Answer :
The equivalent annual cost of the tool is $21,827.42.
The equivalent annual cost of the tool is the cost per year that includes the purchase price, operating and maintenance costs, and the cost of capital used to finance the purchase. To calculate the equivalent annual cost, we need to use the formula:
EAC = A + (i * P) / (1 - (1 + i)^(-n))
where:
- EAC is the equivalent annual cost
- A is the annual operating and maintenance cost
- i is the discount rate
- P is the initial purchase price
- n is the number of years the tool will last
Using the given values, we get:
EAC = 20,000 + (0.12 * 10,000) / (1 - (1 + 0.12)^(-5))
= 20,000 + 1,827.42
= $21,827.42
Therefore, the equivalent annual cost of the tool is $21,827.42. This represents the annual cost of owning and operating the lathe over a 5-year period, taking into account the initial purchase price, operating and maintenance costs, and the cost of capital used to finance the purchase.
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