### Accounting Rate of Return (ARR) Examples

Definition: Accounting rate of return (ARR, also known as average rate of return) is used to estimate the rate of return for an investment project. The higher the ARR, the more attractive the project is. If the ARR is higher than the minimum standard average rate of return, then we will accept the project. However, this technique does not take into account of the time value of money.

Calculation and Formula:

ARR = Average profit / Average investment

Example 1:

An investment of $600,000 is expected to give returns as follows: Year 1 ($50,000), Year 2 ($150,000), Year 3 ($80,000), Year 4 ($20,000).Calculate the average rate of return.

Solution:

Total returns over the four years = 50,000 + 150,000 + 80,000 + 20,000 = $300,000

Average returns per annum = 300,000 / 4 = $75,000

ARR = 75,000 / 600,000 = 12.5%

Example 2:

Western Ltd has an option of two projects: C and D, with the same initial capital investment of $100,000. The profits for both projects are as follows:

Project C: Year 1 ($10,000), Year 2 ($5,000), Year 3 ($15,000)

Project D: Year 1 ($12,000), Year 2 ($11,000), Year 3 ($4,000)

The estimated resale value of both projects at the end of year 3 is $22,000. Calculate the ARR for each project and advise the firm.

Solution:

For Project C:

Average profit = (10,000 + 5,000 + 15,000) / 3 = $10,000

Average investment = (100,000 + 22,000) / 2 = $61,000

Accounting rate of return = 10,000 / 61,000 = 16.39%

For Project D:

Average profit = (12,000 + 11,000 + 4,000) / 3 = $9,000

Accounting rate of return = 9,000 / 61,000 = 14.75%

Since Project C has a higher ARR, it should be chosen.

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Calculation and Formula:

ARR = Average profit / Average investment

Example 1:

An investment of $600,000 is expected to give returns as follows: Year 1 ($50,000), Year 2 ($150,000), Year 3 ($80,000), Year 4 ($20,000).Calculate the average rate of return.

Solution:

Total returns over the four years = 50,000 + 150,000 + 80,000 + 20,000 = $300,000

Average returns per annum = 300,000 / 4 = $75,000

ARR = 75,000 / 600,000 = 12.5%

Example 2:

Western Ltd has an option of two projects: C and D, with the same initial capital investment of $100,000. The profits for both projects are as follows:

Project C: Year 1 ($10,000), Year 2 ($5,000), Year 3 ($15,000)

Project D: Year 1 ($12,000), Year 2 ($11,000), Year 3 ($4,000)

The estimated resale value of both projects at the end of year 3 is $22,000. Calculate the ARR for each project and advise the firm.

Solution:

For Project C:

Average profit = (10,000 + 5,000 + 15,000) / 3 = $10,000

Average investment = (100,000 + 22,000) / 2 = $61,000

Accounting rate of return = 10,000 / 61,000 = 16.39%

For Project D:

Average profit = (12,000 + 11,000 + 4,000) / 3 = $9,000

Accounting rate of return = 9,000 / 61,000 = 14.75%

Since Project C has a higher ARR, it should be chosen.

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in the 1st eg avg invstment is not divided by 2 but in the later 1 it is divided by 2.....the reason is not understood.....explain please....

thanks

In the 1st eg, there is only one time capital investment so we divide the avg return by the original investment; while in the 2nd eg,there is a resale value $22,000 so we need to take this formula: Avg investment = (Initial capital + disposal value) / 2

Take project C as the example, what if the resale value of the project at the end of year 3 is $40,000. Then, average investment = (100,000 + 40,000) / 2 = 70,000; Accounting rate of return = 10,000 / 70,000 = 14.29%. It has a lower ARR and it is not recommended? However, in common sense, shouldn’t be the higher resale value the better if other factors remain the same. Can somebody help me to explain this? Thanks a lot.

@Augustine, Yes you Argument is right and thats one of the weaknesses of the Accounting rate of return.

The use of Average investment creates contradicting conclusions. The alternative method is to Use the formula Average income/initial investment

@butty, how can we treat d question of ARR that involve of scrap value.the effect of depreciation on profit and initial cost?

What is minimum rate in definition

@Roopam. It means the minimum required rate of return fixed by the management.

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