## Accounting Rate of Return (ARR)

ARR measures the average annual net income (incremental income) as a percentage of investment. Unlike payback, it uses accounting profit, not cash flow.

```

ARR = Average annual net income / Investment x 100

```

Numerator: average annual net income (profit after depreciation, and after tax if applicable) over the project's life.
Denominator: either the initial investment (incl. installation) or the average investment.

### Average Investment

```

Average Investment = (Initial Investment + Salvage Value) / 2

= 1/2 (Initial Investment - Salvage) + Salvage

```

If additional working capital is required during the project:

```

Avg Investment = 1/2 (Initial Investment - Salvage) + Salvage + Additional Working Capital

```

### Three Versions of ARR

1. Annual basis: compute ARR each year on opening investment, then average the percentages.

2. Total Investment basis: Average annual profit / Initial investment.

3. Average Investment basis: Average annual profit / Average investment.

Worked example

### Example 1

Setup: Times Ltd invests Rs.3,00,000, life 3 yrs, salvage Rs.90,000, profit before depreciation Rs.1,50,000/yr. Depreciation Rs.70,000/yr -> profit after depreciation Rs.80,000/yr.

Year	Investment (Beg)	Investment (End)
1	3,00,000	2,30,000
2	2,30,000	1,60,000
3	1,60,000	90,000

Version 1 - Annual basis:

```

Yr1: 80,000/3,00,000 = 26.67%

Yr2: 80,000/2,30,000 = 34.78%

Yr3: 80,000/1,60,000 = 50.00%

Average = (26.67+34.78+50)/3 = 37.15%

```

Version 2 - Total Investment basis:

```

= 80,000 / 3,00,000 x 100 = 26.67%

```

Version 3 - Average Investment basis:

```

Avg Investment = (3,00,000 + 90,000)/2 = 1,95,000

ARR = 80,000 / 1,95,000 x 100 = 41.03%

```

### Example 2

With additional working capital Rs.45,000:

```

Avg Investment = 1/2 (3,00,000 - 90,000) + 90,000 + 45,000 = 2,40,000

ARR = 80,000 / 2,40,000 x 100 = 33.33%

```

⚠️ Common exam mistakes

Using cash flows instead of accounting profit (after depreciation) in the numerator - ARR uses net income, not CFAT.
Mixing versions - state clearly whether initial or average investment is being used as the denominator.
Computing average investment as Initial/2 and forgetting to add back salvage value.
Omitting additional working capital from average investment when the project requires it.

Reference:

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Accounting Rate of Return (ARR) - three versions

Worked example

⚠️ Common exam mistakes