A machine costs $60,000. Running costs are $10,000 in year 1, $14,000 in year 2 and $18,000 in year 3. Its resale value is $30,000 after 2 years or $20,000 after 3 years. The cost of capital is 10% (DFs 0.909, 0.826, 0.751; annuity factors 1.736 for 2 years and 2.487 for 3 years). Which replacement cycle minimises cost, and what is its equivalent annual cost (EAC)?

Correct answer: D) Replace every 3 years; EAC $31,826

Explanation

2-year cycle: PV of costs = 60,000 + 10,000 x 0.909 + 14,000 x 0.826 - 30,000 x 0.826 = $55,874; EAC = $55,874 / 1.736 = $32,185. 3-year cycle: PV = 60,000 + 9,090 + 11,564 + 18,000 x 0.751 - 20,000 x 0.751 = $79,152; EAC = $79,152 / 2.487 = $31,826. The 3-year cycle has the lower EAC (rounded to the nearest $). Comparing total PVs is wrong because the cycles are of different lengths.