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Answer :
Final answer:
The equivalent annual cost is calculated using the present worth (PW) method, adding initial cost plus discounted annual costs for each year, and then dividing by the number of years. This takes into account the time value of money with the discount rate. The result shows the average yearly cost of the tool over its lifespan.
Explanation:
In this problem, the concept of the present worth or equivalent annual cost is explored. The present worth (PW) is given by the formula PW = Initial Cost + Annual Cost / (1+discount rate)year. Given that the initial cost is $14,000, the annual operating cost is $24,000, the discount rate is 12% or 0.12 as a decimal, and the lifespan of the tool is 3 years, we can calculate the present worth for each year and then divide by the lifespan to get the equivalent annual cost.
By using the formula, we can calculate as follows: PW = 14000 + (24000 / (1+0.12)1) + (24000 / (1+0.12)2) + (24000 / (1+0.12)3). After that, we can calculate the equivalent annual cost by dividing the total present worth by the number of years: Equivalent Annual Cost = PW / 3 years.
This calculation will give us the annual cost of the tool factoring in the time value of money, which is what the discount rate represents. If the calculated equivalent annual cost is greater than the actual annual cost, the tool might be considered too expensive.
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