90
3	-11,340	0.7513148	-8,519.91
4	-11,340	0.6830135	-7,745.37
5	30,240 [-11,340 + 41,580]	0.6209213	18,776.66
TOTAL		3.7907868	-17,169.61

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

= -$17,169.61 - $490,000

= -$507,169.61

Equivalent Annual Cost (EAC)

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

= -$507,169.61 / 3.7907868

= -$133,790.07 (Negative)

DECISION

We should prefer the “Techron II” since it has the lower Equivalent Annual Cost (EAC) of -$133,790.07 as compared with the Equivalent Annual Cost (EAC) of Techron I.

Equivalent Annual Cost (EAC) for Techron I will be -$1,38,504.44 (Negative)

Equivalent Annual Cost (EAC) for Techron II will be -$133,790.07 (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.