Break-Even Point and Cost-Volume-Profit Analysis

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1 9 Break-Even Point and Cost-Volume-Profit Analysis Objectives After completing this chapter, you should be able to answer the following questions: LO.1 LO.2 LO.3 LO.4 LO.5 LO.6 What is the break-even point (BEP) and why is it important? How is the BEP determined and what methods are used to identify BEP? What is cost-volume-profit (CVP) analysis and how do companies use CVP information in decision making? How do break-even and CVP analysis differ for single-product and multiproduct firms? How are margin of safety and operating leverage concepts used in business? What are the underlying assumptions of CVP analysis? ZTS/ISTOCKPHOTO.COM 381

2 382 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis Introduction Corporate managers have a goal of maximizing shareholder wealth. However, given that no obvious, single course of action leads to fulfillment of that goal, managers must choose a specific course of action and develop plans and controls to pursue that course. Because planning is future oriented, uncertainty exists and information helps reduce that uncertainty. Controlling is making actual performance align with plans, and information is necessary in that process. Much of the information managers use to plan and control reflects relationships among product cost, selling prices, and sales volumes. Changing one of these essential components in the mix will cause changes in other components. For example, a company manager would want to estimate whether an increase in advertising expenditures for a particular product would be justified by the increase in product sales volume and contribution margin that would be generated. This chapter focuses on understanding how cost, volume, and profit interact. Understanding these relationships helps in predicting future conditions (planning) as well as in explaining, evaluating, and acting on results (controlling). Before generating profit, a company must first reach its break-even point, which means that it must generate sufficient sales revenue to cover all cost. Then, by linking cost behavior and sales volume, managers can use the cost-volume-profit model to plan and control. The chapter also presents the concepts of margin of safety and degree of operating leverage. Information provided by these models helps managers focus on the implications that volume changes would have on organizational profitability. LO.1 What is the breakeven point (BEP) and why is it important? Break-Even Point As discussed in Chapter 3, absorption costing is the traditional approach to product costing and is primarily used for external reporting. Alternatively, variable costing is more commonly used for internal purposes because it makes cost behavior more transparent than does absorption costing. The variable costing presentation separates variable from fixed cost and facilitates the use of this chapter s models: break-even point, cost-volume-profit, margin of safety, and degree of operating leverage. A variable costing budgeted income statement for Sesame Company is presented in Exhibit 9 1. Sesame Company manufactures a high-quality line of desk clocks. Product specifications have been established for several years and will continue at least until model year In addition to the traditional income statement information, perunit amounts are shown for sales revenue, variable cost, and contribution margin. The company has a total variable production cost of 62.5 percent, a variable selling expense of 10 percent, and a contribution margin ratio of 27.5 percent. These Sesame Company data are used throughout this chapter to illustrate break-even and cost-volume-profit computations. A company s break-even point (BEP) is that level of activity, in units or dollars, at which total revenue equal total cost. Thus, at BEP, the company generates neither a profit nor a loss on operating activities. Companies, however, do not wish merely to break even on operations. The BEP is calculated to establish a point of reference. Knowing BEP, managers are better able to set sales goals that should result in profits from operations rather than losses. Finding the BEP first requires understanding company revenues and cost. A short summary of revenue and cost assumptions is presented at this point to provide a foundation for BEP calculation and cost-volume-profit (CVP) analysis. These assumptions, and some challenges to them, are discussed in more detail at the end of the chapter.

3 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 383 Exhibit 9 1 Sesame Company Budgeted Income Statement for 2010 Total Per Unit Percentage Sales (600,000 units) $24,000,000 $ Variable cost Production $15,000,000 $ Selling 2,400, Total variable cost (17,400,000) (29.00) (72.5) Contribution margin $ 6,600,000 $ Fixed cost Production $ 3,200,000 Selling and administrative 1,200,000 Total fixed cost (4,400,000) Income before income tax $ 2,200,000 Relevant range: The company is assumed to be operating within the relevant range of activity specified in determining the revenue and cost information used in each of the following assumptions. 1 Revenue: Revenue per unit is assumed to remain constant; fluctuations in per-unit revenue for factors such as quantity discounts are ignored. Thus, total revenue fluctuates in direct proportion to level of activity or volume. Variable cost: On a per-unit basis, variable costs are assumed to remain constant. Therefore, total variable cost fluctuates in direct proportion to level of activity or volume. Variable production costs include direct material, direct labor, and variable overhead; variable selling costs include charges for items such as commissions and shipping. Variable administrative costs can exist in areas such as purchasing; however, in the illustrations that follow, administrative costs are assumed to be fixed. Fixed cost: Total fixed costs are assumed to remain constant, and, as such, per-unit fixed cost decreases as volume increases. (Per-unit fixed cost increases as volume decreases.) Fixed costs include both fixed manufacturing overhead and fixed selling and administrative expenses. Mixed cost: Mixed costs are separated into their variable and fixed elements before they are used in BEP or CVP analysis. Any method (such as regression analysis or the high low method) that validly separates these costs in relation to one or more predictors can be used. An important measure in break-even analysis is contribution margin (CM), which can be defined on either a per-unit or a total basis. CM per unit equals selling price per unit minus total variable cost per unit, which includes production, selling, and administrative cost. Unit contribution margin is constant because revenue and variable cost have been defined as being constant per unit. Total CM is the difference between total revenue and total variable cost for all units sold. This amount fluctuates in direct proportion to sales volume. On either a per-unit or a total basis, CM indicates the amount of revenue remaining after all variable costs have been covered. 2 This amount contributes to the coverage of fixed cost and the generation of profit. 1 As discussed in Chapter 2, the relevant range is the range of activity over which a variable cost will remain constant per unit and a fixed cost will remain constant in total. 2 Contribution margin refers to the total contribution margin. Product contribution margin is the difference between revenues and total variable product cost included in cost of goods sold.

