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Cost-Volume-Profit Analysis CHAPTER revenues and total costs behave. If decisions can Cost-Volume-Profit be significantly improved, managers should 3 Analysis choose a more complex approach that, for example, uses multiple cost drivers and nonlinear cost functions. Overview 3. Because managers want to avoid operating This chapter explains a planning tool called cost- losses, they are interested in the breakeven point volume-profit (CVP) analysis. CVP analysis calculated using CVP analysis. The breakeven examines the behavior of total revenues, total point is the quantity of output sold at which total costs, and operating income (profit) as changes revenues equal total costs. There is neither a profit occur in the output level, selling price, variable nor a loss at the breakeven point. To illustrate, cost per unit, and/or fixed costs of a product or assume a company sells 2,000 units of its only service. The reliability of the results from CVP product for $50 per unit, variable cost is $20 per analysis depends on the reasonableness of the unit, and fixed costs are $60,000 per month. Given assumptions. The Appendix to the chapter gives these conditions, the company is operating at the additional insights about CVP analysis; it breakeven point: illustrates decision models and uncertainty. Revenues, 2,000 × $50 $100,000 Review Points Deduct: Variable costs, 2,000 × $20 40,000 1. CVP analysis is based on several Fixed costs 60,000 assumptions including: Operating income $ -0- a. Changes in the level of revenues and costs arise only because of changes in the number The breakeven point can be expressed two ways: of product (or service) units produced and 2,000 units and $100,000 of revenues. sold (that is, the number of output units is the only driver of revenues and costs). 4. Under CVP analysis, the income b. Total costs can be separated into a fixed statement above is reformatted to show a key line component that does not vary with the output item, contribution margin: level and a component that is variable with respect to the output level. Revenues, 2,000 × $50 $100,000 c. When represented graphically, the behaviors Variable costs, 2,000 × $20 40,000 Contribution margin 60,000 of both total revenues and total costs are linear Fixed costs 60,000 (straight lines) in relation to the output level Operating income $ -0- within the relevant range (and time period). d. The analysis either covers a single product or This format, called the contribution income assumes that the proportion of different statement, is used extensively in this chapter and products when multiple products are sold will throughout the textbook. remain constant as the level of total units sold changes. 5. Contribution margin can be expressed three ways: in total, on a per unit basis, and as a 2. Even though CVP assumptions simplify percentage of revenues. In our example, total real-world situations, many companies have found contribution margin is $60,000. Contribution CVP relationships can be helpful in making margin per unit is the difference between selling decisions about strategic and long-range planning, price and variable cost per unit: $50 − $20 = $30. as well as decisions about product features and Contribution margin per unit is also equal to pricing. Managers, however, must always assess contribution margin divided by the number of whether the simplified CVP relationships generate units sold: $60,000 ÷ 2,000 = $30. Contribution sufficiently accurate predictions of how total margin percentage (also called contribution COST-VOLUME-PROFIT ANALYSIS 23 margin ratio) is contribution margin per unit point because no income taxes arise if operating divided by selling price: $30 ÷ $50 = 60%; it is income is $0. also equal to contribution margin divided by revenues: $60,000 ÷ $100,000 = 60%. This 8. Managers use CVP analysis to guide their contribution margin percentage means that 60 decisions, many of which are strategic decisions. cents in contribution margin is gained for each $1 For example, CVP analysis helps managers decide of revenues. how much to spend on advertising, whether or not to expand into new markets, and which features to 6. In our example, compute the breakeven add to existing products. Of course, different point (BEP) in units and in revenues as follows: choices can affect fixed costs, variable cost per unit, selling prices, units sold, and operating Total fixed costs income. BEP units = Contribution margin per unit $60,000 9. Single-number “best estimates” of input BEP units = = 2,000 units $30 data for CVP analysis are subject to varying Total fixed costs degrees of uncertainty, the possibility that an BEP revenues = Contribution margin percentage actual amount will deviate from an expected $60,000 amount. One approach to deal with uncertainty is BEP revenues = = $100,000 