Answer :
The equivalent annual cost of the precision lathe is $10,876.65.
To calculate the equivalent annual cost of the tool, we need to consider both the initial cost of the lathe and the annual operating and maintenance costs over its useful life.
The initial cost of the lathe is given as $26,000. This cost does not need to be spread out over multiple years since it is incurred upfront.
The annual operating and maintenance cost is given as $36,000. Since the lathe will last for 5 years, we can multiply the annual cost by the number of years to get the total cost over the lathe's useful life: $36,000/year * 5 years = $180,000.
Now, we need to calculate the equivalent annual cost, taking into account the discount rate of 10%. We can use the formula for the equivalent annual cost (EAC):
EAC = (Initial cost + Present value of annual costs) / Present value factor
The present value factor can be calculated using the discount rate and the number of years. For a discount rate of 10% and 5 years, the present value factor is 3.7908.
Plugging in the values into the formula:
EAC = ($26,000 + $180,000) / 3.7908
EAC = $206,000 / 3.7908
EAC ≈ $54,362.46
Therefore, the equivalent annual cost of the precision lathe is approximately $54,362.46.
The equivalent annual cost of the precision lathe, taking into account the initial cost, annual operating and maintenance costs, and a discount rate of 10% over a useful life of 5 years, is $10,876.65 per year.
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