Accounting Rate of Return (ARR) Calculator
Calculate the profitability of an investment relative to its initial cost using the Accounting Rate of Return (ARR).
Enter the total **Initial Investment**, the total **Net Profit** expected over the project's life, and the project's estimated **Life in Years**. This calculator will first determine the average annual profit and then calculate the ARR.
Input Project Financials
Understanding Accounting Rate of Return (ARR)
What is Accounting Rate of Return?
The Accounting Rate of Return (ARR), sometimes called the Average Rate of Return or Book Rate of Return, is a simple capital budgeting technique used to assess the profitability of potential investments. It focuses on the accounting profit rather than cash flows.
ARR helps businesses evaluate how much profit an asset or project is expected to generate relative to its initial cost, averaged over its useful life.
ARR Formula
The core ARR formula is:
ARR = (Average Annual Net Profit / Initial Investment) * 100%
To use this, you first need the Average Annual Net Profit:
Average Annual Net Profit = Total Net Profit Over Project Life / Project Life (in Years)
Therefore, the full calculation sequence is:
- Determine the Total Net Profit expected over the project's entire life (Revenue - Expenses - Depreciation).
- Divide the Total Net Profit by the number of years in the Project Life to get the Average Annual Net Profit.
- Divide the Average Annual Net Profit by the Initial Investment.
- Multiply the result by 100 to express it as a percentage.
The "Net Profit" should typically be the profit after all operating expenses and non-cash expenses like depreciation have been deducted.
Interpreting the ARR Result
- A **higher ARR** generally indicates a more profitable project relative to its initial cost.
- Companies often have a minimum required rate of return (hurdle rate). If a project's ARR is **above** the hurdle rate, it may be accepted. If it's **below**, it may be rejected.
- ARR can be **negative** if the project is expected to result in a net loss over its life.
Limitations of ARR
While simple, ARR has significant drawbacks:
- **Ignores the Time Value of Money:** It treats profits earned early in the project life the same as profits earned later, which is financially inaccurate.
- **Based on Accounting Profit:** Relies on accounting figures rather than actual cash flows, which can sometimes present a misleading picture of liquidity or true economic return.
- **Doesn't Consider Risk:** Does not inherently incorporate the riskiness of the investment.
Accounting Rate of Return Examples
Here are 10 examples demonstrating ARR calculation:
Example 1: Standard Profitable Project
Scenario: A company considers investing in a new machine.
Inputs:
Initial Investment = $100,000
Total Net Profit Over Life = $30,000
Project Life = 5 Years
Calculation:
1. Average Annual Profit = Total Profit / Project Life = $30,000 / 5 Years = $6,000 per year
2. ARR = (Average Annual Profit / Initial Investment) * 100
= ($6,000 / $100,000) * 100
Result: ARR = 6%
Interpretation: The project is expected to yield an average annual return of 6% on the initial investment.
Example 2: Higher Profit Project
Scenario: Another investment opportunity with higher returns.
Inputs:
Initial Investment = $100,000
Total Net Profit Over Life = $50,000
Project Life = 5 Years
Calculation:
1. Average Annual Profit = $50,000 / 5 Years = $10,000 per year
2. ARR = ($10,000 / $100,000) * 100
Result: ARR = 10%
Interpretation: This project offers a higher average return (10%) compared to Example 1, making it potentially more attractive based on ARR.
Example 3: Longer Life, Same Total Profit
Scenario: The same initial investment and total profit, but spread over more years.
Inputs:
Initial Investment = $100,000
Total Net Profit Over Life = $30,000
Project Life = 10 Years
Calculation:
1. Average Annual Profit = $30,000 / 10 Years = $3,000 per year
2. ARR = ($3,000 / $100,000) * 100
Result: ARR = 3%
Interpretation: Spreading the same total profit over a longer life results in a lower average annual profit and thus a lower ARR (3%).
Example 4: Shorter Life, Higher Total Profit
Scenario: A project with a shorter but more intense period of profitability.
Inputs:
Initial Investment = $100,000
Total Net Profit Over Life = $40,000
Project Life = 2 Years
Calculation:
1. Average Annual Profit = $40,000 / 2 Years = $20,000 per year
2. ARR = ($20,000 / $100,000) * 100
Result: ARR = 20%
Interpretation: A higher total profit over a shorter life significantly boosts the average annual profit and the resulting ARR (20%).
Example 5: Zero Total Profit (Break-even)
Scenario: A project is expected to just cover all costs over its life.
Inputs:
Initial Investment = $75,000
Total Net Profit Over Life = $0
Project Life = 3 Years
Calculation:
1. Average Annual Profit = $0 / 3 Years = $0 per year
2. ARR = ($0 / $75,000) * 100
Result: ARR = 0%
Interpretation: An ARR of 0% means the project is expected to break even on average relative to the initial investment.
Example 6: Negative Total Profit (Loss)
Scenario: The project is expected to incur a net loss over its life.