4 384 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis LO.2 How is the BEP determined and what methods are used to identify BEP? Identifying the Break-Even Point Break-even calculations can be demonstrated using the formula, graph, and income statement approaches. Data needed to compute the break-even point and perform CVP analysis are given in the income statement shown in Exhibit 9 1 for Sesame Company. Formula Approach to Breakeven The formula approach to break-even analysis uses an algebraic equation to calculate the BEP. In this analysis, sales volume, rather than production activity, is the focus of the relevant range. The equation represents the variable costing income statement and shows the relationships among revenue, fixed cost, variable cost, volume, and profit as follows: R(X) VC(X) FC P where R revenue (selling price) per unit X volume (number of units) R(X) total revenue VC variable cost per unit VC(X) total variable cost FC total fixed cost P total profit Because this equation is simply a formulaic representation of an income statement, P can be set equal to zero to solve for the break-even point. At the point where P $0, total revenues are equal to total cost, and break-even point (BEP) in units can be found by solving the equation for X. R(X) VC(X) FC $0 R(X) VC(X) FC (R VC)(X) FC X FC (R VC) X FC CM Break-even volume equals total fixed cost divided by contribution margin per unit (revenue per unit minus the variable cost per unit). Using the information in Exhibit 9 1 for Sesame Company ($40 selling price per clock, $29 variable cost per clock, and $4,400,000 of total fixed cost), the BEP for the company is calculated as $40(X) $29(X) $4,400,000 $0 $40(X) $29(X) $4,400,000 $11(X) $4,400,000 X $4,400,000 $11 X 400,000 clocks BEP can be expressed in either units or dollars of revenue. One way to convert a unit BEP to dollars is to multiply the number of units by the selling price per unit. For Sesame, the BEP in sales dollars is $16,000,000 (400,000 clocks $40 per clock). Another method of computing BEP in sales dollars requires the computation of a contribution margin ratio (CM%), which is calculated as contribution margin divided by revenue. This ratio indicates what proportion of revenue remains after variable cost has been deducted from sales or that portion of the revenue dollar that can be used to cover fixed cost and provide profit. The CM% can be calculated using either per-unit, or total, revenue and variable cost information. Dividing total fixed cost by the CM% gives the BEP in sales dollars.

5 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 385 For Sesame Company, the break-even sales dollars are X FC [(R VC) R] X $4,400,000 [($40 $29) $40] X $4,400,000 ($11 $40) X $4,400, X $16,000,000 BEP in units can be determined by dividing the BEP in sales dollars by the unit selling price, or X = $16,000,000 $40 X = 400,000 clocks The CM% allows the BEP to be determined even if unit selling price and unit variable cost are not known. Subtracting the contribution margin ratio from 100 percent gives the variable cost ratio (VC%), which represents variable cost as a proportion of revenue. 3 Graphing Approach to Breakeven Although solutions to BEP problems can be determined using equations, sometimes the information is more effectively conveyed to managers in a visual format. Exhibit 9 2 (p. 386) graphically presents each income statement item for Sesame Company s original budgeted data (see Exhibit 9 1), providing visual representations of revenue, cost, and contribution margin behaviors. The graphs presented in Exhibit 9 2 illustrate individual behaviors, but are not very useful for determining the relationships among the income statement amounts. A breakeven chart can be prepared to graph the relationships among revenue, volume, and cost. The BEP on a break-even chart is located at the point where the total cost and total revenue lines intersect. Two approaches to graphing can be used in preparing break-even charts: the traditional approach and the profit-volume graph approach. Traditional Approach The traditional approach break-even graph shows the relationships among revenue, cost, and profit/loss. This graph does not show contribution margin. A traditional break-even graph for Sesame Company is prepared by completing the following steps. Step 1: As shown in Exhibit 9 3 (p. 386), label each axis and graph the total cost and fixed cost lines. The fixed cost line is drawn parallel to the x-axis (volume). The variable cost line begins where the fixed cost line intersects the y-axis. The slope of the variable cost line is the per-unit variable cost ($29). The resulting line represents total cost. The distance between the fixed cost and the total cost lines represents total variable cost at each activity level. Step 2: Chart the revenue line, beginning at $0. The BEP is located at the intersection of the revenue line and the total cost line. The vertical distance to the right of the BEP and between the revenue and total cost lines represents profit; the distance between the revenue and total cost lines to the left of the BEP represents loss. If exact readings could be taken on the graph in Exhibit 9 4 (p. 387), the break-even point for Sesame Company would be $16,000,000 of sales, or 400,000 clocks. 3 Derivation of the contribution margin ratio formula is as follows: Sales [(VC%)(Sales)] FC (1 VC%)Sales FC Sales FC (1 VC%) because (1 VC%) CM% then Sales FC CM% where VC% variable cost ratio or variable cost as a percentage of sales, CM% contribution margin ratio or contribution margin as a percentage of sales Thus, the VC% plus the CM% is equal to 100 percent.

