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Financial Management · Investment appraisal techniques

Equivalent Annual Cost and Replacement Decisions for ACCA FM

Updated 11 October 2026 · Fact-checked

Equivalent annual cost (EAC) turns the present value of an asset's costs over its life into a level yearly cost: EAC = PV of costs ÷ annuity factor. You compare EACs of options with different lives and choose the lowest. For replacement cycles, work out the EAC for each possible cycle length and pick the cheapest.

Understand Equivalent Annual Cost and Replacement Decisions

Net present value works well when projects have the same life. It fails when you must choose between assets with different lives, such as a machine lasting 3 years and another lasting 5 years. A lower total present value of costs for the shorter-lived asset does not make it cheaper, because it gives you less service.

The fix is to put every option on a per year basis. Equivalent annual cost (EAC) is the level annual cost that has the same present value as the asset's actual costs over its life. You find the present value of all costs (purchase, running costs, less any resale value), then divide by the annuity factor for the asset's life at the cost of capital.

This method assumes you will replace each asset with an identical one, again and again, at the same cost, for the foreseeable future. Under that assumption, comparing yearly costs is a fair comparison. Choose the option with the lowest EAC.

The same idea answers the replacement cycle question: how often should you replace an asset? Running costs usually rise and resale value falls as an asset ages. Replacing early means more capital cost per year. Replacing late means higher maintenance. Calculate the EAC for each possible cycle (replace every 1, 2, 3 years and so on) and choose the cycle with the lowest EAC.

The same logic applies to lease versus buy when the choices have different lives or cash flow patterns: find the PV of the costs of each, then convert to an equivalent annual cost if the periods differ.

Key rules to remember

Equivalent annual cost
EAC = PV of costs over one cycle ÷ annuity factor (n years, r%)
Use costs as positive numbers. Resale value reduces the PV of costs. Lowest EAC is best.
Annuity factor
AF = [1 − (1 + r)^−n] ÷ r
The exam gives annuity tables. Use the factor for the cycle length n, not the number of years you plan to operate.
Replacement cycle decision
Choose the cycle length n with the lowest EAC
Calculate PV of costs for each n, then divide by AF for that n.
Assumptions of EAC
Identical replacement, same costs, infinite chain
State these if asked to discuss limitations. Inflation, technology change and capital rationing weaken them.

How to solve Equivalent Annual Cost and Replacement Decisions questions

Use this method for any EAC or replacement question. Work in present value terms first, then convert.

  1. 1List the cash flows for each option or each cycle length: purchase cost at time 0, running and maintenance costs each year, and resale value at the end of the cycle.
  2. 2Check which costs are relevant. Ignore sunk costs. Include tax effects (capital allowances, tax on costs) only if the question gives a tax rate.
  3. 3Discount all cash flows at the cost of capital to get the PV of costs. Treat costs as positive and resale proceeds as negative.
  4. 4Find the annuity factor for the asset's life (or cycle length) at the same rate.
  5. 5Divide the PV of costs by the annuity factor to get the EAC for each option.
  6. 6Choose the option or cycle with the lowest EAC. For a replacement cycle, state the length in years.
  7. 7Add a short comment on assumptions, such as identical replacement, no inflation change and no capital rationing, if the question asks for discussion.

Quickest way: Table of cycles, then divide

When to use it: Use this when the question asks for the optimal replacement cycle across several possible lives, such as 1 to 4 years.

  1. Set up one column per cycle length. Rows are: purchase, running costs, resale, PV total, annuity factor, EAC.
  2. Discount each year's running cost once using the single-year discount factors, then build each cycle's PV by adding up to that year.
  3. Put the resale value in the last year of each cycle, discounted at that year's factor.
  4. Divide each PV total by the annuity factor for that cycle length.
  5. Circle the lowest EAC. Check the answer is not at the edge of the table by comparing neighbours.

Common mistakes in Equivalent Annual Cost and Replacement Decisions

  • Choosing the option with the lowest PV of costs when the lives are different.

    Students stop after the NPV-style calculation and forget the lives are not comparable.

    Fix: Always divide by the annuity factor for each life and compare EACs.

  • Using the wrong annuity factor, such as the factor for the total planning horizon instead of the cycle length.

    The question mentions a long horizon and students pick that number.

    Fix: The factor must match the number of years in the cycle you are costing.

  • Adding the resale value instead of deducting it from costs.

