COST-VOLUME-PROFIT MODELLING

COST-VOLUME-PROFIT MODELLING Introduction Cost-volume-profit (CVP) analysis focuses on the way costs and profits change when volume changes. The relationships among volume, costs, and profits must be clearly understood if enterprise management is to plan effectively and relate performance to plans. Cost-volume-profit analysis is a simple but powerful tool to assist management at different stages of the planning process. The planning process begins with a forecast of sales, which is then tested to determine whether the forecast of net income meets management's profit objectives. If the forecasted amounts do not meet the objectives, the company searches out changes in operating factors such as prices, product mix, selling efforts, and costs that will bring the budgeted net income closer to the target figure. CVP analysis is a way of merging revenue planning and cost planning in one analysis that shows effects on profit of different levels of sales and costs. CVP analysis can be used to determine the approximate profit outcomes of the sales forecast and to assess the profitability of different strategies in marketing and production that management has under consideration. Learning Objectives Understand the prerequisites and basic elements of Cost-Volume-Profit (CVP) Analysis. Model CVP relationships and depict results in reports using tables and graphs. Consider the simple mathematics of CVP analysis. Recognise Low and High break-even companies and their decision implications. Understand the assumptions and limitations of CVP analysis. Model income statements in both conventional and contribution formats. 300

Cost-Volume-Profit Modelling Key Words Break-even point Contribution margin Cost behaviour CVP analysis Fixed costs Margin of safety Profit-volume graph Relevant range Sales volume Variable costs Prescribed Readings Course Notes 301

Lecture Outline Learning Objectives Key Words Introduction Prerequisites of CVP Analysis The Elements of Cost-Volume-Profit Analysis The Simple Mathematics of CVP Analysis CVP in Multiple Products Comments on the Break-Even Volume of Sales Assumptions of CVP Analysis Income Statements in Contribution Form Summary Appendix 8.1 Tutorial Exercise Self Assessment Questions Self Assessment Answers Self Assessment Exercises Self Assessment Solutions Case Study 302

Cost-Volume-Profit Modelling Course Notes Prerequisites of CVP Analysis A knowledge of a firm's cost behaviour is necessary before an effective CVP analysis can be conducted. Particular forecasts of sales and production levels result in certain levels of expenses and certain levels of profit or loss. If sales increase, expenses will probably also increase and net income should rise as well. However, the change in income is not necessarily proportional to the change in sales. It all depends on how costs change - i.e. on cost behaviour. The relationship of costs or expenses to sales and production volume is also important in evaluating different strategies management may propose in attempting to move the company closer to its profit objectives. Since most strategies considered by management will affect the planned volume of sales and production, management must consider how expenses behave or change when sales volume changes. Once final strategies have been adopted and the sales budget is set for the year, it is important to understand the patterns of cost behaviour in order to determine the correct cost budgets for the year. Hence, our emphasis in this section on cost planning will be on the relationship of expenses or costs to sales and production volume. The discussion that follows is simplified by assuming that sales volume and production volume are the same. That is, the planned sales volume is provided by an equal planned production volume, with the consequence that inventories remain constant. This simplifying assumption will avoid the knotty problem of the effect a change in inventory may have on planned profit. The impact on profit due to changing inventory levels will be dealt with later in this topic. The Elements of Cost-Volume-Profit Analysis CVP analysis deals with the operating and financial factors that affect enterprise profit. These factors are sales volume, sales revenue, and the variable and fixed costs. Managers must make decisions about such important matters as selling prices, advertising costs, raw material costs, and labor costs. CVP analysis shows how these decisions will affect the three factors of sales volume, sales revenue, and costs - i.e. both variable and fixed costs. The three profit factors will be explained before considering two simple examples. Sales volume refers to the physical volume of sales, whereas sales revenue refers to dollar sales. The distinction is useful because decisions that affect sales volume may not have the same effect on sales revenue. For example, a 303