6 386 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis Exhibit 9 2 Sesame Company Graphing Presentation of Income Statement Items 20,000,000 Relevant Range Relevant Range 16,000,000 TR Revenue (in $) 12,000,000 Variable Cost (in $) 14,500,000 11,600,000 8,700,000 TVC 300, , ,000 Number of Clocks 300, , ,000 Number of Clocks Contribution Margin (in $) 5,500,000 4,400,000 3,300,000 Relevant Range TR TCM TVC Fixed Cost (in $) 4,400,000 Relevant Range TFC 300, , ,000 Number of Clocks 300, , ,000 Number of Clocks TR Total Revenue TCM Total Contribution Margin TVC Total Variable Cost TFC Total Fixed Cost Note: Linear functions are always assumed for total revenue, total variable cost, and total fixed cost. These functions are reflected in the basic assumptions given on pp Exhibit 9 3 Sesame Company Graph of Total and Variable Cost $18,900,000 Total Cost Cost $4,400,000 Total Fixed Cost 0 300,000 Number of Clocks 500,000

7 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 387 Exhibit 9 4 Sesame Company Traditional Approach of Graphing Breakeven $20,000,000 Contribution Margin Area Total Revenue Total Cost Total Variable Cost $16,000,000 $4,400, ,000 Number of Clocks 500,000 Profit-Volume Graph The profit-volume (PV) graph provides a depiction of the amount of profit or loss associated with each sales level. The horizontal, or x, axis on the PV graph represents sales volume; the vertical, or y, axis represents dollars of profit or loss. Amounts shown above the x-axis are positive and represent profits; amounts shown below the x-axis are negative and represent losses. Two points can be located on the graph: total fixed cost and break-even point. Total fixed cost is shown on the y-axis below the sales volume line as a negative amount. If no products were sold, the fixed cost would still be incurred and a loss of that amount would result. Location of the BEP in units may be determined algebraically and is shown at the point where the profit line intersects the x-axis; at that point, there is no profit or loss. The amount of profit or loss for any sales volume can be read from the y-axis. The slope of the profit (diagonal) line is determined by the unit contribution margin ($11), and the points on the line represent the contribution margin earned at each volume level. The line shows that no profit is earned until total contribution margin covers total fixed cost. The PV graph for Sesame Company is shown in Exhibit 9 5 (p. 388). Total fixed cost is $4,400,000, and the break-even point is 400,000 clocks. The diagonal line reflects the original Exhibit 9 1 income statement data indicating a profit of $2,200,000 at a sales volume of 600,000 clocks. Clocks sold at BEP 400,000 Sales $ 16,000,000 Total variable cost (11,600,000) Contribution margin $ 4,400,000 Total fixed cost (4,400,000) Profit before tax $ 0

8 388 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis Exhibit 9 5 Sesame Company Profit-Volume Graph $4,400,000 $3,300,000 Profit/Loss $2,200,000 $1,100,000 0 $1,100,000 $2,200,000 $3,300,000 $4,400,000 PROFIT BEP LOSS Number of Clocks (in thousands) Total Fixed Cost The graphing approach to breakeven provides a detailed visual display of the BEP. It does not, however, provide a precise solution because exact points cannot be determined on a graph. A definitive computation of the BEP can be found algebraically using the formula approach or a computer software application. A third approach to illustrating breakeven is the income statement approach. Income Statement Approach LO.3 What is costvolume-profit (CVP) analysis and how do companies use CVP information in decision making? The income statement approach to finding BEP allows accountants to prepare budgeted statements using available revenue and cost information. Income statements can also be used to prove the accuracy of computations made using the BEP formulas or graphs. Because the formula, graphing, and income statement approaches are based on the same relationships, each should align with the other. Following is the income statement proving the prior calculations of the BEP for Sesame Company. Because the profit before tax is $0, the income statement supports the break-even point determinations of the other methods. The BEP provides a starting point for planning future operations. Managers want to earn operating profit rather than simply cover costs. Substituting an amount other than zero for the profit (P) term in the break-even formula converts break-even analysis to cost-volume-profit analysis. CVP Analysis Because profit cannot be achieved until the BEP is reached, the starting point of CVP analysis is the break-even point. Examining shifts in cost and volume and the resulting effects on profits is called cost-volume-profit (CVP) analysis. CVP analysis can be used to calculate the sales volume necessary to achieve a target profit, stated as either a fixed or variable amount on a before- or after-tax basis. Managers use CVP analysis to effectively plan and control by concentrating on the relationships among revenues, cost, volume changes, taxes, and profit. The CVP model can be expressed mathematically or graphically. The CVP model considers all costs, regardless of whether they are product, period, variable, or fixed. The analysis is usually performed on a

