# Accounting Rate of Return

The accounting rate of return is a method of calculating a projects return as a percentage of the investment in the project. It measures the accounting profitability and takes no account of the time value of money.

## Accounting Rate of Return Formula

The accounting rate of return or ARR for short, is calculated by dividing the average accounting net income by the average investment in the project, and for this reason is sometimes referred to as the average rate of return. The ARR formula can be stated as follows:

Accounting rate of return = Average net income / Average investment

So for example if the average net income each year over the term of a project was 4,500, and the average investment in the project was 50,000, then the average rate of return each year is calculated using the formula as follows:

```ARR = Average net income / Average investment
ARR = 4,500 / 50,000
ARR = 9%
```

The average net income used in the formula is calculated by taking the total net income for the project (which allows for the depreciation expense on the investment) and dividing this by the term in years of the project.

The average investment is normally calculated by taking the simple arithmetic average of the beginning investment (normally the initial amount invested), and the ending investment (normally the salvage value, as the original investment has been written down to this by the depreciation expense).

Notice that both the average net income and the average investment are reduced by the depreciation expense.

## Accounting Rate of Return Examples

Suppose a business makes an initial investment of 150,000 in a 3 year project. The total income over the term of the project is expected to be 52,200, and the salvage value at the end of the project is expected to be 24,000.

### Calculate the Average Accounting Net Income

The average net income is simply the total net income divided by the term of the project. This amount already allows for the depreciation expense.

```Average net income = Total net income / Project term
Average net income = 52,200 / 3
Average net income = 17,400
```

The average annual net income for the project is 17,400

### Calculate the Average Investment

The beginning investment is the initial amount invested by the business at the start of year 1 which is 150,000. Over the term of the 3 years the value of the investment is reduced by depreciation to its salvage value of 24,000, and the ending investment is therefore 24,000.

The simple arithmetic average of these two values is calculated as follows:

```Average investment = (Beginning investment value + Ending investment value) / 2
Average investment = (Initial investment + Salvage value) / 2
Average investment = (150,000 + 24,000) / 2
Average investment = 87,000
```

The average investment in the project over the three years is therefore 87,000.

### Calculate the Accounting Rate of Return

The accounting rate of return can now be calculated by applying the ARR formula to the average net income and the average investment value calculated above.

```ARR = Average net income / Average investment
ARR = 17,400 / 87,000
ARR = 20%
```

The accounting rate of return method shows that the return on this project is 20% a year for 3 years.

## Rules for Using the Accounting Rate of Return Method

There are two main rules to be used for making decisions when using the ARR method to calculate project returns.

1. For a single project: If the ARR is greater than the required return, then the project should be accepted, if the ARR is less than the required rate of return then the project should be rejected.
2. For multiple projects: Providing the ARR is greater than the required return, the project with the highest ARR should be chosen.

The accounting rate of return method has the advantage that it provides a simple and familiar way to calculate and compare the annual rate of return a project provides, and is therefore a useful tool for capital budgeting decisions.

The disadvantage of the ARR technique is that it takes no account of the time value of money, the net income over the period of the project is simply averaged.

For example, suppose a project with an initial cost of 380,000 and salvage value of 20,000, has net income of 20,000, 40,000, and 60,000 over three years. The ARR is calculated as follows:

```Average net income = (20,000 + 40,000 + 60000) / 3 = 40,000
Average investment = (380,000 + 20,000) / 2 = 200,000
ARR = Average net income / Average investment
ARR = 40,000 / 200,000
ARR = 20%
```

Consider now the project with completely different net income of 1,000, 3,000 and 116,000. Again the average net income is (1,000 + 3,000 + 1160000) / 3 = 40,000, and the ARR will again be 20%.

Likewise, for the same reason, the ARR technique cannot allow for the inherent risk in a longer term project. If the project in the example above was for a term of 10 years with net income of zero for the first 9 years and 400,000 in year 10, then the average net income would again be 400,000 / 10 = 40,000 a year and, providing the investment and salvage value were the same, the ARR would again be 20%. Clearly the 10 year project has a greater risk than the 3 year project but this is not reflected in the calculation of the ARR.

Accounting Rate of Return November 6th, 2016

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