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In: Finance

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          $  

Solutions

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 2 years ago
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