9 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 389 companywide basis. The same basic CVP model and calculations can be applied to a single- or multiproduct business. CVP analysis requires substitution of known amounts in the formula to solve for an unknown amount. The formula mirrors the income statement when known amounts are used for selling price per unit, variable cost per unit, volume of units, and fixed cost to find the amount of profit generated under given conditions. Because CVP analysis is concerned with relationships among the elements affecting continuing operations, in contrast with nonrecurring activities and events, profits as used in this chapter refer to operating profits before extraordinary and other nonoperating, nonrecurring items. The following quote indicates the pervasive utility of the CVP model: Cost Volume Profit analysis (CVP) is one of the most hallowed, and yet one of the simplest, analytical tools in management accounting. [CVP] allows managers to examine the possible impacts of a wide range of strategic decisions [in] such crucial areas as pricing policies, product mixes, market expansions or contractions, outsourcing contracts, idle plant usage, discretionary expense planning, and a variety of other important considerations in the planning process. Given the broad range of contexts in which CVP can be used, the basic simplicity of CVP is quite remarkable. Armed with just three inputs of data sales price, variable cost per unit, and fixed cost a managerial analyst can evaluate the effects of decisions that potentially alter the basic nature of a firm. 4 CORBIS/JUPITER IMAGES An important application of CVP analysis allows managers to set a desired target profit and focus on the relationships between it and other known income statement amounts to find an unknown. One common unknown in such applications is the sales volume that is needed to generate a particular profit amount. Selling price is generally not as commonly unknown as volume because selling price is often market determined and is not a management decision variable. Additionally, because selling price and volume are often directly related and because certain costs are considered fixed, managers can use CVP to determine how high variable cost can be while allowing the company to produce a desired amount of profit. Variable cost can be affected by modifying product specifications or material quality as well as by being more efficient or effective in the production, service, and/or distribution processes. The following examples continue using the Sesame Company data with different amounts of target profit. A product's selling price is often market-related rather than being a management decision variable. Fixed Amount of Profit Because contribution margin represents the sales dollars remaining after variable cost is covered, each dollar of CM generated by product sales goes first to cover fixed cost and then to produce profits. After the BEP is reached, each dollar of CM is a dollar of before-tax profit. Before Tax Profit can be treated in the break-even formula as an additional cost to be covered. Inclusion of a target profit changes the break-even formula to a CVP equation. 4 Flora Guidry, James O. Horrigan, and Cathy Craycraft, CVP Analysis: A New Look, Journal of Managerial Issues (Spring 1998), pp. 74ff.

10 390 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis R(X) VC(X) FC PBT where PBT fixed amount of profit before tax. R(X) VC(X) FC PBT X (FC PBT) (R VC) or X (FC PBT) CM Assume that Sesame s management desires a $3,300,000 before-tax profit. The calculations in Exhibit 9 6 show that to achieve this profit before tax, the company must sell 700,000 clocks and generate $28,000,000 of revenue. Exhibit 9 6 Sesame Company CVP Analysis Fixed Amount of Profit before Tax In units: Profit before tax (PBT) desired $3,300,000 R(X) VC(X) FC PBT CM(X) FC PBT ($40 $29)X $4,400,000 $3,300,000 $11X $7,700,000 X $7,700,000 $11 700,000 clocks In sales dollars: Sales (FC PBT) CM% Sales $7,700, * Sales $28,000,000 *From Exhibit 9 1. After Tax In choosing a target profit amount, managers must recognize that income tax represents a significant influence on business decision making. A company wanting a particular amount of profit after tax must first determine, given the applicable tax rate, the amount of profit that must be earned on a before-tax basis. The CVP formulas that designate a fixed after-tax profit amount are as follows: PBT [(TR)(PBT)] PAT and R(X) VC(X) FC [(TR)(PBT)] PAT where PBT fixed amount of profit before tax PAT fixed amount of profit after tax TR tax rate PAT is further defined so that it can be integrated into the original CVP formula: PBT (1 TR) PAT or PBT PAT (1 TR)

11 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 391 Substituting into the formula, R(X) VC(X) FC PBT R(X) VC(X) FC PBT (R VC)(X) FC [PAT (1 TR)] CM(X) FC [PAT (1 TR)] Assume Sesame Company managers set an earnings target of $3,300,000 after tax and the company s average tax rate is 25 percent. The number of clocks (800,000) and dollars of sales ($32,000,000) needed to achieve that target are calculated in Exhibit 9 7. Exhibit 9 7 Sesame Company CVP Analysis Fixed Amount of Profit after Tax In units: PAT desired $3,300,000; tax rate 25% PBT PAT (1 TR) PBT $3,300,000 (1 0.25) PBT $3,300, PBT $4,400,000 CM(X) FC PBT $11X $4,400,000 $4,400,000 $11X $8,800,000 X $8,800,000 $11 X 800,000 clocks In sales dollars: Sales (FC PBT) CM ratio Sales ($4,400,000 $4,400,000) Sales $8,800, Sales $32,000,000 Specific Amount of Profit per Unit Managers may want to conduct an analysis of profit on a per-unit basis. As in the prior examples, profit can be stated on either a before-tax or an after-tax basis. For these alternatives, the CVP formula must be adjusted to recognize that profit is related to volume of activity. Before Tax In this situation, the adjusted CVP formula for computing the necessary unit sales volume to earn a specified amount of profit before tax per unit is where P u BT amount of profit per unit before tax Solving for X (volume) gives the following: R(X) VC(X) FC P u BT(X) R(X) VC(X) P u BT(X) FC CM(X) P u BT(X) FC X FC (CM P u BT) The per-unit profit is treated in the CVP formula as if it were an additional variable cost to be covered. This treatment effectively adjusts the original contribution margin and

