# Accounting Rate of Return (ARR)

Accounting rate of return (also known as simple rate of return) is the ratio of estimated accounting profit of a project to the average investment made in the project. ARR is used in investment appraisal.

## Formula

Accounting Rate of Return is calculated using the following formula:

ARR = | Average Accounting Profit |

Average Investment |

Average accounting profit is the arithmetic mean of accounting income expected to be earned during each year of the project's life time. Average investment may be calculated as the sum of the beginning and ending book value of the project divided by 2. Another variation of ARR formula uses initial investment instead of average investment.

## Decision Rule

Accept the project only if its ARR is equal to or greater than the required accounting rate of return. In case of mutually exclusive projects, accept the one with highest ARR.

## Examples

**Example 1:** An initial investment of $130,000 is expected to generate annual cash inflow of $32,000 for 6 years. Depreciation is allowed on the straight line basis. It is estimated that the project will generate scrap value of $10,500 at end of the 6th year. Calculate its accounting rate of return assuming that there are no other expenses on the project.

__Solution__

Annual Depreciation = (Initial Investment − Scrap Value) ÷ Useful Life in Years

Annual Depreciation = ($130,000 − $10,500) ÷ 6 ≈ $19,917

Average Accounting Income = $32,000 − $19,917 = $12,083

Accounting Rate of Return = $12,083 ÷ $130,000 ≈ 9.3%

**Example 2:** Compare the following two mutually exclusive projects on the basis of ARR. Cash flows and salvage values are in thousands of dollars. Use the straight line depreciation method.

**Project A:**

Year 0 1 2 3 Cash Outflow -220 Cash Inflow 91 130 105 Salvage Value 10

**Project B:**

Year 0 1 2 3 Cash Outflow -198 Cash Inflow 87 110 84 Salvage Value 18

__Solution__

**Project A:**

Step 1: Annual Depreciation = ( 220 − 10 ) / 3 = 70 Step 2: Year 1 2 3 Cash Inflow 91 130 105 Salvage Value 10 Depreciation* -70 -70 -70 Accounting Income 21 60 45 Step 3: Average Accounting Income = ( 21 + 60 + 45 ) / 3 = 42 Step 4: Accounting Rate of Return = 42 / 220 = 19.1%

**Project B:**

Step 1: Annual Depreciation = ( 198 − 18 ) / 3 = 60 Step 2: Year 1 2 3 Cash Inflow 87 110 84 Salvage Value 18 Depreciation* -60 -60 -60 Accounting Income 27 50 42 Step 3: Average Accounting Income = ( 27 + 50 + 42 ) / 3 = 39.666 Step 4: Accounting Rate of Return = 39.666 / 198 ≈ 20.0%

Since the ARR of the project B is higher, it is more favorable than the project A.

## Advantages and Disadvantages

**Advantages**

- Like payback period, this method of investment appraisal is easy to calculate.
- It recognizes the profitability factor of investment.

**Disadvantages**

- It ignores time value of money. Suppose, if we use ARR to compare two projects having equal initial investments. The project which has higher annual income in the latter years of its useful life may rank higher than the one having higher annual income in the beginning years, even if the present value of the income generated by the latter project is higher.
- It can be calculated in different ways. Thus there is problem of consistency.
- It uses accounting income rather than cash flow information. Thus it is not suitable for projects which having high maintenance costs because their viability also depends upon timely cash inflows.

Written by Irfanullah Jan