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Financial Management · Specific investment decisions (lease or buy, asset replacement, capital rationing)

Asset Replacement and Equivalent Annual Cost for ACCA FM

Updated 11 October 2026 · Fact-checked

Equivalent annual cost (EAC) turns the present value of an asset's costs over one replacement cycle into a yearly equivalent. Calculate the PV of costs for each possible cycle length, divide by the annuity factor for that length, and choose the cycle with the lowest EAC. Use it when assets are replaced repeatedly.

Understand Asset Replacement and Equivalent Annual Cost

Some assets are replaced again and again: vehicles, machines, computers. The question is how long to keep each one. Keep it longer and you save on buying new assets, but running costs rise and the resale value falls. Replace early and running costs stay low, but you buy more often.

You cannot compare the PV of costs for a 2-year cycle with a 3-year cycle directly. The 3-year cycle covers a longer time, so its total is naturally larger. You need a common basis: cost per year.

The equivalent annual cost gives that basis. It is the level annual payment, over the cycle, that has the same present value as the actual costs. You find the PV of all costs in one cycle (purchase, running costs, less resale value), then divide by the annuity factor for the cycle length at the cost of capital.

The cycle with the lowest EAC is the best. The method assumes the asset is replaced by an identical one, again and again, with the same costs. It also works for choosing between two different machines with different lives, when you must pick one. Always work with costs, so you are looking for the smallest figure, not the largest.

EAC is a cost-comparison tool, not a profit measure. Use it when the asset will be needed for a long time and revenues are the same under each choice.

Key rules to remember

Equivalent annual cost
EAC = PV of costs over one cycle ÷ annuity factor (n years, cost of capital)
Use the annuity factor for the length of the cycle being tested. Use a PV of costs, so the EAC is a positive cost.
PV of costs for one cycle
PV = purchase cost + PV of running costs (after tax if given) − PV of resale value (and tax benefits treated as reductions in cost)
Resale proceeds at the end of the cycle reduce the cost. Capital allowance tax savings also reduce it.
Decision rule
Choose the replacement cycle with the lowest EAC
Only valid when costs are the only difference and the asset is replaced indefinitely by identical assets.
Annuity factor
AF = [1 − (1 + r)^−n] ÷ r
Normally taken from the tables provided in the exam.

How to solve Asset Replacement and Equivalent Annual Cost questions

Follow this method for any replacement cycle or machine-choice question.

  1. 1List the cycle lengths to test (for example 1, 2 and 3 years) or the machines to compare.
  2. 2For each option, set out the cash flows by year: purchase at time 0, running and maintenance costs, and the resale value at the end of the cycle.
  3. 3Adjust for the question's details. If inflation is given, inflate flows and use the nominal rate. If tax is given, apply tax to running costs and include capital allowance savings and any balancing adjustments, with the timing stated.
  4. 4Discount each option's flows at the cost of capital to get the PV of costs for one cycle. Treat resale value as a deduction.
  5. 5Divide each PV by the annuity factor for that cycle length (same rate, n = cycle length) to get the EAC.
  6. 6Compare the EACs and choose the lowest. State the replacement period in words.
  7. 7Mention the assumptions: identical replacement, constant costs and no capital rationing. Add non-financial factors if asked, such as reliability or technology change.

Quickest way: Table-and-divide approach

When to use it: Use this when the question gives costs and resale values for several cycle lengths and no complications beyond a single discount rate.

  1. Draw one row per cycle length and columns for the PV of purchase, running costs, resale and total.
  2. Build running-cost PVs cumulatively: the year 1 and year 2 PVs are reused in the 3-year row.
  3. Compute each total PV, then divide by the annuity factor for that row only.
  4. Circle the lowest EAC. Do not waste time comparing total PVs.
  5. Write one line stating the decision and the key assumption.

Common mistakes in Asset Replacement and Equivalent Annual Cost

  • Choosing the cycle with the lowest total PV of costs.

    Students forget that longer cycles cover more years, so their totals are not comparable.

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

  • Using the wrong annuity factor, such as the 3-year factor for a 2-year cycle.

    The factor is copied down the page without checking the row.

    Fix: Label each row with n and write the factor next to it before dividing.

  • Adding resale value instead of deducting it.

    Students treat every cash flow as an outflow because the table is about costs.

    Fix: Resale proceeds are inflows. Show them in brackets and subtract.

  • Ignoring tax effects, or applying tax with the wrong timing.

    Capital allowances and tax on running costs add detail, and the timing is easy to misread.

    Fix: Follow the exam's stated tax timing. Tax relief on running costs reduces them. Capital allowance savings reduce the cost. Discount them in the right years.

  • Mixing real and nominal figures, for example inflated costs discounted at a real rate.

    The question gives inflation and a money rate and students do not match them.

    Fix: Use nominal cash flows with the nominal rate, or real cash flows with the real rate. Never mix them.

