Question

3. (18 points) You are considering two different systems for pollution control. System I costs $965,000, has an eight year life, and has pre-tax operating costs of $7,350 per year. System II costs $560,000, has a five year life, and has pre-tax operating costs of $38,100 per year. For both systems use straight line depreciation and assume neither system has any salvage value. If your tax rate is 34% and your discount rate is 12 % , which do you prefer? Show me with calculations.

Answer 1

System I:

Cost of Machine = $965,000
Useful Life = 8 years

Annual Depreciation = Cost of Machine / Useful Life
Annual Depreciation = $965,000 / 8
Annual Depreciation = $120,625

Annual OCF = Pretax Operating Costs * (1 - tax) + tax * Depreciation
Annual OCF = -$7,350 * (1 - 0.34) + 0.34 * $120,625
Annual OCF = $36,161.50

NPV = -$965,000 + $36,161.50 * PVIFA(12%, 8)
NPV = -$965,000 + $36,161.50 * 4.967640
NPV = -$785,362.68614

EAC = NPV / PVIFA(12%, 8)
EAC = -$785,362.68614 / 4.967640
EAC = -$158,095.73

System II:

Cost of Machine = $560,000
Useful Life = 5 years

Annual Depreciation = Cost of Machine / Useful Life
Annual Depreciation = $560,000 / 5
Annual Depreciation = $112,000

Annual OCF = Pretax Operating Costs * (1 - tax) + tax * Depreciation
Annual OCF = -$38,100 * (1 - 0.34) + 0.34 * $112,000
Annual OCF = $12,934

NPV = -$560,000 + $12,934 * PVIFA(12%, 5)
NPV = -$560,000 + $12,934 * 3.604776
NPV = -$513,375.827216

EAC = NPV / PVIFA(12%, 5)
EAC = -$513,375.827216 / 3.604776
EAC = -$142,415.46

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