## Accounting Rate of Return (ARR)

The Accounting Rate of Return (also called Average Rate of Return) is a non-discounting capital budgeting technique. It measures the average annual net income (accounting profit) of a project as a percentage of the investment.

> ARR uses profit after depreciation (accounting profit) — not cash flows. This is what distinguishes it from payback and the discounting methods.

### Core formula

$$\text{ARR} = \frac{\text{Average annual net income}}{\text{Investment}} \times 100$$

Numerator — the average annual net income (profit after depreciation, and after tax where applicable) generated over the project's useful life.
Denominator — can be measured two ways:
Initial investment (including installation cost), or
Average investment over the useful life.

Average investment = the average amount of funds remaining blocked during the project's life.

### Three versions of ARR

Because both numerator and denominator can be defined differently, three versions are commonly used:

Version	Numerator	Denominator
1. Annual basis	Profit after depreciation (each year)	Investment at beginning of that year
2. Total investment basis	Average annual profit	Initial investment
3. Average investment basis	Average annual profit	Average investment

Average investment can be computed as:

$$\text{Average Investment} = \frac{\text{Initial Investment} + \text{Salvage Value}}{2}$$

or equivalently:

$$\text{Average Investment} = \tfrac{1}{2}(\text{Initial Investment} - \text{Salvage Value}) + \text{Salvage Value}$$

### Adjusting for additional working capital

A project may need additional working capital during its life (beyond initial working capital). The average investment formula is then modified to:

$$\tfrac{1}{2}(\text{Initial Investment} - \text{Salvage Value}) + \text{Salvage Value} + \text{Additional Working Capital}$$

Adding working capital increases the denominator and therefore lowers the ARR.

### Decision rule

Accept a project if its ARR exceeds the firm's required/cut-off rate; for ranking, prefer the project with the higher ARR.

Worked example

### Example 1

Example — ARR computed three ways (Times Ltd.)

Times Ltd. invests ₹3,00,000 in a project; life = 3 years; salvage value = ₹90,000; profit before depreciation = ₹1,50,000 each year. Straight-line depreciation = (3,00,000 − 90,000)/3 = ₹70,000/yr, so profit after depreciation = ₹80,000 each year.

Year	PBD (₹)	Depreciation (₹)	PAD (₹)	Investment: Beginning (₹)	End (₹)
1	1,50,000	70,000	80,000	3,00,000	2,30,000
2	1,50,000	70,000	80,000	2,30,000	1,60,000
3	1,50,000	70,000	80,000	1,60,000	90,000

Version 1 — Annual basis (PAD ÷ beginning investment, then average the yearly ARRs):

Year 1: 80,000/3,00,000 = 26.67%
Year 2: 80,000/2,30,000 = 34.78%
Year 3: 80,000/1,60,000 = 50.00%
Average ARR = (26.67 + 34.78 + 50.00)/3 = 37.15%

Version 2 — Total investment basis:

$$\text{ARR} = \frac{(80{,}000+80{,}000+80{,}000)/3}{3{,}00{,}000}\times100 = \frac{80{,}000}{3{,}00{,}000}\times100 = \textbf{26.67\%}$$

Version 3 — Average investment basis:

Average investment = (3,00,000 + 90,000)/2 = ₹1,95,000

$$\text{ARR} = \frac{80{,}000}{1{,}95{,}000}\times100 = \textbf{41.03\%}$$

### Example 2

Example — ARR with additional working capital

Continuing the Times Ltd. data, suppose ₹45,000 additional working capital is required during the project life.

Average investment = ½(3,00,000 − 90,000) + 90,000 + 45,000 = 1,05,000 + 90,000 + 45,000 = ₹2,40,000

$$\text{ARR} = \frac{80{,}000}{2{,}40{,}000}\times100 = \textbf{33.33\%}$$

Note how adding working capital lowers ARR from 41.03% to 33.33%.

⚠️ Common exam mistakes

Using cash flows (profit before depreciation) instead of accounting profit (profit AFTER depreciation) in the numerator — ARR is income-based, not cash-flow based.
Forgetting that ARR has multiple versions, then mismatching the numerator and denominator (e.g., using average profit over beginning-of-year investment) — quote the version being used.
Computing average investment as Initial ÷ 2 and ignoring salvage value; correct formula is (Initial + Salvage)/2.
Omitting additional working capital from the average investment denominator when the question gives it.
Treating ARR as if it accounts for the time value of money — it does not; that is its key limitation.

Reference:

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Accounting Rate of Return (ARR) / Average Rate of Return

Worked example

⚠️ Common exam mistakes