  • Picking the cycle with the highest EAC, or reporting the EAC without a decision.

    Students confuse costs with benefits or stop after the calculation.

    Fix: This is a cost comparison, so the lowest EAC wins. Finish with a clear recommendation.

Worked examples

Example 1

A machine costs $50,000. Running costs are $10,000 in year 1, $12,000 in year 2 and $15,000 in year 3, paid at the end of each year. Resale values at the end of years 1, 2 and 3 are $30,000, $22,000 and $15,000. The cost of capital is 10%. Ignore tax and inflation. Find the replacement cycle that minimises the equivalent annual cost. Discount factors at 10%: year 1 0.909, year 2 0.826, year 3 0.751. Annuity factors: 1 year 0.909, 2 years 1.736, 3 years 2.487.

Show the solution
  1. 1-year cycle: PV = 50,000 + 10,000 × 0.909 − 30,000 × 0.909 = 50,000 + 9,090 − 27,270 = $31,820.
  2. EAC (1 year) = 31,820 ÷ 0.909 = about $35,006.
  3. 2-year cycle: PV = 50,000 + 9,090 + 12,000 × 0.826 − 22,000 × 0.826 = 50,000 + 9,090 + 9,912 − 18,172 = $50,830.
  4. EAC (2 years) = 50,830 ÷ 1.736 = about $29,280.
  5. 3-year cycle: PV = 50,000 + 9,090 + 9,912 + 15,000 × 0.751 − 15,000 × 0.751 = 50,000 + 9,090 + 9,912 + 11,265 − 11,265 = $69,002.
  6. EAC (3 years) = 69,002 ÷ 2.487 = about $27,745.
  7. Compare: 1 year $35,006, 2 years $29,280, 3 years $27,745. The 3-year cycle is lowest.

Answer: Replace the machine every 3 years, with an equivalent annual cost of about $27,745. This assumes identical replacement machines and unchanged costs.

Example 2

A firm must choose one of two machines. Machine A costs $40,000, lasts 3 years and has running costs of $8,000 a year. Machine B costs $55,000, lasts 5 years and has running costs of $6,000 a year. Neither has a resale value. The cost of capital is 8%. Annuity factors at 8%: 3 years 2.577, 5 years 3.993. Ignore tax and inflation. Which machine should be chosen?

Show the solution
  1. Machine A: PV of running costs = 8,000 × 2.577 = $20,616.
  2. PV of costs = 40,000 + 20,616 = $60,616.
  3. EAC of A = 60,616 ÷ 2.577 = about $23,522.
  4. Machine B: PV of running costs = 6,000 × 3.993 = $23,958.
  5. PV of costs = 55,000 + 23,958 = $78,958.
  6. EAC of B = 78,958 ÷ 3.993 = about $19,774.
  7. Compare the EACs. Machine B has the lower annual cost, even though its total PV is higher. The PVs are not comparable because the lives differ.

Answer: Choose Machine B. Its EAC is about $19,774 a year, against about $23,522 for Machine A.

Exam tips

  • In Section C, set out a clear table by cycle length. Marks are given for the PV of each cycle, the annuity factor used and the EAC, so show each one.
  • In objective test questions, look for the line that asks for the lowest cost. Calculate the EAC for each option quickly and watch for options that are the unconverted PV.
  • If tax and inflation appear, deal with them in the cash flows first: inflate, apply tax, then discount. Keep the rate consistent with the cash flows.
  • Always write the decision in words and name the assumptions: replacement by identical assets, constant costs and no capital rationing.
  • Know when EAC is not the right tool. It is not for one-off projects, and it cannot compare assets with different revenues.

Practice questions from Specific investment decisions (lease or buy, asset replacement, capital rationing)

Asset Replacement and Equivalent Annual Cost in other exams

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

Asset Replacement and Equivalent Annual Cost: frequently asked questions

What is equivalent annual cost in ACCA FM?

It is the annual cost of owning and running an asset over one replacement cycle, in present value terms. You calculate the PV of the cycle's costs and divide by the annuity factor. It lets you compare cycles or assets of different lengths.

Why not just compare the NPV or PV of costs for each cycle?

Cycles of different lengths cover different time spans. A 3-year cycle will usually have a higher total cost than a 2-year cycle simply because it lasts longer. The EAC converts each to a per-year cost so they can be compared fairly.

How do tax and inflation affect the EAC calculation?

Inflate the cash flows if the question gives inflation rates, apply tax to running costs, and include capital allowance savings and any balancing adjustment on disposal. Then discount at a rate that matches the cash flows (nominal with nominal) before dividing by the annuity factor.

Does the lowest EAC always give the right answer?

It gives the cheapest cycle on the stated assumptions. These are replacement by identical assets with constant costs, and no capital rationing. In practice, technology change, reliability and finance availability also matter, and you can mention these in a written answer.