12 392 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis contribution margin ratio. When setting the desired profit as a percentage of selling price, the profit percentage cannot exceed the contribution margin ratio. If it does, an infeasible problem is created because the adjusted contribution margin is negative. In such a case, the variable cost ratio plus the desired profit percentage would exceed 100 percent of the selling price, and such a condition cannot exist. Assume that Sesame s president wants to know what level of sales (in clocks and dollars) would be required to earn a 15 percent before-tax profit on sales. This rate of return translates into a set amount of profit per unit of $6. The calculations shown in Exhibit 9 8 provide the answers to these questions. Exhibit 9 8 Sesame Company CVP Analysis Set Amount of Profit per Unit before Tax In units: P u BT desired 15% of sales revenue P u BT 0.15($40) P u BT $6 CM(X) P u BT(X) FC $11X $6X $4,400,000 $5X $4,400,000 X 880,000 clocks In sales dollars, the following relationships exist: Per Clock Percentage Selling price $ Variable cost (29) (72.5) Set amount of profit before tax (6) (15.0) Adjusted contribution margin ratio $ Sales FC Adjusted CM%* Sales $4,400, Sales $35,200,000 *It is not necessary to have per-unit data; all computations can be made with percentage information only. After Tax Adjusting the CVP formula to determine unit profit on an after-tax basis involves stating profit in relation to both the volume and the tax rate. Algebraically, the formula is: where P u AT amount of profit per unit after tax R(X) VC(X) FC {(TR)[P u BT(X)]} P u AT(X) P u AT is further defined so that it can be integrated into the original CVP formula: P u AT(X) P u BT(X) {(TR)[P u BT(X)]} P u AT(X) P u BT(X)[(1 TR)] P u BT(X) [P u AT (1 TR)](X)

13 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 393 Thus, the following relationship exists: R(X) VC(X) FC [P u AT (1 TR)](X) CM(X) FC P u BT(X) CM(X) P u BT(X) FC X FC (CM P u BT) Sesame s managers want to earn an after-tax profit of 10 percent of revenue and the company has a 25 percent tax rate. The necessary sales in units and dollars are given in Exhibit 9 9. Exhibit 9 9 Sesame Company CVP Analysis Set Amount of Profit per Unit after Tax In units: P u AT desired 10% of revenue; tax rate 25% P u AT 0.10($40) P u AT $4 P u BT $4 ( ) P u BT $ P u BT $5.33 (rounded) CM(X) P u BT(X) FC $11.00X $5.33X $4,400,000 $5.67X $4,400,000 X $4,400,000 $5.67 X 776,014 clocks (rounded) Per Clock Percentage Selling price $ Variable cost (29.00) (72.50) Set amount of profit before tax (5.33) (13.33) (rounded) Adjusted contribution margin $ Sales FC Adjusted CM ratio Sales $4,400, Sales $31,051,517 (rounded) Exhibit 9 10 (p. 394) proves each of the computations made in Exhibits 9 6 through 9 9 for Sesame Company. The answers provided by break-even or CVP analysis are valid only in relation to specific selling price and cost relationships. Changes that occur in the company s selling price or cost structure will cause a change in the BEP or in the sales needed to obtain a desired profit. However, the effects of revenue and cost changes on a company s BEP or sales volume can be determined through incremental analysis. Incremental Analysis for Short-Run Changes The break-even point can increase or decrease, depending on revenue and cost changes. Other things being equal, the BEP will increase if there is an increase in the total fixed cost or a decrease in the unit (or percentage) contribution margin. A decrease in contribution margin could arise because of a reduction in selling price, an increase in variable cost per

14 394 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis Exhibit 9 10 Sesame Company s Income Statement Approach to CVP Proof of Computations Previous computations: Break-even point: 400,000 clocks Fixed profit ($255,000) before tax: 700,000 clocks Fixed profit ($3,300,000) after tax: 800,000 clocks Set amount of profit (15% on revenues) before tax: 880,000 clocks Set amount of profit (10% on revenues) after tax: 776,014 clocks R $40 per clock; VC $29 per clock; FC $4,400,000 Tax rate 25% for Exhibits 9 3 and 9 5 Clocks Sold Basic Data 400,000 Exh ,000 Exh ,000 Exh ,000 Exh ,014 Sales $16,000,000 $28,000,000 $32,000,000 $35,200,000 $31,040,560 Total variable cost (11,600,000) (20,300,000) (23,200,000) (25,520,000) (22,504,406) Contribution margin $ 4,400,000 $ 7,700,000 $ 8,800,000 $ 9,680,000 $ 8,536,154 Total fixed cost (4,400,000) (4,400,000) (4,400,000) (4,400,000) (4,400,000) Profit before tax $ 0 $ 3,300,000 $ 4,400,000 $ 5,280,000 a $ 4,136,154 Tax (25%) (1,100,000) (1,034,039) Profit after tax (NI) $ 3,300,000 $ 3,102,115 b a Desired profit before tax 15% on revenue; 0.15 $35,200,000 $5,280,000. b Desired profit after tax 10% on revenue; 0.10 $31,040,560 $3,104,056 (differs from $3,102,115 only because of rounding error). unit, or a combination of the two. The BEP will decrease if total fixed cost decreases or unit (or percentage) contribution margin increases. A change in the BEP will also cause a shift in total profit or loss at any level of activity. Incremental analysis is a process that focuses only on factors that change from one course of action or decision to another. In CVP situations, incremental analysis is focused on changes occurring in revenue, cost, and/or volume. Following are some examples of changes that could occur in a company and the incremental computations that can be used to determine the effects of those changes on the BEP or on profit. In most situations, incremental analysis is sufficient to determine the feasibility of contemplated changes, and a complete income statement need not be prepared. The basic facts presented for Sesame Company in Exhibit 9 1 are continued. All of the following examples use before-tax information to simplify the computations. After-tax analysis would require the application of the (1 tax rate) adjustment to all profit figures. Case 1 Sesame Company wants to earn a before-tax profit of $2,750,000. How many clocks must the company sell to achieve that profit? The incremental analysis relative to this question addresses the number of clocks above the BEP that must be sold. Because each dollar of contribution margin after BEP is a dollar of profit, the incremental analysis focuses only on the profit desired: $2,750,000 $11 250,000 clocks above BEP

