# Accounting Rate of Return (ARR)

## Definition

Accounting Rate of Return, shortly referred to as ARR, is the percentage of average accounting profit earned from an investment in comparison with the average accounting value of investment over the period.

Accounting Rate of Return is also known as the Average Accounting Return (AAR) and Return on Investment (ROI).

## Formula

Accounting Rate of Return  =   (Average Profit / Average Book Value) %

Where:

Average Profit:

= Total accounting profit over the investment period ÷ Years of Investment

Average Book Value:

= (Initial investment + Scrap Value + Working Capital) ÷ 2

OR

Average Book Value:

= (N.B.V. (year 0) + N.B.V. (year 1) + N.B.V. (year 2) + …) ÷ (Years of Investment + 1)

## Explanation

ARR is a measure of accounting profitability of investments.

An ARR of 10% for example means that the investment would generate an average of 10% annual accounting profit over the investment period based on the average investment.

ARR may be compared with the target return on investment. Investments may be accepted if the ARR exceeds the target return. However, it is preferable to evaluate investments based on theoretically superior appraisal methods such as NPV and IRR due to the limitations of ARR discussed below.

The calculation of ARR requires finding the average profit and average book values over the investment period. Whereas average profit is fairly simple to calculate, there are several ways to calculate the average book value of investment.

How should average book value be calculated?

One of the simplest and quickest ways of calculating the average net book value of investment assets is by finding a simple average of:

• the value of assets at the start of investment (this will be equal to the amount of the initial investment); and
• the value of those assets at the end of the investment period (this should be equal to the non-depreciated part of non-current assets (i.e. salvage value) and any current assets (i.e. working capital))

This can be summarized into the following formula:

Average Book Value:

= (Initial investment + Scrap Value + Working Capital) ÷ 2

In case where subsequent investments are to be made after the initial investment, the above formula would not account for the additional investment. Instead, the average book value shall be found by adding the net book value (N.B.V.) of investment assets at the end of each year as follows:

Average Book Value:

= (N.B.V. (year 0) + N.B.V. (year 1) + N.B.V. (year 2) + …) ÷ (Years of Investment + 1)

Note: Net Book Value of Year 0 will be equal to the initial investment.

You may see the example below for an illustration of how to apply the above formulas.

## Example

ABC PLC is planning to invest in a 5-year project.

The initial cost of the project shall be \$100 million comprising \$60 million for capital expenditure and \$40 million for working capital requirements.

Annual net cash flows from the project are expected to be as follows:

Year               Cash Flows \$M
1                            (10,000)
2                             20,000
3                             30,000
4                             40,000
5                             30,000

Further information:

• Year 5 cash inflows include \$10m in respect of the estimated scrap value of property, plant and equipment expected to be recovered at the end of the end of the year.
• Working capital shall be maintained at the same level throughout the investment period.
• Depreciation is to be calculated on straight-line basis.

ABC PLC’s target return on investments is 15%.

Calculate the Accounting Rate of Return for the proposed project and comment.

## Solution

Accounting Rate of Return:

= (Average Profit ÷ Average Book Value )%

= \$12m (W1) ÷ \$75m (W2)

=  16%

As the ARR exceeds the target return on investment, the project should be accepted.

W1: Average Profit:

= 60 (W3) ÷ 5  =  \$12m

W2:

Average Book Value:

= (100 (initial investment) + 10 (scrap value) + 40 (working capital)) ÷ 2

= \$150 m ÷ 2

= \$75m

or

Average Book Value:

= Sum of net book values ÷ (Years of investment +1)

= \$450m (W4) ÷ (5+1)

=\$75m*

Year Cash Flows Depreciation Profits W3 Net Book Value at the year end W4

\$M

\$M

\$M

\$M

0

100

1

(10)

(10)

(20)

90

2

20

(10)

10

80

3

30

(10)

20

70

4

40

(10)

30

60

5

30

(10)

20

50

110

(50)

60

450

*Note:

Using working 4 in the above table, we can confirm that the accuracy of \$75 m (and the formulas used to calculate it!) average book value calculated above by finding the average of the mid-year net book values as follows:

Year Net Book Value at the year end W4 Net Book Value at the mid-year Working

\$M

\$M

0

100

1

90

95

(100 + 90) ÷ 2

2

80

85

(90 + 80) ÷ 2

3

70

75

(80 + 70) ÷ 2

4

60

65

(70 + 60) ÷ 2

5

50

55

(60 + 50) ÷ 2

110

(50)

60

Average Book Value:

= \$375 m ÷ 5

=  \$75m

Note that the value of investment assets at the end of 5th year (i.e. \$50m) is the sum of scrap value (\$10 m) and working capital (\$40 m).

ARR illustrates the impact of a proposed investment on the accounting profitability which is the primary means through which stakeholders assess the performance of an enterprise.

## Limitations

ARR is considered to be theoretically inferior than other investment appraisal methods such NPV and IRR for the following reasons:

• ARR is not based on cash flows.
While most cash flows will be reflected in accounting profits, many incomes and expenses relevant to investment appraisal may be omitted when applying ARR (e.g. opportunity costs and benefits).
Conversely, some cash flows recognized in accounting profits will not be relevant to investment appraisal such as sunk costs and committed costs.
One way to partially solve this problem to calculate ARR based on incremental profits. However, it will be more efficient to use appraisal techniques that are already based on cash flows such as IRR than to adjust accounting profit in ARR if the primary objective of the analysis is to measure the incremental return on investment based on cash flows.
• ARR does not consider time value of money unlike other discounted cash flow investment appraisal methods such as NPV and IRR.
• ARR does not provide a theoretically sound decision rule such as that of NPV (i.e. accept investments with positive NPV) or IRR (i.e. accept investment if IRR > Cost of Capital).