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Answer :
The equivalent annual cost of the precision lathe is $31,345.30.
To calculate the equivalent annual cost of the tool, you can use the formula: EAC = (C + RCW)/A, where: C is the initial cost of the tool, RCW is the present value of the cost of running and maintaining the tool, A is the annuity factor for the life of the tool.
To use the formula above, you need to find the annuity factor for the life of the tool. The annuity factor can be found using the formula: A = [(1 - [tex](1 + r)^{-n[/tex])/r], where: r is the discount rate, n is the life of the tool in years.
Substituting the given values, we get:
A = [(1 - [tex](1 + 0.12)^{-5[/tex])/0.12]
A = 3.6049.
Rounding up to four decimal places, we get: A = 3.605.
The present value of the cost of running and maintaining the tool, RCW can be calculated using the formula: RCW = R * [1 - [tex](1 + i)^{-n[/tex]]/i, where: R is the annual cost of running and maintaining the tool, i is the discount rate, n is the life of the tool in years.
Substituting the given values, we get:
RCW = 20,000 * [1 - (1 + 0.12)^-5]/0.12
RCW = $77,986.22.
The equivalent annual cost of the tool is thus:
EAC = (30,000 + 77,986.22)/3.605
EAC = $31,345.30.
Therefore, the equivalent annual cost of the tool is $31,345.30.
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