Q. Evaluate Equivalent annual cost?

There are a number of techniques to answering this question and two are presented. The first difficulty is in deciding which broad approach to use. The broad approach which appears best is to inflate the cash flows at their different inflation rates and to discount at the money discount rate. Using this wider approach the lowest common multiple method would look like

The lowest common multiple is 2 × 3 = 6 years therefore the cash flows for each of the alternatives will be presented in these terms.

2 year cycle: (cash flows are overstated according to their individual inflation rates)

3 year cycle: (cash flows are overstated according to their individual inflation rates)

Therefore a two year replacement cycle is preferable since it represents the lowest cost.

On the other hand an equivalent annual cost approach could be used

2 year cycle: (cash flows are overstated according to their individual inflation rates)

Equivalent annual cost = 12705/ (annuity factor at 15% for two years) = 12705/1·626 = 7813

3 year cycle (cash flows are inflated according to their individual inflation rates)