    Students treat all cash flows as positive in a cost table.

    Fix: Show costs as positive and resale proceeds as negative, then total.

  • Forgetting to discount running costs, or using the year 0 factor for year 1 costs.

    Rushing through the table and mixing up timing.

    Fix: Write the year and discount factor beside each cash flow before multiplying.

  • Picking the cycle with the lowest total cost rather than the lowest EAC.

    Shorter cycles have smaller totals, which looks attractive.

    Fix: Compare only the per-year EAC figures across cycles.

  • Ignoring inflation or tax when the question gives them.

    Students treat EAC as a separate simple formula.

    Fix: Build the full PV of costs first, including tax and inflation as instructed, then divide.

Worked examples

Example 1

A company can buy Machine A, costing $40,000, lasting 3 years with running costs of $8,000 a year and no resale value. Machine B costs $55,000, lasts 5 years, has running costs of $6,000 a year and no resale value. The cost of capital is 10%. Annuity factors at 10%: 3 years 2.487, 5 years 3.791. Which machine should be chosen?

Show the solution
  1. Machine A PV of costs = 40,000 + 8,000 × 2.487 = 40,000 + 19,896 = 59,896.
  2. Machine A EAC = 59,896 ÷ 2.487 = 24,084 (to the nearest $).
  3. Machine B PV of costs = 55,000 + 6,000 × 3.791 = 55,000 + 22,746 = 77,746.
  4. Machine B EAC = 77,746 ÷ 3.791 = 20,508 (to the nearest $).
  5. Compare: B has the lower EAC, even though its total PV is higher.

Answer: Choose Machine B. Its EAC is about $20,508 a year against about $24,084 for Machine A.

Example 2

A vehicle costs $30,000. Running costs are $5,000 in year 1 and $8,000 in year 2. Resale value is $18,000 after 1 year and $13,000 after 2 years. The cost of capital is 10%. Discount factors at 10%: year 1 0.909, year 2 0.826. Annuity factors: 1 year 0.909, 2 years 1.736. Should the vehicle be replaced every 1 year or every 2 years?

Show the solution
  1. One-year cycle: PV of costs = 30,000 + 5,000 × 0.909 − 18,000 × 0.909 = 30,000 + 4,545 − 16,362 = 18,183.
  2. One-year EAC = 18,183 ÷ 0.909 = 20,003 (to the nearest $).
  3. Two-year cycle: PV of costs = 30,000 + 5,000 × 0.909 + 8,000 × 0.826 − 13,000 × 0.826.
  4. This is 30,000 + 4,545 + 6,608 − 10,738 = 30,415.
  5. Two-year EAC = 30,415 ÷ 1.736 = 17,520 (to the nearest $).
  6. Compare: the two-year cycle has the lower EAC.

Answer: Replace every 2 years. The EAC is about $17,520 a year, against about $20,003 for a 1-year cycle.

Exam tips

  • In Section C, set out a clear table with years across and cash flows down. Marks go for correct method even if arithmetic slips.
  • In objective test questions, you only get marks for the right final value. Check that you divided by the annuity factor and did not stop at the PV.
  • Read for the words 'replace', 'cycle' and 'unequal lives'. They signal EAC.
  • If a tax rate is given, include tax on running costs and capital allowances before discounting. If not, do not invent tax.
  • Be ready to give one or two limitations of EAC, such as the assumption of identical replacement and constant costs.

Practice questions from Investment appraisal techniques

Equivalent Annual Cost and Replacement Decisions in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Equivalent Annual Cost and Replacement Decisions: frequently asked questions

What is equivalent annual cost in ACCA FM?

It is the level annual cost that has the same present value as the total costs of owning an asset over its life. You get it by dividing the PV of costs by the annuity factor. It lets you compare assets with different lives.

How do I choose the optimal replacement cycle?

Calculate the EAC for each possible cycle length, using the purchase cost, running costs and resale value for that length. Choose the cycle with the lowest EAC. Do not choose by lowest total cost.

Can I use EAC for lease versus buy?

Yes, when the options have different lives or cash flow patterns. Find the PV of costs for each, then divide by the matching annuity factor. The lower EAC is the cheaper option, subject to the question's assumptions.

Should I use the cost of capital or a risk-free rate?

Use the discount rate given in the question, normally the company's cost of capital. Use the same rate for the PV and for the annuity factor.