15 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 395 Because the BEP has already been computed as 400,000 clocks, the company must sell a total of 650,000 clocks. Case 2 Sesame Company estimates that spending an additional $425,000 on advertising will result in an additional 50,000 clocks being sold. Should the company incur this extra fixed cost? The contribution margin from the additional clocks must first cover the additional fixed cost before additional profits can be generated. Increase in contribution margin (50,000 clocks $11 CM per clock) $550,000 Increase in fixed cost (425,000) Net incremental benefit $125,000 Because there is a net incremental profit of $125,000, the company should undertake the advertising campaign. An alternative computation is to divide the additional fixed cost of $425,000 by the $11 contribution margin. The result indicates that 38,636 clocks (rounded) would be required to cover the additional cost. Because the company expects to sell 50,000 clocks, the remaining 11,364 clocks would produce $11 of profit per clock, or $125,004. Case 3 Sesame Company estimates that reducing a clock s selling price to $37.50 will result in an additional 90,000 clocks per year being sold. Should the company reduce the clock s selling price? Budgeted sales volume, given in Exhibit 9 1, is 600,000 clocks. If the selling price is reduced, the contribution margin per unit will decrease to $8.50 per clock ($37.50 SP $29.00 VC). Sales volume will increase to 690,000 clocks (600,000 90,000). Total new contribution margin (690,000 clocks $8.50 CM per clock) $5,865,000 Total fixed cost (unchanged) (4,400,000) New profit before tax $1,465,000 Current budgeted profit before tax (from Exhibit 9 1) (2,200,000) Net incremental loss $ (735,000) Because the reduction in sales price will cause profit to decrease by $735,000, Sesame Company should not reduce the clock s selling price. The company, however, might want to investigate the possibility that a reduction in price could, in the long run, increase demand to more than the additional 90,000 clocks per year and, thus, make the price reduction a profitable action. Case 4 Sesame Company has an opportunity to sell 100,000 clocks to a nonrecurring customer for $27 per clock. The clocks will be packaged and sold using the customer s own logo. Packaging cost will increase by $1 per clock, but the company will not incur any of the current variable selling cost. If Sesame accepts the job, it will pay a $30,000 commission to the salesperson calling on this customer. This sale will not interfere with budgeted sales and is within the company s relevant range of activity. Should Sesame make this sale? The new variable cost per clock is $26 ($25 total budgeted variable production cost $1 additional variable packaging cost $0 variable selling cost). The $27 selling price minus the

16 396 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis $26 new total variable cost provides a contribution margin of $1 per clock sold to the nonrecurring customer. Total additional contribution margin (100,000 clocks $1 CM per clock) $100,000 Additional fixed cost (commission) related to this sale (30,000) Net incremental benefit $ 70,000 The total CM generated by the sale more than covers the additional fixed cost. Thus, the sale produces incremental profit and, therefore, should be made. However, as with all proposals, this one should be evaluated on the basis of its long-range potential. Is the commission a one-time payment? Will the customer possibly return in future years to buy additional clocks? Will such sales affect regular business in the future? Is the sales price to the new customer a legal one? 5 If all of these questions can be answered yes, Sesame should seriously consider this opportunity. In addition, referral business by the new customer could also increase sales. The incremental approach is often used to evaluate alternative pricing strategies in economic downturns. In such stressful times, companies must confront the reality that they might be unable to sell a normal volume of goods at normal prices. With this understanding, companies can choose to maintain normal prices and sell a lower volume of goods or reduce prices and attempt to maintain market share and normal volume. LO.4 How do break-even and CVP analysis differ for single-product and multiproduct firms? CVP Analysis in a Multiproduct Environment Companies typically produce and sell a variety of products, some of which may be related (such as bats and baseballs or sheets, towels, and bedspreads). To perform CVP analysis in a multiproduct company, one must assume either that the product sales mix stays constant as total sales volume changes or that the average contribution margin ratio stays constant as total sales volume changes. The constant mix assumption can be referred to as the bag (or basket ) analogy. The analogy is that the sales mix represents a bag of products that are sold together. For example, when some product A is sold, set amounts of products B and C are also sold. Use of an assumed constant sales mix allows a weighted average contribution margin ratio to be computed for the bag of products being sold. Without the assumption of a constant sales mix, BEP cannot be calculated, nor can CVP analysis be used effectively. 6 In a multiproduct company, the CM% is weighted by the quantities of each product included in the bag. This weighting process means that the CM% of the product composing the largest proportion of the bag has the greatest impact on the average contribution margin of the product mix. Suppose that, because of the success of its desk clocks, Sesame management is considering the production of clock wall-mounting kits. The vice president of marketing estimates that, for every three clocks sold, the company will sell one clock wall-mounting kit. Therefore, the bag of products has a 3:1 product ratio. Sesame will incur an additional $514,000 in fixed plant asset cost (depreciation, insurance, and so forth) to support a higher relevant range of production. Exhibit 9 11 provides relevant company information and shows the break-even computations. Breakeven occurs at sales of 126,000 bags of product, which contain 378,000 clocks and 126,000 wall-mounting kits. 5 The Robinson-Patman Act addresses the legal ways in which companies can price their goods for sale to different purchasers. 6 After the constant percentage contribution margin in a multiproduct firm has been determined, all situations regarding profit points can be treated in the same manner as they were earlier in the chapter. One must remember, however, that the answers reflect the bag assumption.

