COST-VOLUME-PROFIT ANALYSIS

Cost-volume-profit analysis (CVP), or break-even analysis, is used to compute the volume level at which total revenues are equal to total costs. When total costs and total revenues are equal, the business organization is said to be breaking even. The analysis is based on a set of linear equations for a straight line and the separation of variable and fixed costs.

Total variable costs are considered to be those costs that vary as the production volume changes. In a factory, production volume is considered to be the number of units produced, but in a governmental organization with no assembly process, the units produced might refer, for example, to the number of welfare cases processed. There are a number of costs that vary or change, but if the variation is not due to volume changes, it is not considered to be a variable cost. Examples of variable costs are direct materials and direct labor. Total fixed costs do not vary as volume levels change within the relevant range. Examples of fixed costs are straight-line depreciation and annual insurance charges. Total variable costs can be viewed as a 45° line and total fixed costs as a straight line. In the break-even chart shown in Figure 1, the upward slope of line DFC represents the change in variable costs. Variable costs sit on top of fixed costs, line DE. Point F represents the breakeven point. This is where the total cost (costs below the line DFC) crosses and is equal to total revenues (line AFB).

All the lines in the chart are straight lines: linearity is an underlying assumption of CVP analysis. Although no one can be certain that costs are linear over the entire range of output or production, this is an assumption of CVP. To help alleviate the limitations of this assumption, it is also assumed that the linear relationships hold only within the relevant range of production. The relevant range is represented by the high and low output points that have been previously reached with past production. CVP analysis is best viewed within the relevant range, that is, within our previous actual experience. Outside of that range, costs may vary in a nonlinear manner. The straight-line equation for total cost is:
Total cost = total fixed cost + total variable cost

Total variable cost is calculated by multiplying the cost of a unit, which remains constant on a per-unit basis, by the number of units produced. Therefore the total cost equation could be expanded as:
Total cost = total fixed cost + (variable cost per unit × number of units)

Total fixed costs do not change.

A final version of the equation is:
Y = a + bx

In this equation, a is the fixed cost, b is the variable cost per unit, x is the level of activity, and Y is the total cost. Assume that the fixed costs are $5,000, the volume of units produced is 1,000, and the per-unit variable cost is $2. In that case the total cost would be computed as follows:
Y = $5,000 + ($2 × 1,000) Y = $7,000

It can be seen that it is important to separate variable and fixed costs. Another reason it is important to separate these costs is because variable costs are used to determine the contribution margin, and the contribution margin is used to determine the break-even point. The contribution margin is the difference between the per-unit variable cost and the selling price per unit. For example, if the per-unit variable cost is $15 and selling price per unit is $20, then the contribution margin is equal to $5. The contribution margin may provide a $5 contribution toward the reduction of fixed costs or a $5 contribution to profits. If the business is operating at a volume above the break-even point volume (above point F), then the $5 is a contribution (on a per-unit basis) to additional profits. If the business is operating at a volume below the break-even point

(below point F), then the $5 provides for a reduction in fixed costs and continues to do so until the break-even point is passed.

Once the contribution margin is determined, it can be used to calculate the break-even point in volume of units or in total sales dollars. When a per-unit contribution margin occurs below a firm's break-even point, it is a contribution to the reduction of fixed costs. Therefore, it is logical to divide fixed costs by the contribution margin to determine how many units must be produced to reach the break-even point:

Assume that the contribution margin is the same as in the previous example, $5. In this example, assume that the total fixed costs are increased to $8,000. Using the equation, we determine that the break-even point in units:

In Figure 1, the break-even point is shown as a vertical line from the x-axis to point F. Now, if we want to determine the break-even point in total sales dollars (total revenue), we could multiply 1600 units by the assumed selling price of $20 and arrive at $32,000. Or we could use another equation to compute the break-even point in total sales directly. In that case, we would first have to compute the contribution margin ratio. This ratio is determined by dividing the contribution margin by selling price. Referring to our example, the calculation of the ratio involves two steps:

Going back to the break-even equation and replacing the per-unit contribution margin with the contribution margin ratio results in the following formula and calculation:

Figure 1 shows this break-even point, at $32,000 in sales, as a horizontal line from point F to the y-axis. Total sales at the break-even point are illustrated on the y-axis and total units on the x-axis. Also notice that the losses are represented by the DFA triangle and profits in the FBC triangle.

The financial information required for CVP analysis is for internal use and is usually available only to managers inside the firm; information about variable and fixed costs is not available to the general public. CVP analysis is good as a general guide for one product within the relevant range. If the company has more than one product, then the contribution margins from all products must be averaged together. But, any cost-averaging process reduces the level of accuracy as compared to working with cost data from a single product. Furthermore, some organizations, such as nonprofit organizations, do not incur a significant level of variable costs. In these cases, standard CVP assumptions can lead to misleading results and decisions.