Question

Your business can continue to use an older, less efficient machine at a cost of $8,000 annually. Alternatively, you can purchase a more efficient machine for $12,000 today plus $5,000 annual maintenance costs at the end of each year. If the new machine lasts 5 years and the cost of capital is 15% p.a., which alternative should you choose? Show all your workings and explain your choice.

Answer 1

NPV of new machine is computed as shown below:

= $ 12,000 + $ 5,000 / 1.15¹ + $ 5,000 / 1.15² + $ 5,000 / 1.15³ + $ 5,000 / 1.15⁴ + $ 5,000 / 1.15⁵

= $ 28,760.77549

Equivalent annual cost is computed as follows:

= $ 28,760.77549 / Present value annuity factor of 15% for 5 years

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, Equivalent annual cost will be as follows:

= $ 28,760.77549 / 3.352155098

= $ 8,579.79 Approximately

Since the annual cost of old machine of $ 8,000 is less than the annual cost of new machine of $ 8,579.59, hence old machine shall be retained.

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