# 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.