Cost-Volume-Profit Analysis

Cost-volume-profit analysis is the managerial model that reads how operating profit changes when selling price, variable cost per unit, total fixed cost or sales volume moves. It works by sorting every cost into a fixed component that does not move with output and a variable component that does, then treating the number of units sold as the driver of both revenue and cost. The Institute of Chartered Accountants of India (ICAI) defines it as an analysis of the reciprocal effect of changes in cost, volume and profitability, one that explores the relationship between costs, revenue, activity levels and the resulting profit (ICAI, Cost and Management Accounting, Marginal Costing). CVP is the everyday abbreviation.

It is an internal planning tool, so it belongs to managerial accounting rather than to the statements that go to outside readers.

The CVP Equation

The model is one identity read in different directions. Revenue less variable costs less fixed costs is operating income, also called operating profit, the subtotal defined in the equation for operating income, which reaches it by what a cost is for rather than by how it behaves. The two cuts land on the same figure only where the fixed and variable totals hold the entity’s operating costs and nothing else.

(price per unit x units) - (variable cost per unit x units) - fixed costs = operating income

The Association of Chartered Certified Accountants (ACCA) writes it in that form in its Performance Management material, and is specific about one term. Total fixed costs are used rather than a fixed cost per unit, because a unit fixed cost varies with the level of output and would therefore be inappropriate to hold constant, while selling price and variable cost per unit are assumed to remain constant for all levels of output in the short run (ACCA, Performance Management, Cost-volume-profit analysis). ICAI writes the same relationship compactly as sales less variable cost equals contribution, which equals fixed cost plus or minus profit (ICAI, Cost and Management Accounting, Marginal Costing).

The middle term carries its own name and its own entries. Revenue less variable costs is contribution margin, defined and worked in contribution margin, and the same figure stated as a percentage of revenue is the contribution margin ratio. The fixed, variable and semi-variable behavior split that the sorting depends on is set out in overhead.

What the Model Produces

Two of the three answers the model is used for are that same equation solved for a different unknown, and the third measures how far expected sales sit above the break-even answer.

Set operating income to zero and the answer is break-even, the level of sales where an entity neither earns profit nor incurs loss, which ICAI notes is indicated in both quantity and monetary value terms (ICAI, Cost and Management Accounting, Marginal Costing).

Set it instead to the profit the business wants and the answer is the target-profit volume. ACCA solves the same equation with the desired profit in place of zero, so the required quantity is fixed costs plus target profit divided by contribution per unit (ACCA, Performance Management, Cost-volume-profit analysis).

The distance between the expected level of sales and the break-even level is the margin of safety (ICAI, Cost and Management Accounting, Marginal Costing). ACCA reads the same measure as the amount by which sales can decrease before a loss occurs, the excess of budgeted revenues over break-even revenues, and states it three ways, in units, as a percentage of budgeted sales, or in sales revenue (ACCA, Performance Management, Cost-volume-profit analysis).

A Worked Example

Say a seasonal tax line charges a flat fee per return and buys its preparation capacity by the return, so that cost moves with volume while the office and the salaried reviewers do not. Break-even on these inputs is the division set out in contribution margin, and everything under that line is what the wider model adds.

Fee per return                                        $750
Variable cost per return                              $450
Contribution per return      $750 - $450            = $300

Fixed costs for the season                        $240,000
Break-even                   $240,000 / $300        = 800 returns

Budgeted returns                                     1,000
Operating income             (1,000 x $300) - $240,000
                                                   = $60,000

Margin of safety             1,000 - 800            = 200 returns
                             200 / 1,000            = 20% of budget
                             200 x $750             = $150,000 of fees

Target profit of $90,000     ($240,000 + $90,000) / $300
                                                   = 1,100 returns
Check                        (1,100 x $300) - $240,000  = $90,000

The line can lose a fifth of its budgeted volume before it stops covering its fixed costs, and it needs a tenth more than budget to earn the target. How far operating income travels for each of those volume moves is measured on its own as the degree of operating leverage, in operating leverage.

The Assumptions and the Relevant Range

Every figure the model produces is conditional, and ICAI sets out six assumptions the analysis rests on.