reduction in selling price may increase sales volume by 5% while increasing sales revenue by only 3%, the difference being due to a reduced selling price. In basic CVP analysis it is generally assumed that selling prices do not change. Therefore, sales volume and sales revenue have a 1 : 1 relationship, and sales revenue can be used as a convenient substitute for sales volume. The physical volume of sales can easily be identified in a company that manufactures only one product or a few closely related products. For example, the sales volume of a flour mill might be measured in pounds of finished flour. Most companies however, deal in a number of different products whose sales cannot be added together unless they are converted to a common denominator; usually dollar sales. For example, the sales volume of a department store that has thousands of different merchandise items must be expressed in sales dollars. Thus, sales volume is generally expressed as sales revenue. The second factor, sales revenue, is dollar sales, or units of products sold times selling price. Sales revenue varies directly with sales volume as long as selling prices remain constant, whether volume is expressed in units or in dollars. The sales revenue graph is a straight line beginning at the origin, as is illustrated in the CVP graph in Figure 8.1. The third factor, costs, refers to all of the expenses of the company except corporate taxes. These expenses or costs are divided into their fixed and variable components. Total variable costs are directly proportional to sales volume; total fixed costs tend to remain at a constant amount as sales volume changes. The relationships are shown in Figure 8.1. The lines in Figure 8.1 are drawn all the way to the dollar axis. This is not strictly correct, because fixed costs remain fixed and variable costs vary directly with sales only over the relevant range, which covers only part of the total range of sales volume. Illustrations in this Topic will usually have lines extended all the way to zero volume. The relevant range will be indicated on some figures: when this range is not indicated, it should be assumed by the reader. Illustration of CVP Analysis We now turn to Example 8.1 for illustrations of the basic features of CVP analysis. Notice that the income statement in Example 8.1 does not include the categories of expenses usually seen on published income statements. Cost of goods sold, selling expenses, and administrative expenses do not appear on the statement. These expenses have been analysed into their variable expense and fixed expense elements, commonly called "variable costs" and "fixed costs" in CVP analysis. 304

Cost-Volume-Profit Modelling Figure 8.1 Cost-Volume-Profit Graph $ Sales Total costs Variable costs Fixed costs Relevant range 0 Volume Example 8.l The Mudfridge Company produces and sells one product. In year 1, the company produced and sold 28,000 units of product. The following income statement summarises year 1 operations. MUDFRIDGE COMPANY Income Statement for Year 1 Sales Variable costs Contribution margin Fixed costs Net income before taxes Per Unit Total Amount Percent of Sales $20.00 (8.00) 12.00 $560,000 (224,000) 336,000 (300,000) $36,000 100.0 (40.0) 60.0 305

The subtotal labelled contribution margin is defined as sales minus variable costs; it is the margin remaining after variable costs are covered. Contribution margin can be expected to vary directly with sales volume. Thus, if sales increase by 10%, the contribution margin increases by 10%. This direct relationship is useful in analysing different profit-planning problems. Two columns included in the income statement in Example 8.1 reflect the variability feature of variable costs and contribution margin. The per unit column shows the effect on revenue and costs of one additional unit of product. Thus, if the Mudfridge Company sold one more unit of product, sales would increase by $20.00, total variable costs would increase by $8.00, and contribution margin would increase by $12.00, while fixed costs would remain at $300,000. The percent of sales, in the right-hand column, shows the degree of variability of total variable costs and total contribution margin. That is, as long as selling price is $20.00 and per unit variable cost is $8.00, total variable costs will be 40% of sales and contribution margin will be 60% of sales. Thus, if the Mudfridge Company were to increase its total sales by $1.00, total variable costs would increase by $.40, total contribution margin would increase by $.60, and net income before taxes would increase by $.60. Similarly, a decrease in total sales of $1.00 would bring a decrease in total variable costs of $.40 and a decrease in total contribution margin and net income before taxes of $.60. No unit cost or percent figures are given for fixed costs. Such figures would be meaningless, since total fixed costs of a given year generally are not related directly to the volume of sales. The total fixed costs tend to remain at a constant figure until the company management makes decisions that change the capacity costs and/or the discretionary costs that constitute the total fixed costs. Figure 8.2 shows the relationships of sales volume, sales revenue, and variable and fixed costs for the Mudfridge Company. Total sales revenue increases at the rate of $20.00 per unit as sales volume increases. We expect this, since the selling price is $20.00. When sales volume is 10,000 units, sales revenue is $200,000; when sales volume is 30,000 units, sales revenue is $600,000. Total fixed costs remain at $300,000 over the entire range of sales volume in the figure. Total variable costs are not shown directly but rather as the difference between total costs and total fixed costs. We note that total costs change at the rate of $8.00 per unit. When sales volume is 10,000 units, total costs are $380,000; when sales volume is 30,000 units, total costs are $540,000. Thus, an increase of 20,000 units in sales volume brings an increase of $160,000 in total costs, a rate of increase of $8.00 per unit, which is the variable cost per unit of product. In this financial model, therefore, the change in total costs is attributed only to the change in variable costs. 306

Cost-Volume-Profit Modelling Figure 8.2 Cost-Volume-Profit Graph MUDFRIDGE COMPANY ($000s) 600 Sales Revenue Total costs 500 400 300 Fixed costs 200 Relevant range 100 10 20 30 40 Sales Volume in Units (000s) The effect of changes in sales volume, sales revenue, and costs on net income before taxes is shown in Figure 8.2. Profit before taxes (PBT) is shown as the difference between the sales revenue graph and the total cost graph. Thus, when the sales volume is 10,000 units, PBT is: PBT = Sales revenue - Total costs (8-1) PBT = $200,000 - $380,000 = ($180,000) or a loss of $180,000 When sales volume is 25,000 units, PBT is: PBT = $500,000 - $500,000 = 0 307

