Question

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2) You are evaluating two different aluminum milling machines. The Alumina I costs $240,000, has a three-year life, and has pretax operating costs of $63,000 per year. The Alumina II costs $420,000, has a five-year life, and has pretax operating costs of $36,000 per year. For both milling machines, use straight-line depreciation to zero over the project's life and assume a salvage value of $40,000. If your tax rate is 35 percent and your discount rate is 10 percent, which do you prefer? Why?

Answer 1

Alumina I:

Cost of Machine = $240,000
Useful Life = 3 years

Annual Depreciation = Cost of Machine / Useful Life
Annual Depreciation = $240,000 / 3
Annual Depreciation = $80,000

Annual OCF = Pretax Operating Costs * (1 - tax) + tax * Depreciation
Annual OCF = -$63,000 * (1 - 0.35) + 0.35 * $80,000
Annual OCF = -$12,950

Salvage Value = $40,000

After-tax Salvage Value = $40,000 * (1 - 0.35)
After-tax Salvage Value = $26,000

NPV = -$240,000 - $12,950 * PVIFA(10%, 3) + $26,000 * PVIF(10%, 3)
NPV = -$240,000 - $35,250 * 2.486852 + $42,000 * 0.7513148
NPV = -$296,106.311082

EAC = NPV / PVIFA(10%, 3)
EAC = -$296,106.311082 / 2.486852
EAC = -$119,068.73

Alumina II:

Cost of Machine = $420,000
Useful Life = 5 years

Annual Depreciation = Cost of Machine / Useful Life
Annual Depreciation = $420,000 / 5
Annual Depreciation = $84,000

Annual OCF = Pretax Operating Costs * (1 - tax) + tax * Depreciation
Annual OCF = -$36,000 * (1 - 0.35) + 0.35 * $84,000
Annual OCF = $6,000

Salvage Value = $40,000

After-tax Salvage Value = $40,000 * (1 - 0.35)
After-tax Salvage Value = $26,000

NPV = -$420,000 + $6,000 * PVIFA(10%, 5) + $26,000 * PVIF(10%, 5)
NPV = -$420,000 +$6,000 * 4.32947667058+ $26,000 * 0.78352617
NPV = -$373,651.46

EAC = NPV / PVIFA(10%, 5)
EAC = -$373,651.46 / 4.32947667058
EAC = -$86,304.07

So, you should prefer Alumina II as its EAC is lower than that of Alumina I