A machine costs $72,000 and has a maximum life of 3 years.The running costs each year are as follows:Year1 7,2002 9,6003 12,000The estimated scrap values are as follows:Year1 24,0002 16,6003 9,600The cost of capital is 15%How often should the machine be replaced?September 2023 to June 2024 exams Watch free ACCA FM lectures 55
Question
A machine costs $72,000 and has a maximum life of 3 years.The running costs each year are as follows:Year1 7,2002 9,6003 12,000The estimated scrap values are as follows:Year1 24,0002 16,6003 9,600The cost of capital is 15%How often should the machine be replaced?September 2023 to June 2024 exams Watch free ACCA FM lectures 55
Solution
To determine how often the machine should be replaced, we need to calculate the equivalent annual cost (EAC) for each year and then choose the year with the lowest EAC.
The EAC is calculated as follows:
EAC = (Initial cost - Salvage value) / (Present value annuity factor for the cost of capital) + Annual running cost
Let's calculate the EAC for each year:
Year 1: EAC = (72000 - 24000) / (1/0.15) + 7200 = $38,400
Year 2: EAC = (72000 - 16600) / ((1 - (1 + 0.15)^-2) / 0.15) + (7200 + 9600) / 2 = $35,600
Year 3: EAC = (72000 - 9600) / ((1 - (1 + 0.15)^-3) / 0.15) + (7200 + 9600 + 12000) / 3 = $34,800
The machine should be replaced every 3 years, as this is when the equivalent annual cost is the lowest.
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