Accounting Rate of Return (ARR)

Core idea

Overview

The Accounting Rate of Return (ARR) is a capital budgeting metric used to evaluate the profitability of an investment project based on expected accounting profit. Unlike other methods, it uses net income figures from the income statement rather than cash flows to determine the percentage return on the capital cost.

When to use: ARR is typically used during the initial screening of capital projects to quickly compare the accounting profitability of various assets. It is most appropriate when managers want to see how an investment will affect future financial statements and reported earnings per share.

Why it matters: This metric is significant because it aligns with standard accounting practices, making it easier for stakeholders to understand project performance in the context of a company's financial reports. It provides a simple percentage that allows for quick comparisons across different industries or project types without complex cash flow forecasting.

Symbols

Variables

ARR = ARR, AAP = Avg Annual Profit, INV = Initial Investment

ARR

%

AAP

Avg Annual Profit

£

INV

Initial Investment

£

Walkthrough

Derivation

Derivation/Understanding of Accounting Rate of Return (ARR)

This derivation explains how the Accounting Rate of Return (ARR) is calculated to assess the average annual profitability of an investment relative to its initial cost.

Profits are accounting profits (after depreciation, before tax).
The initial investment is the full capital outlay at the start of the project.
It does not account for the time value of money.

1

Defining the Objective:

The primary goal of ARR is to provide a simple percentage figure that indicates the average annual profitability an investment is expected to yield relative to the capital initially committed.

ARR aims to measure the average annual return generated by an investment as a percentage of its initial cost.

2

Calculating Average Annual Profit:

To obtain a representative annual profit figure, the total accounting profit expected over the entire lifespan of the project is summed and then divided by the number of years the project is expected to run.

Average Annual Profit = \frac{Total Profit over Project Life}{Number of Years}

3

Expressing Return Relative to Investment:

This step establishes a ratio that compares the average annual profit generated by the project to the initial capital outlay, showing the profit earned per unit of currency invested.

Return Ratio = \frac{Average Annual Profit}{Initial Investment}

4

Final Calculation of ARR:

Multiplying the return ratio by 100 converts it into a percentage. This makes the ARR figure easily comparable with other investment opportunities or a company's target rate of return.

ARR = \frac{Average Annual Profit}{Initial Investment} \times 100

Result

ARR = \frac{Average Annual Profit}{Initial Investment} \times 100

Source: AQA A-level Business by Hall, Jones, Raffo, Wall, and Whitfield

Free formulas

Rearrangements

Solve for AAP

Make AAP the subject

AA P = \frac{A R R \times I N V}{100}

Deterministic rearrangement generated from calculator baseLaTeX for AAP.

Difficulty: 2/5

Solve for INV

Make INV the subject

I N V = \frac{AA P \times 100}{A R R}

Deterministic rearrangement generated from calculator baseLaTeX for INV.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin because the Accounting Rate of Return is directly proportional to the Average Annual Profit. For a finance student, this linear relationship means that doubling the Average Annual Profit will always result in a doubling of the Accounting Rate of Return. Small values on the x-axis represent low profitability relative to the investment, while large values indicate a high return on that investment. The most important feature of this curve is that the slope is determined entirely by the investment amount, showing that the rate of return scales consistently as profit grows.

Graph type: linear

Why it behaves this way

Intuition

Imagine the initial investment as a fixed pool of capital; the ARR illustrates what percentage of that pool is replenished, on average, each year through the project's accounting profits.

ARR

The average annual accounting profit generated by an investment, expressed as a percentage of the initial capital outlay.

It quantifies how efficiently the initial capital is converted into reported earnings over the project's life, providing a simple measure of accounting profitability.

Avg Annual Profit

The total accounting profit (revenue minus expenses, including depreciation and taxes) expected from an investment over its useful life, divided by the number of years.

This represents the average yearly 'gain' or increase in a company's reported net income directly attributable to the investment project.

Initial Investment

The total capital expenditure required at the start of a project, encompassing the cost of acquiring all necessary assets.

This is the 'cost' or the total amount of capital committed upfront to undertake the project, serving as the base against which the average annual profit is measured.

Signs and relationships

Initial Investment (denominator): Placing the initial investment in the denominator normalizes the average annual profit, expressing it as a return per unit of capital invested.
×100: This factor scales the fractional return into a percentage, which is the conventional and most intuitive format for expressing financial rates of return and facilitates easy comparison with other percentage-based

Free study cues

Insight

Canonical usage

The Accounting Rate of Return (ARR) is typically expressed as a dimensionless percentage, representing the average annual profit relative to the initial investment.

Common confusion

A common confusion is to interpret the 'annual' in 'Average Annual Profit' as implying that ARR has units of 'per year' or 'percentage per year'. However, ARR is a pure, dimensionless percentage.

Dimension note

The Accounting Rate of Return is inherently dimensionless because it is a ratio of two quantities with the same dimension (money). The 'annual' aspect of the average annual profit refers to the period over which the profit is measured, not a separate unit in the ratio.

Unit systems

Avg Annual Profitcurrency (e.g., USD, GBP, EUR) - This is the total profit over the project's life divided by the number of years, resulting in an average monetary amount. For the purpose of ARR, its unit is simply currency.

Initial Investmentcurrency (e.g., USD, GBP, EUR) - The total capital outlay required for the project.

One free problem

Practice Problem

A logistics firm is considering purchasing a new fleet of delivery trucks for 150,000. These trucks are expected to generate an average annual profit of 22,500 over their useful life. Calculate the Accounting Rate of Return (ARR) for this investment.

Avg Annual Profit22500 £

Initial Investment150000 £

Solve for: ARR

Hint: Divide the annual profit by the total initial cost and multiply by 100 to get a percentage.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

In an economic or financial decision involving Accounting Rate of Return (ARR), Accounting Rate of Return (ARR) is used to calculate ARR from Avg Annual Profit and Initial Investment. The result matters because it helps compare incentives, policy effects, market outcomes, or financial decisions in context.

Study smarter

Tips

Ensure the average annual profit accounts for depreciation and taxes.
Be aware that ARR does not account for the time value of money.
Compare the resulting ARR against the company's internal hurdle rate or cost of capital.

Avoid these traps

Common Mistakes

Forgetting to deduct initial cost from total inflows to find total profit.
Using total profit instead of average annual profit.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

This derivation explains how the Accounting Rate of Return (ARR) is calculated to assess the average annual profitability of an investment relative to its initial cost.

ARR is typically used during the initial screening of capital projects to quickly compare the accounting profitability of various assets. It is most appropriate when managers want to see how an investment will affect future financial statements and reported earnings per share.

This metric is significant because it aligns with standard accounting practices, making it easier for stakeholders to understand project performance in the context of a company's financial reports. It provides a simple percentage that allows for quick comparisons across different industries or project types without complex cash flow forecasting.

Forgetting to deduct initial cost from total inflows to find total profit. Using total profit instead of average annual profit.