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ACCA Applied Skills · Financial Management · Investment appraisal techniques

Harlow Ltd is deciding between two machines, both of which would be replaced identically at the end of their lives. Machine A has a present value of costs of $48,000 over a 4-year life. Machine B has a present value of costs of $62,000 over a 6-year life. The cost of capital is 10%. Annuity factors at 10%: 4 years 3.170; 6 years 4.355. Which machine should be chosen and why?

Machine B should be chosen. Equivalent annual cost divides present value of costs by the annuity factor for each life: Machine A is $15,142 and Machine B is $14,238. Because lives are unequal, comparing total present values is misleading, and the lower annual cost wins.

  1. AMachine A, because its equivalent annual cost is about $15,142 against about $14,238 for Machine B
  2. BMachine B, because its equivalent annual cost is about $14,238 against about $15,142 for Machine ACorrect
  3. CMachine A, because its present value of costs is lower at $48,000
  4. DMachine B, because its life is longer so its annual cost must be lower

Explanation

EAC = PV of costs / annuity factor. Machine A: 48,000/3.170 = 15,142. Machine B: 62,000/4.355 = 14,238. Machine B has the lower annual cost, so it is preferred. Option C is wrong because it compares PVs over unequal lives without adjusting.

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