0.60 to use sensitivity analysis (discussed in paragraphs 10 through 12). Another approach is to compute While the breakeven point is often of interest to expected values using probability distributions managers, CVP analysis considers a broader (discussed in paragraph 19). question: What amount of sales in units or in revenues is needed to achieve a specified target 10. Sensitivity analysis is a “what if” operating income? The answer is easily obtained technique that managers use to examine how an by adding target operating income to total fixed outcome will change if the original predicted data costs in the numerator of the formulas above. are not achieved or if an underlying assumption Assuming target operating income (TOI) is changes. In the context of CVP analysis, $15,000: sensitivity analysis examines how operating income (or the breakeven point) changes if the $60,000 + $15,000 predicted data for selling price, variable cost per Unit sales to = = 2,500 units achieve TOI $30 unit, fixed costs, or units sold are not achieved. The sensitivity to various possible outcomes $60,000 + $15,000 broadens managers’ perspectives as to what might Revenues to = = $125,000 achieve TOI 0.60 actually occur before they make cost commitments. Electronic spreadsheets, such as 7. Because for-profit organizations are Excel, enable managers to conduct CVP-based subject to income taxes, their CVP analyses must sensitivity analyses in a systematic and efficient include this factor. For example, if a company way. earns $50,000 before income taxes and the tax rate is 40%, then: 11. An aspect of sensitivity analysis is margin of safety, the amount by which budgeted Operating income $50,000 (or actual) revenues exceed breakeven revenues. Deduct income taxes (40%) 20,000 The margin of safety answers the “what-if” Net income $30,000 question: If budgeted revenues are above breakeven and drop, how far can they fall below To state a target net income figure in terms of the budget before the breakeven point is reached? operating income, divide target net income by 1 − tax rate: $30,000 ÷ (1 − .40) = $50,000. Note, the 12. CVP-based sensitivity analysis highlights income-tax factor does not change the breakeven the risks and returns that an existing cost structure 24 CHAPTER 3 holds for a company. This insight may lead managers to consider alternative cost structures. 15. Recall from paragraph 1d that, in multiple For example, compensating a salesperson on the product situations, CVP analysis assumes a given basis of a sales commission (a variable cost) rather sales mix of products remains constant as the level than a salary (a fixed cost) decreases the of total units sold changes. In this case, the company’s downside risk if demand is low but breakeven point is some number of units of each decreases its return if demand is high. The risk- product, depending on the sales mix. To illustrate, return tradeoff across alternative cost structures assume a company sells two products, A and B. can be measured as operating leverage. Operating The sales mix is 4 units of A and 3 units of B. The leverage describes the effects that fixed costs have contribution margins per unit are $80 for A and on changes in operating income as changes occur $40 for B. Fixed costs are $308,000 per month. To in units sold and hence in contribution margin. compute the breakeven point: Companies with a high proportion of fixed costs in their cost structures have high operating leverage. Let 4X = No. of units of A to break even Consequently, small changes in units sold cause Then 3X = No. of units of B to break even large changes in operating income. At any given $308,000 BEP in X units = level of sales: 4($80) + 3($40) $308,000 BEP in X units = = 700 units Contribution margin $440 Degree of operating leverage = A units to break even = 4 × 700 = 2,800 units Operating income B units to break even = 3 × 700 = 2,100 units Proof of breakeven point: Knowing the degree of operating leverage at a A: 2,800 × $80 $224,000 given level of sales helps managers calculate the B: 2,100 × $40 84,000 effect of changes in sales on operating income. Total contribution margin 308,000 Fixed costs 308,000 13. The time horizon being considered for a Operating income $ -0- decision affects the classification of costs as variable or fixed. The shorter the time horizon, the 16. CVP analysis can be applied to service greater the proportion of total costs that are fixed. organizations and nonprofit organizations. The For example, virtually all the costs of an airline key is measuring their output. Unlike flight are fixed one hour before takeoff. When the manufacturing and merchandising companies that time horizon is lengthened to one year and then measure their output in units of product, the five years, more and more costs become variable.
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