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You are given the following information about equipment that is required for your business. Assume that the equipment will be replaced as it wears out and that straight-line depreciation to zero is used for each. The required return is 15% and ignore taxes. Machine A has an initial cost of $200,000, an operating cost per year of $15,000, and an expected life of 8 years. Machine B has an initial cost of $300,000, an operating cost per year of $17,500, and an expected life of 10 years. How does the equivalent annual cost of Machine A compare to that of Machine B

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Answer:

Machine B EAC is $17,705.78 more than Machine A EAC.

Explanation:

First find the present values of the cost of both machines.

Machine A:

= 200,000 + (15,000 * Present value of annuity interest factor, 15%, 8 years)

= 200,000 + ( 15,000 * 4.4873)

= $‭267,309.5‬0

Machine B

= 300,000 + (17,500 * Present value of annuity interest factor, 15%, 10 years)

= 300,000 + 17,500 * 5.0188

= $‭387,829‬

Equivalent Annual cost Machine A:

= [(NPV * Required return) / 1 - (1 + Required return) ^–Number of Periods

=[(267,309.50 * 15%) / 1 - 1.15⁻⁸

= $59,569.95

Equivalent Annual cost Machine B:

= (387,829 * 15%) / (1 - 1.15⁻¹⁰)

= $77,275.73

Difference:

= 77,275.73 - 59,569.95

= $‭17,705.78‬

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The Machine B EAC is $17,705.78 more than Machine A EAC.

Calculation of equivalent annual cost:

Here we first determine the present values of the cost of both machines.

For Machine A:

= 200,000 + (15,000 * Present value of annuity interest factor, 15%, 8 years)

= 200,000 + ( 15,000 * 4.4873)

= $‭267,309.5‬0

For Machine B

= 300,000 + (17,500 * Present value of annuity interest factor, 15%, 10 years)

= 300,000 + 17,500 * 5.0188

= $‭387,829‬

Now

Equivalent Annual cost Machine A:

= [(NPV * Required return) / 1 - (1 + Required return) ^–Number of Periods

=[(267,309.50 * 15%) / 1 - 1.15⁻⁸

= $59,569.95

Equivalent Annual cost Machine B:

= (387,829 * 15%) / (1 - 1.15⁻¹⁰)

= $77,275.73

Now the Difference is

= 77,275.73 - 59,569.95

= $‭17,705.78‬

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