# Accounting Rate of Return

December 13, 2021

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## Definition of Accounting Rate of Return

Accounting rate of return (ARR) is commonly known as a simple rate of return which focuses on the project’s net income rather than its cash flow. It is one of the oldest evaluation techniques. In its most commonly used form, the accounting rate of return is measured as the ratio of the project’s average annual expected net income to its average investment.

## Accounting Rate of Return Formula

The accounting rate of return formula is as follows

Accounting Rate of Return (ARR) = Average Accounting Profit / Average Investment

The first element, average accounting profit is the arithmetic mean of accounting income expected to be earned during each year of the project's lifetime.

The next element, the average investment is calculated as the sum of the beginning and ending book value of the project divided by 2. Another alternative of ARR formula uses initial investment instead of average investment.

## Example of Accounting Rate of Return

An initial investment of Tk 130,000 by an Indonesian company MAX Ltd in Bangladesh is expected to generate annual revenue of Tk 32,000 for 6 years. Depreciation is allowed on a straight-line basis. Further it is estimated that the project will have salvage value of Tk 10,500 at end of the 6th year.

The accounting rate of return assuming that there are no other expenses on the project would be as follows:

 Steps Description Formula Workings Step 1 Average Investment per year (Depreciation) [ Initial Investment (-) Scrap Value] / Useful Life in Years ( Tk 130,000 – Tk 10,500 ) / 6 = Tk 19,917 Step 2 Average Accounting profit Annual Revenue – (Annual depreciation + Expenses) Tk 32,000 - Tk 19,917 = Tk 12,083 Step 3 Accounting Rate of Return ( ARR ) ( in percentage ) Average Accounting profit/ Average Investment (Initial Value + Book Value at end /2) Tk 12,083 / Tk 70,250 = 17.2%

The accounting rate of return of MAX Ltd from this project will be 17.2%.

## How to Choose Project Based on ARR projection

### Mutually inclusive project

The decision rule is simple that the ARR calculations will choose only those projects which have equal or greater accounting rate of return compared to required rate of return.

### Mutually exclusive project

In case of mutually exclusive projects, the accounting rate of return calculations will choose the project with highest ARR. Let us understand this with an example.

Rajesh Ltd of India has two mutually exclusive projects to be laid in UAE. The details of cash inflows and outflows are as follows : -

 Project A Time Cash Inflow Cash outflow Other details Year 0 220 Dirhams Year 1 91 Dirhams SLM Deprecation Year 2 130 Dirhams SLM Depreciation Year 3 105 Dirhams SLM Deprecation Salvage Value = 10 Dirhams

 Project B Time Cash Inflow Cash outflow Other details Year 0 198 Dirhams Year 1 87 Dirhams SLM Deprecation Year 2 110 Dirhams SLM Depreciation Year 3 84 Dirhams SLM Deprecation Salvage Value = 18 Dirhams

Average Rate of Return calculations of both the projects are below:

Project A

 Steps Description Formula Workings Step 1 Annual Depreciation [ Initial Investment ( - ) Scrap Value ] / ( Useful Life in Years ) ] [ 220 ( - ) 10 ] / 3 = 70 Step 2 Average Accounting Profit Average of Net Income = Inflows ( - ) Outflows [ ( 91 – 70 ) + ( 130 – 70 ) + ( 105 – 70 ) ] / 3 = 38.67 Step 3 Accounting Rate of Return ( ARR ) ( in percentage ) Average Accounting profit/ Average Investment (Initial value + Book value at end /2) 42 / 115 = 33.62%

Project B

 Steps Description Formula Workings Step 1 Annual Depreciation [ Initial Investment ( - ) Scrap Value ] / ( Useful Life in Years ) ] [ 30% ( - ) 18 ] / 3 = 60 Step 2 Average Accounting Profit Average of Net Income = Inflows ( - ) Outflows [ ( 87 – 60 ) + ( 110 – 60 ) + ( 84 – 60 ) ] / 3 = 33.67 Step 3 Accounting Rate of Return ( ARR ) ( in percentage ) Average Accounting profit / Average Investment (Initial Value + Book Value at end /2) 33.67 / 108 = 31.17.%

Project A with higher ARR is the one which Rajesh Ltd will choose. This because, in the case of mutually exclusive projects, the accounting rate of return calculations will choose the project with the highest ARR.

## Advantages and Disadvantages of Accounting Rate of Return

• This method of investment appraisal using average annual return is easy to calculate.
• It recognizes the profitability factor of investment.

• It ignores the time value of money. Suppose, if we use ARR to compare two projects having equal initial investments, it will rank the on which has a higher annual income in the beginning though the other project has potential for higher annual income in the latter years of its useful life.
• The problem of consistency in the results since it can be calculated in different ways with varying formulas.

Read More on Accounting

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