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A precision lathe costs $11,800 and will cost $29,000 a year to operate and maintain. If the discount rate is 12% and the lathe will last for 6 years, what is the equivalent annual cost of the tool?

(Enter your answer as a positive value. Round your answer to 2 decimal places.)

Answer :

The equivalent annual cost of the tool is $116,445.00.

To calculate the equivalent annual cost of the precision lathe, we need to consider both the initial cost and the annual operating and maintenance cost.

First, we calculate the equivalent annual cost (EAC) using the formula:

EAC = Initial cost (A) + Annual cost (B) * Present value annuity factor (PVAF)

The initial cost (A) is $11,800, the annual cost (B) is $29,000, and the discount rate is 12%.

To calculate the Present Value Annuity Factor (PVAF), we use the formula:

PVAF = (1 - (1 + r)^-n) / r

Where r is the discount rate and n is the number of years.

Plugging in the values, we have:

PVAF = (1 - (1 + 0.12)^-6) / 0.12

= (1 - 0.5674) / 0.12

= 0.4326 / 0.12

= 3.605

Now we can calculate the equivalent annual cost (EAC):

EAC = $11,800 + $29,000 * 3.605

= $11,800 + $104,645

= $116,445

Rounded to 2 decimal places, the equivalent annual cost of the tool is $116,445.00.

Learn more about discount rate here:

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