17 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 397 Exhibit 9 11 Sesame Company CVP Analysis Multiple Products Clocks Clock Wall-Mounting Kits Product Cost Information (Percentage) (Percentage) Selling price $ $ Total variable cost (29) (72.5) (4) (40) Contribution margin $ $ 6 60 Total fixed cost (FC) $4,400,000 previous $514,000 additional $4,914,000 Clocks Clock Wall- Mounting Kits Total Percentage Number of products per bag 3 1 Revenue per product $40 $10 Total revenue per "bag" $120 $10 $ Variable cost per product (29) (4) Total variable cost per "bag" (87) (4) (91) (70) Contribution margin product $11 $ 6 Contribution margin "bag" $ 33 $ 6 $ BEP in units (where B number of "bags" of products) CM(B) FC $39B $4,914,000 B 126,000 bags Note: Each "bag" consists of 3 clocks and 1 clock wall-mounting kit; therefore, it will take 378,000 clocks and 126,000 clock wall-mounting kits to break even, assuming the constant 3:1 mix. BEP in sales dollars (where S$ sales dollars; CM% weighted average CM per "bag") S$ FC CM% S$ $4,914, S$ $16,380,000 Note: The break-even sales dollars also represent the assumed constant sales mix of $120 of clocks to $10 of clock wall-mounting kits to represent a 92.3% (rounded) to 7.7% (rounded) ratio. Thus, the company must have $15,120,000 ($16,380, %) in sales of clocks and $1,260,000 in sales of clock wall-mounting kits to break even. Proof of these computations using the income statement approach: Clocks Clock Wall-Mounting Kits Total Sales $15,120,000 $1,260,000 $16,380,000 Variable cost (10,962,000) (504,000) (11,466,000) Contribution margin $ 4,158,000 $ 756,000 $ 4,914,000 Fixed cost (4,914,000) Income before tax $ 0

18 398 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis Any shift in the product sales mix will change the weighted average CM% and BEP. If the sales mix shifts toward a product with a lower dollar contribution margin, the BEP will increase and profits will decrease unless there is a corresponding increase in total revenues. A shift toward higher dollar contribution margin products without a corresponding decrease in revenues will cause a lower BEP and increase profits. The financial results shown in Exhibit 9 12 indicate that a shift toward the product with the lower dollar contribution margin (clock wall-mounting kits) causes a higher BEP and lower profits. This exhibit assumes that Sesame sells 126,000 bags of product (the break-even level in Exhibit 9 11), but the mix was not in the exact proportions assumed in Exhibit Instead of a 3:1 ratio, the sales mix was 2.5 clocks to 1.5 clock wall-mounting kits. A loss of $315,000 resulted because Sesame sold a higher proportion of the clock wall-mounting kits, which have a lower unit contribution margin than the clocks. Exhibit 9 12 Sesame Company s Effects of Product Mix Shift Clocks Clock Wall- Mounting Kits Total Percentage Number of products per bag Revenue per product $40 $10 Total revenue per bag $ $15 $ Variable cost per product (29) (4) Total variable cost per bag (72.50) (6) (78.50) (68.3) Contribution margin product $11 $ 6 Contribution margin "bag" $ $ 9 $ BEP in units (where B number of bags of products) CM(B) FC $36.50B $4,914,000 B 134,631 bags (rounded up) Actual results: 126,000 bags with a sales mix ratio of 2.5 clocks to 1.5 clock wall-mounting kits; thus, the company sold 315,000 clocks and 189,000 clock wall-mounting kits. 315,000 Clocks 189,000 Clock Wall-Mounting Kits Total Sales $12,600,000 $1,890,000 $14,490,000 Variable cost (9,135,000) (756,000) (9,891,000) Contribution margin $ 3,465,000 $1,134,000 $ 4,599,000 Fixed cost (4,914,000) Net loss $ (315,000)

19 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 399 Managing Risk of CVP Relationships CVP relationships can be formally analyzed using standard metrics to evaluate risk/reward relationships at existing sales levels or prospective sales levels. Two of these metrics are margin of safety and degree of operating leverage. LO.5 How are margin of safety and operating leverage concepts used in business? Margin of Safety When making decisions about business opportunities and changes in sales mix, managers often consider the margin of safety (MS), which is the excess of budgeted or actual sales over break-even sales. The MS is the amount that sales can drop before reaching the BEP and, thus, provides a measure of the amount of cushion against losses. The MS can be expressed in units, in dollars, or as a percentage (MS%). The following formulas are applicable: Margin of safety in units Actual sales in units Break-even sales in units Margin of safety in $ Actual sales in $ Break-even sales in $ Margin of safety % Margin of safety in units Actual unit sales or MS% Margin of safety in $ Actual sales $ The BEP for Sesame based on the Exhibit 9 1 data is 400,000 units or $16,000,000 of sales. The company s budgeted income statement presented in Exhibit 9 1 shows sales for 2010 of $24,000,000 for 600,000 clocks. Sesame s MS is quite high because the company is operating far above its BEP (see Exhibit 9 13). Exhibit 9 13 Sesame Company s Margin of Safety In units: 600,000 actual 400,000 BEP 200,000 clocks In sales $: $24,000,000 actual sales $16,000,000 BEP sales $8,000,000 As a percentage: 200, , % or $8,000,000 $24,000, % MS calculations allow management to determine how close to a danger level the company is operating and, as such, provide an indication of risk. The lower the MS, the more carefully management must watch revenue and control cost to avoid operating losses. At low margins of safety, managers are less likely to take advantage of opportunities that, if incorrectly analyzed or forecasted, could send the company into a loss position. Operating Leverage Another measure that is closely related to the MS and provides useful management information is the company s degree of operating leverage. The relationship between a company s variable and fixed costs is reflected in its operating leverage. Typically, highly labor-intensive organizations have high variable cost and low fixed cost; these organizations have low operating leverage. (An exception to this rule is a sports team, which is highly labor intensive, but its labor cost is fixed rather than variable.)

