A precision lathe costs $13,500 and will cost $22,000 a year to operate and maintain. If...

A precision lathe costs $13,500 and will cost $22,000 a year to operate and maintain. If the discount rate is 14% and the lathe will last for 5 years, what is the equivalent annual cost of the tool? (Enter your answer as positive value. Round your answer to the nearest cent.

The equivalent annual cost $

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Expert Solution

Net Present Value

Year	Annual cash flows ($)	Present Value Factor (PVF) at 14.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]

1	(22,000)	0.877193	(19,298.25)
2	(22,000)	0.769468	(16,928.29)
3	(22,000)	0.674972	(14,849.37)
4	(22,000)	0.592080	(13,025.77)
5	(22,000)	0.519369	(11,426.11)

TOTAL		3.433081	(75,527.78)

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$75,527.78 - $13,500

= -$89,027.78 (Negative)

Equivalent Annual Cost (EAC)

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 14%, 5 Years]

= -$89,027.78 / 3.433081

= -$25,932.33 (Negative EAC)

Therefore, the Equivalent Annual Cost is $25,932.33 (Entered as positive value)

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.

jeff jeffy answered 1 year ago

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