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Answer :
Final answer:
The equivalent annual cost of the precision lathe is calculated by determining the total expenditure over its 5-year lifespan, discounting it to its present value using the given discount rate and then distributing it over 5 years. This gives us a value of $19,523.
Explanation:
To calculate the equivalent annual cost (EAC) of the precision lathe, we need to find the total expenditure over its 5-year lifespan and then discount it back to the present value using the discount rate. After that, we distribute this discounted total expense over the 5-year period to get the EAC.
First, we calculate the total operation and maintenance cost for 5 years, which is $28,500 * 5 = $142,500.
Adding to this the initial purchase cost, we get $142,500 + $11,700 = $154,200.
We discount this total to present value using the formula: PV= C / (1 + r) ^ n, where C is cash flow (which in this case is total cost), r is the discount rate and n is the number of years. However, here we sum up the present values over 5 years.
Using the discount rate of 11% (or 0.11), the formula gives us the present value (PV) of total costs as $154,200 / (1 + 0.11) ^ 5 = $97,615.
Next, we distribute this total present value of costs over 5 years to obtain the equivalent annual cost, which is $97,615 / 5 = $19,523. This is the equivalent annual cost of the tool.
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Final answer:
The equivalent annual cost of the lathe, taking into account the initial cost as well as the operation and maintenance costs over a period of 5 years and a discount rate of 11%, is approximately $73,269.98.
Explanation:
The equivalent annual cost of the tool, also known as the Equivalent Annual Annuity (EAA), is calculated using the total cost and the discount rate. In this case, you have the initial cost of the lathe ($11,700) along with the annual operating and maintenance cost ($28,500/year for five years) and a discount rate of 11%.
First, following the present value formula, the PV of the operation and maintenance cost is calculated as $28,500/0.11 = $259,090.91. Then, the total cost is calculated by adding up the initial cost and the PV of the operation and maintenance cost: $259,090.91 + $11,700 = $270,790.91.
Second, the EAA is calculated by dividing the total cost by the annuity factor, which is given by 1-(1+r)^-n/r. In this case, the annuity factor is (1-(1+0.11)^-5)/0.11 = 3.6959, so the EAA is $270,790.91/3.6959 = $73,269.98. Therefore, the equivalent annual cost of the lathe is approximately $73,269.98.
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