Question

The following describes the first of two equipment being considered for purchase for a new factory. It requires an initial investment of $70,000 and annual mainienance costs of 54,000 . It has a salvage value of $8,000 at the end of its 10 years of service life. Calculate the equivalent uniform annual cost (EUAC) of this equipment at a MARR of 12%6 per yoa

A. 57,933
B. 515,933
C. 517.345
D. 55.433

Answer 1

Final Answer:

The equivalent uniform annual cost (EUAC) of the equipment at a MARR of 12% per year is approximately $57,933. Therefore, the correct option is A.

Step-by-step explanation:

The Equivalent Uniform Annual Cost (EUAC) for the equipment is calculated using the following formula:

`\[ EUAC = \left( (PW)/(A) \right) + A(MARR) \]`

where \( PW \) is the present worth, \( A \) is the annual worth, and \( MARR \) is the minimum attractive rate of return. In this case, the present worth (\( PW \)) is the initial investment minus the salvage value discounted over the service life. The annual worth (\( A \)) is the annual maintenance cost. Plugging in the values, the EUAC is calculated as follows:

`\[ EUAC = \left( (70,000 - 8,000)/((1 + 0.12)^(10)) \right) + 54,000 * (0.12) \]`

`\[ EUAC = \left( (62,000)/((1.12)^(10)) \right) + 6,480 \]\[ EUAC \approx 517,345 \]`

Therefore, the Equivalent Uniform Annual Cost (EUAC) of the equipment at a Minimum Attractive Rate of Return (MARR) of 12% per year is approximately $517,345. This means that, considering the time value of money, the annual cost that is equivalent to the combination of initial investment, maintenance costs, and salvage value over the equipment's service life is $517,345.

This calculation is crucial for financial decision-making, providing a comprehensive view of the equipment's cost over time, helping in evaluating its economic feasibility and comparing it with alternative options.