Question

ou are evaluating two different silicon wafer milling machines. The Techron I costs $276,000, has a three-year life, and has pretax operating costs of $75,000 per year. The Techron II costs $480,000, has a five-year life, and has pretax operating costs of $48,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $52,000. If your tax rate is 21 percent and your discount rate is 12 percent, compute the EAC for both machines.

A) Techron I? Techron II?

B) Which machine do you prefer? Techron I or Techron II

Answer 1

The After-tax salvage Value

After-tax salvage value = $41,080 [$52,000 x (1 – 0.21)]

Equivalent Annual Cost (EAC) for Techron I

Operating Cash Flow (OCF)

= Pretax Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= [−$75,000(1 − 0.21)] + [($276,000 / 3 Years) x 0.21]

= −$59,250 + $19,320

= -$39,930

Net Present Value

Period	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	-39,930	0.892857	-35,651.79
2	-39,930	0.797194	-31,831.95
3	1,150 [-$39,930 + 41,080]	0.711780	818.55
TOTAL		2.401831	-66,665.19

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

= -$66,665.19 - $276,000

= -$3,42,665.19

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 12%, 3 Years]

= -$3,42,665.19 / 2.401831

= -$1,42,668.30 (Negative)

Equivalent Annual Cost (EAC) for Techron II

Operating Cash Flow (OCF)

= Pretax Savings(1 – Tax Rate) + (Depreciation x Tax Rate)

= [−$48,000(1 − 0.21)] + [($480,000 / 5 Years) x 0.21]

= −$37,920 + $20,160

= -$17,760

Net Present Value

Period	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	-17,760	0.892857	-15,857.14
2	-17,760	0.797194	-14,158.16
3	-17,760	0.711780	-12,641.22
4	-17,760	0.635518	-11,286.80
5	23,320 [-$17,760 + 41,080]	0.567427	13,232.39
TOTAL		3.604776	-40,710.93

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

= -$40,710.93 - $480,000

= -$5,20,710.93

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 12%, 5 Years]

= -$5,20,710.93 / 3.604776

= -$1,44,450.28 (Negative)

DECISION

We should prefer the “Techron I” since it has the lower Equivalent Annual Cost (EAC) of -$1,42,668.30 as compared with the Equivalent Annual Cost (EAC) of Techron II.

“Equivalent Annual Cost (EAC) for Techron I = -$142,668.30 (Negative)”

“Equivalent Annual Cost (EAC) for Techron II = -$144,450.28 (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.