What is the Accounting Rate of Return (ARR)?
– Definition: ARR is a simple capital‑budgeting measure that expresses an investment’s expected annual accounting profit as a percentage of the initial outlay. It helps compare project profitability on an annual average basis using reported accounting profit rather than cash flows.
Core formula
– ARR = (Average annual profit) / (Initial investment)
– “Average annual profit” = total accounting profit over the project’s life divided by the number of years (profit here is accounting net income after expenses such as depreciation).
Step-by-step checklist to compute and use ARR
1. Identify the initial investment (cash paid at time zero).
2. Project accounting profit for each year (include operating income minus expenses and depreciation; exclude non‑recurring items).
3. Compute average annual profit = (sum of yearly accounting profits) / (project life in years).
4. Divide average annual profit by the initial investment to get ARR (express as a percentage).
5. Compare ARR to your required rate of return (hurdle rate). Accept projects with ARR at or above the hurdle; when comparing projects, prefer the one with the higher ARR (subject to other constraints).
6. Document assumptions about depreciation, tax, and profit recognition.
Worked numeric example
– Situation: A company considers a 5‑year project requiring a $250,000 initial investment.
– Accounting profits (after taxes and operating expenses, including depreciation) are projected to be $25,000 per year for five years.
– Average annual profit = (25,000 × 5) / 5 = $25,000.
– ARR = 25,000 / 250,000 =
= 0.10 = 10%. Interpretation: if the firm’s required rate of return (hurdle rate) is ≤ 10%, the project would be acceptable on ARR grounds; if the hurdle is higher, reject.
Alternative ARR formula (common)
– ARR = Average annual profit / Average investment
– Average investment often = (Initial investment + Salvage value) / 2 when straight‑line depreciation is used, or the mean of book values over the project life.
Worked example with salvage value and uneven profits
– Situation: initial cost $250,000; expected after‑tax accounting profits over five years: $10k, $20k, $30k, $40k, $50k; salvage at end = $50,000.
– Average annual profit = (10k + 20k + 30k + 40k + 50k) / 5 = $30,000.
– Average investment = (250,000 + 50,000) / 2 = $150,000.
– ARR = 30,000 / 150,000 = 0.20 = 20%.
Step‑by‑step checklist to compute ARR (practical)
1. Gather projected accounting profits for each period (after taxes and operating expenses; include depreciation per the firm’s accounting method).
2. Compute average annual profit = (sum of annual profits) / (number of years).
3. Decide which investment base you will use: initial investment, average investment, or average book value. Document the choice and rationale.
4. Compute ARR = Average annual profit / Investment base. Express as a percentage.
5. Compare to hurdle rate and to ARR of alternative projects.
6. Document assumptions about taxes, depreciation method, timing of cash flows, and salvage value. Run sensitivity checks (see next).
Key limitations and risks (what ARR ignores)
– Time value of money: ARR does not discount future profits; it treats a dollar in year 5 the same as year 1.
– Profit vs. cash flow: ARR uses accounting profit, not cash flow; noncash items (depreciation) and timing differences can distort the metric.
– Project scale and duration: ARR may favour short projects or those with high early accounting profits even if NPV is low.
– Multiple definitions: different practitioners use different denominators (initial vs average investment), so ensure consistent comparison.
– Accounting policies: depreciation method, tax timing, and expense recognition materially affect accounting profit and thus ARR.
When to use ARR (practical guidance)
– Use ARR for quick screening when accounting profitability and return on book investment matter (e.g., internal accounting targets, regulatory reporting).
– Do not use ARR as the sole decision rule for capital budgeting. For economically sound decisions, complement ARR with discounted‑cash‑flow (DCF) measures such as net present value (NPV) and internal rate of return (IRR).
Complementary analyses to run
– NPV (discounted cash flows) — accounts for time value of money.
– IRR — the discount rate that makes NPV zero; useful for ranking projects but has limitations with nonstandard cash flows.
– Payback period — simple measure of liquidity/timing of recouping investment.
– Sensitivity analysis — vary sales, margins, taxes, and salvage to see ARR volatility.
– Recompute ARR using cash flows or taxable income if stakeholders require that basis.
Practical tips for students and traders
– Always state which ARR formula you use and why.
– Reconcile accounting profits to cash flows to understand noncash items’ impact.
– If comparing projects, use the same ARR definition across all projects.
– Use ARR as part of a dashboard of metrics, not as a lone decision maker.
Quick formula summary
– ARR (initial base) = Average annual accounting profit / Initial investment.
– ARR (average base) = Average annual accounting profit / Average investment [(Initial + Salvage)/2 or mean book value].
– Average annual accounting profit = (Sum of after‑tax accounting profits over project life) / (Number of years).
Sources for further reading
– Investopedia — Accounting Rate of Return (ARR): https://www.investopedia.com/terms/a/arr.asp
– Corporate Finance Institute — Accounting Rate of Return (ARR): https://corporatefinanceinstitute.com/resources/valuation/arr-accounting-rate-of-return/
– U.S. Securities and Exchange Commission (Investor.gov) — Basic concepts about returns and risk: https://www.investor.gov/introduction-investing/basic-investing/role-investment