The first is that changes in the levels of revenues and costs arise only because of changes in the number of product or service units produced and sold, so the number of output units is the only revenue driver and the only cost driver. The second is that total costs separate into a fixed component that does not vary with output level and a variable component that does, and that the split runs through indirect costs as well as direct ones. The third is that the behaviors of total revenues and total costs are linear in relation to output level within a relevant range and time period (ICAI, Cost and Management Accounting, Marginal Costing).

The fourth is that selling price, variable cost per unit and total fixed costs, within that same relevant range and time period, are known and constant. The fifth is that the analysis either covers a single product or assumes that the proportion of different products will remain constant as the level of total units sold changes. The sixth is that all revenues and costs can be added, subtracted and compared without taking the time value of money into account (ICAI, Cost and Management Accounting, Marginal Costing).

The qualifier doing the most work there is the relevant range, and it is the piece most often stated loosely. It is not a synonym for the short run. ACCA defines it as the levels of activity in which the business has experience and can therefore perform a degree of accurate analysis, having either operated at those activity levels before or studied them carefully enough to make accurate predictions of fixed costs in that range (ACCA, Performance Management, Cost-volume-profit analysis). Fixed costs hold constant inside that band and are not warranted outside it, so a volume the business has never run at is outside what the model covers rather than simply a larger number to feed it.

The limits follow from the assumptions rather than from the arithmetic. ICAI traces the practical limitations of break-even analysis and break-even charts back to those assumptions, calling linear cost behavior, sales revenue remaining constant at different sales levels and stocks remaining constant period after period unrealistic, and calling the assumption that activity level is the only factor influencing costs erroneous, since other factors such as inflation also bear on cost (ICAI, Cost and Management Accounting, Marginal Costing). ACCA adds that the two-way split is itself an approximation, because some costs are semi-fixed, carrying a standing monthly charge alongside a usage-driven one (ACCA, Performance Management, Cost-volume-profit analysis).

Where the Assumptions Bend in a CPA Firm

A firm pointing the model at its own book meets the sales-mix assumption first. A practice does not sell one product. It sells individual returns, entity returns, monthly bookkeeping and advisory work, and each leaves a different contribution behind, so a firm-wide break-even is a composite figure that holds only while the mix holds. ICAI handles that case by weighting the contribution across products, with the weights taken from sales mix quantity or sales mix values (ICAI, Cost and Management Accounting, Marginal Costing), and ACCA computes a weighted average contribution to sales ratio as total contribution divided by total sales revenue, noting that when the constant mix assumption changes the break-even point changes with it (ACCA, Performance Management, Cost-volume-profit analysis). A season that sells more of the thin work and less of the rich work therefore moves the answer without a single price or cost having changed.

The relevant range is the next to go, and a firm leaves it deliberately. Adding a preparer, a reviewer or a seat steps the fixed base up rather than raising it smoothly, and the band the old fixed-cost figure was true inside ends at that step. A break-even computed before the step describes a cost structure the firm no longer has.

The single-driver assumption is the one to test last. Return count drives cost only where the variable element is genuinely charged by the return. Where it is charged by the hour instead, two returns carrying the same fee can absorb very different preparation and review time, so volume on its own will not carry the model. Which parts of a firm’s cost base behave which way is worked through in the contribution margin ratio.

What Cost-Volume-Profit Analysis Is Confused With

Break-Even Analysis

Break-even analysis is a method used to study CVP analysis rather than a rival to it, and ICAI explains the technique in two ways. In the narrow sense it is concerned with computing the break-even point, the level of production and sales at which there is no profit and no loss because total cost equals total sales revenue. In the broad sense the same technique is used to determine the possible profit or loss at any given level of production or sales (ICAI, Cost and Management Accounting, Marginal Costing).

So the narrow sense is one point on the model and the broad sense is the model itself, which is why the two names get swapped so freely. The practical difference is what you get back. One is a single volume. The other is the whole relationship, which also yields the margin of safety and the volume that reaches a target profit.

Common Questions

Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms, and a trial task lets a firm’s own reviewer grade a real block of work before any client file depends on it.