Question

Cabot Enterprise is analyzing two machines to determine which one it should purchase. Whichever machine is purchased will be replaced at the end of its useful life. The company requires a 15 percent rate of return and uses straight-line depreciation to a zero book value over the life of the machine. Machine A has a cost of $720,000, annual operating costs of $50,000, and a 8-year life. Machine B costs $350,000, has annual operating costs of $110,000, and a 5-year life. The firm currently pays no taxes. Which machine should be purchased and why?

Answer 1

The Equivalent Annual Cost of Machine A is computed as shown below:

= (Initial investment + present value of future cost) / Present value annuity factor of 15% for 8 years

Initial investment + present value of future cost is computed as follows:

= $ 720,000 + $ 50,000 / 1.15¹ + $ 50,000 / 1.15² + $ 50,000 / 1.15³ + $ 50,000 / 1.15⁴ + $ 50,000 / 1.15⁵ + $ 50,000 / 1.15⁶ + $ 50,000 / 1.15⁷ + $ 50,000 / 1.15⁸

= $ 944,366.0754

Present value annuity factor of 15% for 8 years is computed as follows:

= [ (1 – 1 / (1 + r)ⁿ) / r ]

= [ (1 - 1 / (1 + 0.15)⁸ ) / 0.15 ]

= 4.487321508

So, the equivalent annual cost of Machine A is computed as follows:

= $ 944,366.0754 / 4.487321508

= $ 210,452.06 Approximately

The Equivalent Annual Cost of Machine B is computed as shown below:

= (Initial investment + present value of future cost) / Present value annuity factor of 15% for 5 years

Initial investment + present value of future cost is computed as follows:

= $ 350,000 + $ 110,000 / 1.15¹ + $ 110,000 / 1.15² + $ 110,000 / 1.15³ + $ 110,000 / 1.15⁴ + $ 110,000 / 1.15⁵

= $ 718,737.0608

Present value annuity factor of 15% for 5 years is computed as follows:

= [ (1 – 1 / (1 + r)ⁿ) / r ]

= [ (1 - 1 / (1 + 0.15)⁵ ) / 0.15 ]

= 3.352155098

So, the equivalent annual cost of Machine B is computed as follows:

= $ 718,737.0608 / 3.352155098

= $ 214,410.44 Approximately

Since the EAC of cost of Machine A is smaller as compared to the EAC of Machine B, hence Machine A shall be purchased.

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