# Cost-Volume-Profit Analysis

## Cost-Volume-Profit Analysis (Encyclopedia of Business and Finance)

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

where 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 in creased 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.

## Cost-Volume-Profit Analysis (Encyclopedia of Management)

Cost-volume-profit (CVP) analysis expands the use of information provided by breakeven analysis. A critical part of CVP analysis is the point where total revenues equal total costs (both fixed and variable costs). At this breakeven point (BEP), a company will experience no income or loss. This BEP can be an initial examination that precedes more detailed CVP analyses.

Cost-volume-profit analysis employs the same basic assumptions as in breakeven analysis. The assumptions underlying CVP analysis are:

1. The behavior of both costs and revenues in linear throughout the relevant range of activity. (This assumption precludes the concept of volume discounts on either purchased materials or sales.)
2. Costs can be classified accurately as either fixed or variable.
3. Changes in activity are the only factors that affect costs.
4. All units produced are sold (there is no ending finished goods inventory).
5. When a company sells more than one type of product, the sales mix (the ratio of each product to total sales) will remain constant.
Figure 1
Cost-Volume-Profit Analysis, Production = Sales

In the following discussion, only one product will be assumed. Finding the breakeven point is the initial step in CVP, since it is critical to know whether sales at a given level will at least cover the relevant costs. The breakeven point can be determined with a mathematical equation, using contribution margin, or from a CVP graph. Begin by observing the CVP graph in Figure 1, where the number of units produced equals the number of units sold. This figure illustrates the basic CVP case. Total revenues are zero when output is zero, but grow linearly with each unit sold. However, total costs have a positive base even at zero output, because fixed costs will be incurred even if no units are produced. Such costs may include dedicated equipment or other components of fixed costs. It is important to remember that fixed costs include costs of every kind, including fixed sales salaries, fixed office rent, and fixed equipment depreciation of all types. Variable costs also include all types of variable costs: selling, administrative, and production. Sometimes, the focus is on production to the point where it is easy to overlook that all costs must be classified as either fixed or variable, not merely product costs.

Where the total revenue line intersects the total costs line, breakeven occurs. By drawing a vertical line from this point to the units of output (X) axis, one can determine the number of units to break even. A horizontal line drawn from the intersection to the dollars (Y) axis would reveal the total revenues and total costs at the breakeven point. For units sold above the breakeven point, the total revenue line continues to climb above the total cost line and the company enjoys a profit. For units sold below the breakeven point, the company suffers a loss.

Illustrating the use of a mathematical equation to calculate the BEP requires the assumption of representative numbers. Assume that a company has total annual fixed cost of \$480,000 and that variable costs of all kinds are found to be \$6 per unit. If each unit sells for \$10, then each unit exceeds the specific variable costs that it causes by \$4. This \$4 amount is known as the unit contribution margin. This means that each unit sold contributes \$4 to cover the fixed costs. In this intuitive example, 120,000 units must be produced and sold in order to break even. To express this in a mathematical equation, consider the following abbreviated income statement:
Unit Sales = Total Variable Costs + Total Fixed Costs + Net Income
Inserting the assumed numbers and letting X equal the number of units to break even:
\$10.00X = \$6.00X + \$480,000 + 0

Note that net income is set at zero, the breakeven point. Solving this algebraically provides the same intuitive answer as above, and also the shortcut formula for the contribution margin technique:
Fixed Costs ÷ Unit Contribution Margin = Breakeven Point in Units
\$480,000 ÷ \$4.00 = 120,000 units

If the breakeven point in sales dollars is desired, use of the contribution margin ratio is helpful. The contribution margin ratio can be calculated as follows:
Unit Contribution Margin ÷ Unit Sales Price = Contribution Margin Ratio
\$4.00 ÷ \$10.00 = 40%

To determine the breakeven point in sales dollars, use the following mathematical equation:
Total Fixed Costs ÷ Contribution Margin Ratio = Breakeven Point in Sales Dollars
\$480,000 ÷ 40% = \$1,200,000

The margin of safety is the amount by which the actual level of sales exceeds the breakeven level of sales. This can be expressed in units of output or in dollars. For example, if sales are expected to be 121,000 units, the margin of safety is 1,000 units over breakeven, or \$4,000 in profits before tax.