Inputs:
Initial Investment = $120,000
Total Net Profit Over Life = -$10,000
Project Life = 4 Years
Calculation:
1. Average Annual Profit = -$10,000 / 4 Years = -$2,500 per year
2. ARR = (-$2,500 / $120,000) * 100
Result: ARR = -2.0833%
Interpretation: A negative ARR indicates the project is expected to result in a net loss, making it generally undesirable.
Example 7: Small Investment, High Profit
Scenario: A small upgrade leading to significant profit increase.
Inputs:
Initial Investment = $5,000
Total Net Profit Over Life = $2,000
Project Life = 2 Years
Calculation:
1. Average Annual Profit = $2,000 / 2 Years = $1,000 per year
2. ARR = ($1,000 / $5,000) * 100
Result: ARR = 20%
Interpretation: A high ARR (20%) suggests this relatively small investment is very efficient at generating profit over its short life.
Example 8: Large Investment, Moderate Profit
Scenario: A major expansion project.
Inputs:
Initial Investment = $1,000,000
Total Net Profit Over Life = $250,000
Project Life = 10 Years
Calculation:
1. Average Annual Profit = $250,000 / 10 Years = $25,000 per year
2. ARR = ($25,000 / $1,000,000) * 100
Result: ARR = 2.5%
Interpretation: Despite a large total profit, the significant initial investment and long life result in a relatively low ARR (2.5%).
Example 9: Comparing Two Simple Projects (Manual)
Scenario: Comparing Project A and Project B using ARR.
Project A Inputs: Inv = $80k, Total Profit = $24k, Life = 4 Years
Project A Calculation: Avg Profit A = $24k / 4 = $6k. ARR A = ($6k / $80k) * 100 = 7.5%
Project B Inputs: Inv = $60k, Total Profit = $15k, Life = 3 Years
Project B Calculation: Avg Profit B = $15k / 3 = $5k. ARR B = ($5k / $60k) * 100 ≈ 8.33%
Result: ARR A = 7.5%, ARR B ≈ 8.33%
Interpretation: Based purely on ARR, Project B (8.33%) appears slightly more attractive than Project A (7.5%).
Example 10: Project with Specific Depreciation Note
Scenario: A machine costing $60,000 with $10,000 salvage value, depreciated straight-line over 5 years. Expected total revenue $80,000, total operating expenses $20,000.
Inputs Derivation:
Initial Investment = $60,000
Total Depreciation = Cost - Salvage = $60,000 - $10,000 = $50,000
Total Net Profit Over Life = Total Revenue - Total Operating Expenses - Total Depreciation = $80,000 - $20,000 - $50,000 = $10,000
Project Life = 5 Years
Calculation:
1. Average Annual Profit = Total Profit / Project Life = $10,000 / 5 Years = $2,000 per year
2. ARR = (Average Annual Profit / Initial Investment) * 100
= ($2,000 / $60,000) * 100
Result: ARR ≈ 3.33%
Interpretation: The project has an ARR of approximately 3.33% after accounting for all costs including depreciation.
Frequently Asked Questions about ARR
1. What does ARR stand for?
ARR stands for Accounting Rate of Return. It's also sometimes called the Average Rate of Return or Book Rate of Return.
2. How is the Accounting Rate of Return calculated?
The basic calculation is: (Average Annual Net Profit / Initial Investment) * 100%. Average Annual Net Profit is found by dividing the Total Net Profit over the project's life by the number of years in the project life.
3. What financial information do I need to calculate ARR?
You need the total Initial Investment, the total Net Profit expected over the entire project's life, and the estimated Project Life in years.
4. What does a high ARR indicate?
A higher ARR suggests that a project is expected to generate a larger average annual profit relative to its initial cost compared to projects with lower ARRs.
5. Can ARR be negative?
Yes, ARR can be negative if the total net profit expected over the project's life is negative (i.e., the project is expected to incur a net loss).
6. Does ARR consider cash flow?
No, ARR is based on accounting profit, which includes non-cash items like depreciation. It does not measure the actual timing or amount of cash coming in or going out of the business.
7. Does ARR account for the time value of money?
No, this is a major limitation. ARR treats profits earned in year 1 the same as profits earned in year 10, ignoring the fact that money received sooner is more valuable.
8. Is ARR suitable for comparing different investment projects?
ARR can provide a simple initial comparison, but because it ignores the time value of money and cash flows, it's generally not the preferred method for comparing projects, especially if they have different lifespans or different patterns of cash flows.
9. How does depreciation affect the ARR calculation?
Depreciation is included as an expense when calculating the Net Profit. A higher depreciation expense will result in a lower Net Profit, and thus a lower Average Annual Profit and a lower ARR.
10. What is a typical good ARR?
There's no universal "good" ARR. It depends heavily on the industry, the company's required rate of return (hurdle rate), and the risk level of the project. Companies usually set a minimum acceptable ARR.
