The accounting rate of return (ARR) is a financial ratio of Average Profit to the Average Investment made in the particular project.
It is a quick method of calculating the rate of return of a project – ignoring the time value of money.
Formula
The formula to calculate Accounting Rate of Return (ARR) is as follows:
\[\text{ARR=}\frac{\text{Average Profits}}{\text{Average Investment}}\text{ }\!\!\times\!\!\text{ 100 }\!\!%\!\!\text{ }\]
Accounting Rate of Return Example
You have a project which lasts three years and the expected annual operating profit (excluding depreciation) for the three years are $100,000, $150,000 and $200,000. The initial investment is $300,000 with a residual value of $60,000. Calculate the Accounting Rate of Return (ARR).
Solution
Step 1: Calculate the average annual profit
\[\frac{\left\{ \left( 100,000+150,000+200,000 \right)-\left( 300,000-60,000 \right) \right\}}{3}=70,000\]
In the first part of the calculation you simply calculate the operating profit for all three years before depreciation is accounted for. In the second part of the calculation you work out the total depreciation for the three years. Remember the depreciation must be the cost of investment less the residual value. Finally, when you subtract the deprecation from the profits you divide by three to work out the average operating profit over the life of the project.
Step 2: Calculate the average investment
\[\frac{\left( 300,000+60,000 \right)}{2}=180,000\]
If there is no residual value you simply take the cost of the initial investment and divide by two. One thing to watch out for here is that it is easy to presume you subtract the residual value from the initial investment. You should not do this; you must add the initial investment to the residual value.
Step 3: Divide the average investment into the average annual profit
\[\frac{70,000}{180,000}\times 100=38.89%\]
ARR can be problematic in that it is subject to accounting policies which will vary from one organization to another and can be subject to manipulation.