A useful extension of knowing breakeven data is the prediction of target income. If a company with the cost structure described above wishes to earn a target income of \$100,000 before taxes, consider the condensed income statement below. Let X = the number of units to be sold to produce the desired target income:
Target Net Income = Required Sales Dollars Variable Costs Fixed Costs
\$100,000 = \$10.00X \$6.00X \$480,000

Solving the above equation finds that 145,000 units must be produced and sold in order for the company to earn a target net income of \$100,000 before considering the effect of income taxes.

A manager must ensure that profitability is within the realm of possibility for the company, given its level of capacity. If the company has the ability to produce 100 units in an 8-hour shift, but the breakeven point for the year occurs at 120,000 units, then it appears impossible for the company to profit from this product. At best, they can produce 109,500 units, working three 8-hour shifts, 365 days per year (3 X 100 X 365). Before abandoning the product, the manager should investigate several strategies:

1. Examine the pricing of the product. Customers may be willing to pay more than the price assumed in the CVP analysis. However, this option may not be available in a highly competitive market.
2. If there are multiple products, then examine the allocation of fixed costs for reasonableness. If some of the assigned costs would be incurred even in the absence of this product, it may be reasonable to reconsider the product without including such costs.
3. Variable material costs may be reduced through contractual volume purchases per year.
4. Other variable costs (e.g., labor and utilities) may improve by changing the process. Changing the process may decrease variable costs, but increase fixed costs. For example, state-of-the-art technology may process units at a lower per-unit cost, but the fixed cost (typically, depreciation expense) can offset this advantage. Flexible analyses that explore more than one type of process are particularly useful in justifying capital budgeting decisions. Spreadsheets have long been used to facilitate such decision-making.

One of the most essential assumptions of CVP is that if a unit is produced in a given year, it will be sold in that year. Unsold units distort the analysis. Figure 2 illustrates this problem, as incremental revenues cease while costs continue. The profit area is bounded, as units are stored for future sale.

Unsold production is carried on the books as finished goods inventory. From a financial statement perspective, the costs of production on these units are deferred into the next year by being reclassified as assets. The risk is that these units will not be salable in the next year due to obsolescence or deterioration.

Figure 2
Cost-Volume-Profit Analysis, Production > Sales

While the assumptions employ determinate estimates of costs, historical data can be used to develop appropriate probability distributions for stochastic analysis. The restaurant industry, for example, generally considers a 15 percent variation to be "accurate."

APPLICATIONS

While this type of analysis is typical for manufacturing firms, it also is appropriate for other types of industries. In addition to the restaurant industry, CVP has been used in decision-making for nuclear versus gas- or coal-fired energy generation. Some of the more important costs in the analysis are projected discount rates and increasing governmental regulation. At a more down-to-earth level is the prospective purchase of high quality compost for use on golf courses in the Carolinas. Greens managers tend to balk at the necessity of high (fixed) cost equipment necessary for uniform spreadability and maintenance, even if the (variable) cost of the compost is reasonable. Interestingly, one of the unacceptably high fixed costs of this compost is the smell, which is not adaptable to CVP analysis.

Even in the highly regulated banking industry, CVP has been useful in pricing decisions. The market for banking services is based on two primary categories. First is the price-sensitive group. In the 1990s leading banks tended to increase fees on small, otherwise unprofitable accounts. As smaller account holders have departed, operating costs for these banks have decreased due to fewer accounts; those that remain pay for their keep. The second category is the maturity-based group. Responses to changes in rates paid for certificates of deposit are inherently delayed by the maturity date. Important increases in fixed costs for banks include computer technology and the employment of skilled analysts to segment the markets for study.

Even entities without a profit goal find CVP useful. Governmental agencies use the analysis to determine the level of service appropriate for projected revenues. Nonprofit agencies, increasingly stipulating fees for service, can explore fee-pricing options; in many cases, the recipients are especially price-sensitive due to income or health concerns. The agency can use CVP to explore the options for efficient allocation of resources.

Project feasibility studies frequently use CVP as a preliminary analysis. Such major undertakings as real estate/construction ventures have used this technique to explore pricing, lender choice, and project scope options.

Cost-volume-profit analysis is a simple but flexible tool for exploring potential profit based on cost strategies and pricing decisions. While it may not provide detailed analysis, it can prevent "do-nothing" management paralysis by providing insight on an overview basis.

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