**Definition of ARR**

ARR Stands for Accounting Rate of Return (ARR) or Average Rate of Return (ARR). It is the annual rate of return that can be expected from the initial investment. Sometimes it is also referred to as the simple rate of return. Accounting Rate is the most important capital budgeting technique that does not involve discounting cash flows.

## Reasons of using ARR

ARR can be used when considering multiple projects with the same period and cash flow stream since it provides the expected rate of return from each project.

ARR is calculated by dividing the average revenue from an asset by the company’s initial investment.

## Steps of calculation of ARR

Following steps to be followed to calculate ARR:

- Calculate the average investment of the project
- Determine the profits (after depreciation and taxes) of the project
- Determine the average annual profits of the company
- Express the annual average profits as a percentage of the average invested capital
- Accept the project with a higher rate of return

## Advantages of ARR

- Very simple to understand and easy to calculate
- Consider the profits of the project earned over the life of the project
- Allows projecting to compare which require different amounts of initial capital investment.

## Limitations of ARR

- It is based on accounting profits and not on cash flows
- It ignores the time value of money. Profits earned in different years are considered at “par”.
- It doesn’t consider that earned profits can be reinvested
- It only considers the rate of return of the project but ignores the length of project lives

## Methods of ARR Calculation

The following two methods are usually used for ARR calculation:

- Average Investment Method
- Original Investment Method

**i)** Average Investment method = Average Annual profits/ Average investment over the life of the project * 100%

Where,

Profits = Net Cash Benefits – Depreciation

Average Investment = (Initial Investment + Salvage value)/2

ii) Original Investment Method = Average Profits / Original investment * 100

## Accepts/Reject Criteria

If the actual accounting rate of return is more than the predetermined required rate of return, the project would be accepted. If not it would be rejected. In case pf mutually exclusive project, accept the project with highest ARR.

## Worked Example

**Worked Example – 1: Where there is no Salvage value:**

Peter Enterprise wants to buy a machine at a cost of $ 150,000 and the life of the project is 5 years. The project’s net profits after tax are as follows:

Year -1 : $20,000

Year -2: $18,000

Year -3: $15,000

Year -4: $17,000

Year -5: $15,000

Requirement:

Calculate ARR Using – Average Investment Method and Original Investment Method

**Solution:**

Total Profits for 5 years = $ (20,000+18,000+15,000+17,000+15,000) = $85,000

Average profit = $85,000/5 years = $17,000

Average Investment = $150,000/2 = $75,000

Using Average Investment Method = $17,000/75,000 *100% = 22.67%

Using the Original Investment Method = $17,000/150,000 *100% = 11.33%

**Worked Example – 2 : Where there is a Salvage value:**

Peter Enterprise wants to buy a machine at a cost of $150,000 and the life of the project is 5 years. The residual/ salvage value of the machine is $25,000 project’s profits before depreciation are as follows:

Year -1 : $50,000

Year -2: $38,000

Year -3: $25,000

Year -4: $57,000

Year -5: $35,000

Requirement:

Calculate ARR Using – Average Investment Method and Original Investment Method

**Solution:**

Total Profits for 5 years = $ (80,000+38,000+25,000+57,000+35,000) = $235,000

Total Depreciation = Original Cost – Residual value = $(150,000 – 25,000) = $125,000

Average profit = $(235,000 – 125,000)/5 years = $22,000

Average Investment = $ (150,000 – 25,000)/2 = $62,500

Using Average Investment Method = $22,000/62,500 *100% = 35.20%

Using the Original Investment Method = $22,000/150,000 *100% = 14.67%