Accounting Rate of Return Equation

The accounting rate of return (ARR) equation is average annual accounting profit divided by the investment made, expressed as a percentage. The profit in the numerator is measured after depreciation has been charged, which is what makes this an accounting measure rather than a cash one. The investment in the denominator is either the initial outlay or the average investment, and the same project returns two different percentages depending on which one is used.

The Accounting Rate of Return Equation, Term by Term

The formula for the accounting rate of return is average annual accounting profits divided by investment, times 100% (ACCA, Accounting rate of return).

accounting rate of return  =  (average annual accounting profit / investment) x 100%

Average annual accounting profit is the profit for the whole project divided by the number of years the project runs. Profit for the project includes not only cash revenue and cash costs but also other costs such as depreciation and amortization.

That inclusion is the whole reason the word accounting sits in the name. Unlike investment appraisal methods such as net present value, the accounting rate of return considers profits, not cash flows, and the measure is also known as the return on investment (ACCA, Accounting rate of return). That phrase is applied loosely to other return-over-cost ratios, so ask which equation produced a figure before setting it beside this one.

The Two Denominators, and Why They Disagree

The investment figure can be either the initial investment or the average investment, and the average investment is calculated as the initial investment plus scrap value, divided by 2 (ACCA, Accounting rate of return).

Scrap value is what the asset is expected to be worth when it comes out of service, the same estimate that appears as salvage value in a straight line depreciation calculation. The average investment is the midpoint of the outlay and that estimate.

ACCA’s instruction to exam candidates is that where the figures do not say which definition of investment applies, use the average investment method and state that it has been used (ACCA, Accounting rate of return). The reason to state it holds outside the exam too, and it sits in the arithmetic. Whenever the scrap estimate is below the outlay, the average investment is the smaller denominator, so the same project scores higher under it.

A Worked Example

Say a firm buys equipment on the inputs below, keeps it for five years, and sells it at the end for the scrap value shown.

Initial investment                                   50,000
Scrap value at the end of year five                  10,000
Project life, in years                                    5
Net cash savings, each year                          17,000

Total cash savings over five years                   85,000
Depreciation (50,000 less 10,000)                   (40,000)
Total profit for the project                         45,000

Average annual accounting profit    45,000 / 5   =    9,000

Initial investment                                   50,000
   9,000 / 50,000                                =      18%

Average investment    (50,000 + 10,000) / 2      =   30,000
   9,000 / 30,000                                =      30%

Both percentages are correct arithmetic on one project. Set a target anywhere between them and the purchase is accepted under one denominator and rejected under the other, so changing the calculation method can change the decision on whether to accept the project (ACCA, Accounting rate of return).

The Decision Rule

The percentage on its own decides nothing. It has to be compared with a target set by the organization, and if the accounting rate of return is greater than the target the project is accepted, while if it is less the project is rejected (ACCA, Accounting rate of return).

Two things weaken that rule. The target could be arbitrary, because nothing inside the method says where it should be set. And the choice of denominator can flip the verdict on a project that has not changed at all.

Where a CPA Firm Meets the Equation

A firm meets this equation on a capital purchase decision, a replacement scanning and workflow setup for example, appraised out of figures its own books already produce. The method holds its place there for three practical reasons. It is simple to calculate from readily available accounting data with no discount factors to work out, the concept of profit is easily understood by managers, and the answer is easily interpreted as whether the project gives the necessary accounting return (ACCA, Accounting rate of return).

Each input sits where the firm already keeps it. The outlay is a fixed asset addition, the depreciation that reduces the numerator is the charge computed on that asset, and the profit being averaged is accrual profit of the kind the income statement produces on its way down to net income.

What the Equation Leaves Out

Three weaknesses come with the method, and together they decide when a firm should not lean on it.

The time value of money is ignored (ACCA, Accounting rate of return). Nothing in the equation treats a dollar arriving in the last year as worth less than one arriving now.

The timing of the cash flows is not considered (ACCA, Accounting rate of return). A project that receives nearly all of its cash in the final year scores the same as one that receives it evenly, and the organization may have hit liquidity trouble in the lean years before that last inflow ever lands.

It is a relative measure rather than an absolute one, and takes no account of the size of the investment (ACCA, Accounting rate of return). A small project and a large one can report the same percentage while the money at risk is nothing alike.

A fourth limit follows from the equation itself. Because the numerator is profit after depreciation, the useful life and scrap estimates that set the depreciation charge move the answer, and neither of those is a cash fact.

What It Is Confused With

Payback Period

The payback period is a duration in years rather than a percentage, and it runs on cash alone, so depreciation stays out of it while the accounting rate of return keeps depreciation inside. The two also cover different stretches of a project. The accounting rate of return looks at the whole life of the project (ACCA, Accounting rate of return), while payback stops counting once the outlay is recovered, so the cash flows after that point are ignored (ACCA, Payback and discounted payback).

Net Profit Margin

Net profit margin states profit as a percentage of revenue for one closed period, while the accounting rate of return states it as a percentage of an investment across a project’s whole life.

Common Questions

Because an appraisal like this waits on the close that produces its book profit, a trial task puts a block of that closing work through Accountably’s review chain before your own reviewer depends on it.