20 400 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis Conversely, organizations that are highly capital intensive or automated have cost structures that include low variable and high fixed cost, providing high operating leverage. Because variable cost is low relative to selling price, the contribution margin is high. However, high fixed cost means that BEP also tends to be high. If the market predominantly sets selling prices, volume has the primary impact on profitability. As companies become more automated, they face this type of cost structure and become more dependent on volume increases to raise profits. Thus, a company s cost structure strongly influences the degree to which its profits respond to sales volume changes. Companies with high operating leverage have high contribution margin ratios. Although such companies must establish fairly high sales volumes to initially cover fixed cost, once that cost is covered, each unit sold after breakeven adds significantly to profits. Thus, a small increase in sales can have a major impact on a company s profits. The degree of operating leverage (DOL) measures how a percentage change in sales from the current level will affect company profits. In other words, DOL indicates how sensitive the company s profit is to sales volume increases and decreases. The computation for DOL follows. DOL CM Profit before tax This calculation assumes that fixed costs do not increase when sales increase. Assume that Sesame Company is currently selling 600,000 clocks. The income statement in Exhibit 9 14 reflects this sales level and shows that the company has a DOL of If Sesame increases sales by 20 percent, the 60 percent change in profits equals the DOL multiplied by the percentage change in sales or ( %). If sales decrease by the same 20 percent, the impact on profits is a negative 60 percent. These amounts are confirmed in Exhibit Exhibit 9 14 Sesame Company s Degree of Operating Leverage Current (600,000 clocks) 20 Percent Increase (720,000 clocks) 20 Percent Decrease (480,000 clocks) Sales $24,000,000 $28,800,000 $19,200,000 Variable cost ($29.00 per clock) (17,400,000) (20,880,000 (13,920,000) Contribution margin $ 6,600,000 $ 7,920,000 $ 5,280,000 Fixed cost (4,400,000) (4,400,000) (4,400,000) Profit before tax $ 2,200,000 $ 3,520,000 a $ 880,000 b Degree of operating leverage Contribution margin Profit before tax ($6,600,000 $2,200,000) 3.00 ($7,920,000 $3,520,000) 2.25 ($5,280, ,000) 6.00 a Profit increase $3,520,000 $2,200,000 $1,320,000 (or 60.00% of the original profit). b Profit decrease $880,000 $2,200,000 ($1,320,000) (or 60% of the original profit). The DOL decreases as sales move upward from the BEP. Thus, when the margin of safety is low, the degree of operating leverage is high. In fact, at the BEP, the DOL is infinite because any increase from zero is an infinite percentage change. If a company is operating close to BEP, each percentage increase in sales can make a dramatic impact on net income. As sales increase from the break-even point, margin of safety increases but the

21 Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis 401 degree of operating leverage declines. The relationship between the MS percentage (MS%) and DOL is as follows: MS% 1 DOL DOL 1 MS% This relationship is proved in Exhibit 9 15 using the 600,000-clock sales level information for Sesame. Therefore, if one of the two measures is known, the other can be easily calculated. Exhibit 9 15 Sesame Company s Margin of Safety and Degree of Operating Leverage Relationship Break-even sales 400,000 units; Current sales 600,000 units Margin of safety % Margin of safety in units Actual sales in units [(600, ,000) 600,000] 0.33, or 33% (rounded) Degree of operating leverage Contribution margin Profit before tax $6,600,000 $2,200,000 3 Margin of safety (1 DOL) (1 3) 0.33, or 33% (rounded) Degree of operating leverage (1 MS%) (1 0.33) 3 (rounded) Underlying Assumptions of CVP Analysis CVP analysis is a short-run model that focuses on relationships among selling price, variable cost, fixed cost, volume, and profit. This model is a useful planning tool that can provide information about the impact on profit when changes are made in the cost structure or in the sales level. Although limiting the accuracy of the results, several important but necessary assumptions are made in the CVP model. These assumptions follow: LO.6 What are the underlying assumptions of CVP analysis? 1. All revenue and variable cost behavior patterns are constant per unit and linear within the relevant range. 2. Total contribution margin (total revenue total variable cost) is linear within the relevant range and increases proportionally with output. This assumption follows directly from assumption Total fixed cost is constant within the relevant range. This assumption, in part, indicates that no capacity additions will be made during the period under consideration. 4. Mixed costs can be accurately separated into fixed and variable elements. Although accuracy of separation can be questioned, reliable estimates can be developed from the use of regression analysis or the high low method (as discussed in Chapter 3). 5. Sales and production are equal; thus, there is no material fluctuation in inventory levels. This assumption is necessary because fixed cost can be allocated to inventory at a different rate each year. Thus, variable costing information must be available. Because CVP and variable costing both focus on cost behavior, they are distinctly compatible with one another. 6. In a multiproduct firm, the sales mix remains constant. This assumption is necessary so that a weighted average contribution margin and CM% can be computed.

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