# Accounting rate of return

FFM study guide reference E3b) requires candidates to not only be able to calculate the accounting rate of return, but also to be able to discuss the usefulness of the accounting rate of return as a method of investment appraisal.

Recent FFM exam sittings have shown that candidates are struggling with the concept of the accounting rate of return and this article aims to help candidates with this topic.

Candidates should note that accounting rate of return can not only be examined within the FFM syllabus, but also the F9 syllabus.

### Definition

The accounting rate of return, also known as the return on investment, gives the annual accounting profits arising from an investment as a percentage of the investment made.

As we can see from this, the accounting rate of return, unlike investment appraisal methods such as net present value, considers profits, not cash flows. This is a vital point that many candidates forget in the exam.

Calculation
The formula for the accounting rate of return is (average annual accounting profits/investment) x 100%

Let us look at an example:

A company is considering in investing a project which requires an initial investment in a machine of \$40,000. Net cash inflows of \$15,000 will be generated for each of the first two years, \$5,000 in each of years three and four and \$35,000 in year five, after which time the machine will be sold for \$5,000.

Calculating the numerator
We need the average annual accounting profit. To find this, the profit for the whole project needs to be calculated, which is then divided by the number of years for which the project is running (in this case five years).

Considering the profit for the project, let us draw up a simple profit and loss statement for the whole project:

\$
Cash inflow years 1 and 2 (\$15,000 x 2)
30,000

Cash inflow years 3 and 4 (\$5,000 x 2)
10,000

Cash inflow year 535,000
Depreciation
(\$40,000 – \$5,000)

(35,000)

Total profit for the project40,000

Next we need to convert this profit for the whole project into an average figure, so dividing by five years gives us \$8,000 (\$40,000/5).

Calculating the denominator
Now we have the numerator, we need to consider the denominator, i.e. the investment figure.

The investment figure can either be

• the initial investment, or
• the average investment, where the average investment is calculated:
(the initial investment + scrap value)/2

So in this case:

• the initial investment is \$40,000
• the average investment is (\$40,000 + \$5,000)/2 = \$22,500

Calculating the accounting rate of return
The accounting rate of return can now be calculated as either:

• (\$8,000/\$40,000) x 100% = 20% or
• (\$8,000/\$22,500) x 100% = 36%

This approach should be used for any accounting rate of return calculation, no matter how easy or difficult:

Calculate the numerator:

1. Calculate the profit for the whole project. Include not only cash revenue and cash costs, but also other costs such as depreciation, amortisation etc.
2. Calculate the average annual profit, by dividing the profit over the whole project by the life of the project.

Calculate the denominator
Look in the question to see which definition of investment is to be used. If the question does not give the information, then use the average investment method, and state this in your answer.

Calculate the accounting rate of return.

Usefulness
Having calculated the percentage answer, how can this be used for project appraisal?

The accounting rate of return percentage needs to be compared to a target set by the organisation. If the accounting rate of return is greater than the target, then accept the project, if it is less then reject the project.

This leads to a couple of problems:

• How is the target set? Should it be 25%, or 30%? The target set could be arbitrary
• Which calculation method should be used? If in the above example, the target was 25%, the project would be rejected under one calculation method but accepted under the other, so changing the calculation method can change the decision as to whether the project should be accepted or rejected.

Other problems with the accounting rate of return:

• The timing of the cash flows is not considered. In our example, the biggest cash flow arises in year five, but by then, the organisation may have ceased trading due to liquidity issues in years three and four when only \$5,000 cash is being received in each year.
• It is a relative measure rather than an absolute measure – it takes no account of the size of the investment.
• The time value of money is ignored.

There are, however, some positive aspects to the accounting rate of return:

• It is simple to calculate from readily available accounting data – no complicated discount factors to calculate!
• The concept of profit is easily understood by managers, and the answer is easily interpreted – does the project give the necessary accounting return or not?
• The method looks at the whole life of the project, unlike, for example, the payback method which may not.

### Conclusion

Candidates need to be able to calculate the accounting rate of return, and assess its usefulness as an investment appraisal method. It is hoped that this article will help candidates with both of these.

Written by a member of the FFM examining team