The sales volume that produced zero profit is known as the break-even point. This point, where sales revenue equals total costs, occurs at the intersection of the sales revenue line and total cost line. Its algebraic solution for modelling purposes will be developed in the next section; its significance for management will be discussed toward the end of the Topic. Profit-Volume Graph The relationship of PBT to sales volume can be shown directly in a profit-volume graph, as in Figure 8.3, where the difference between sales revenue and total costs is plotted in relation to sales volume. Thus, there is a loss shown until the breakeven volume of 25,000 units is reached. After the break-even point, a positive PBT is shown. The slope of the profit graph is $12.00 per unit, which is the contribution margin per unit. This illustrates the point made earlier: a change in total contribution margin provides an equal change in profit before taxes. Figure 8.3 Profit-Volume Graph MUDFRIDGE COMPANY ($000s) +200 +100 0-100 Profit before taxes 5 10 15 20 25 30 35 40 Loss -200-300 Sales Volume in Units (000s) 308

Cost-Volume-Profit Modelling Model Use in Planning Example 8.2 further illustrates the use of CVP modelling and analysis. The solution is simply another income statement. It was constructed by using the basic price and cost relationships shown in Example 8.1. The Mudfridge Company expects to sell 2,000 more units in year 2 than in year 1, so sales are expected to increase by $40,000. Variable costs should increase by 40% of $40,000, or by $16,000. As a result, contribution margin is expected to increase by 60% of $40,000, or by $24,000. The year 2 fixed costs are expected to remain at $300,000 because no change in those costs is planned by the Mudfridge management, and the unit amounts do not exceed the company's "relevant range". Example 8.2 The Mudfridge Company plans to sell 30,000 units of its product in year 2 at a price of $20.00. There are no changes in the cost structure planned for year 2. What is the expected net income before taxes for year 2? Solution: MUDFRIDGE COMPANY Planned Income Statement for Year 2 Percent of Sales Sales $600,000 100.0 Variable costs (240,000) 40.0 Contribution margin $360,000 60.0 Fixed costs (300,000) Net income before taxes $60,000 Net income before taxes is expected to increase by $24,000. This is the same amount as the increase in contribution margin. This shows that a change in the amount of contribution margin will generate the same amount of change in net income before taxes when there is no change in fixed costs. This relationship should be tested in the simple financial model developed in this area. 309

The Simple Mathematics of CVP Analysis Let us now examine the mathematics of CVP analysis. Cost volume-profit analysis often begins with the determination of the break-even point. The break-even point is that volume of sales at which the company has a zero profit or loss; it is the point at which sales exactly equal costs. This yields the following.: At break-even point Sales = Total costs (8-2) to expand: Sales = Fixed costs + Variable costs (8-3) or, in symbols: S = FC + VC (8-3) To solve this equation, the three unknowns must be reduced to one unknown. In many situations the fixed costs are known or given. The remaining unknowns, sales and variable costs, are related, in that both vary with volume. Variable costs can often be expressed as a percentage of the sales, and thus the equation can be reduced to the one unknown, sales. Alternatively, both sales and variable costs can be expressed in terms of dollars per unit of volume. Example 8.3 illustrates the process, using data from Example 8.1. Example 8.3 What volume of sales is required by the Mudfridge Company to break even? Solution: A. Expressing Variable Costs as a Percentage of Sales: S = VC + FC S =.40S + 300,000.60S = 300,000 S = 300,000/.60 S = 500,000 Check: 310

Cost-Volume-Profit Modelling S = VC + FC (8-3) 500,000 = (.40)(500,000) + 300,000 500,000 = 500,000 B. Expressing Sales and Variable Costs in Dollars Per Unit: S = VC + FC (8-3) $20U = $8U + 300,000 (where U is units of product sold) 12U = 300,000 U = 300,000/12 U = 25,000, number of units at break-even point Note that the (A) solution in Example 8.3 involves dividing the fixed costs by the contribution margin expressed as a fraction of sales. The break-even equation can be expressed in terms of contribution margin, as follows: Let CM = contribution margin fraction expressed in decimal form (8-4) = 1.00 - variable cost fraction (8-4) Then, at the break-even point, the sales multiplied by the contribution margin fraction must provide enough dollars to cover the fixed costs: S x CM = FC (8-5) Applying the contribution margin approach to the Mudfridge Company of our previous example, we have the following: CM = 1 -.40S =.60 of sales At break-even point.60s = $300,000 Break-even sales = $300,000/.60 = $500,000 This form of the break-even equation emphasises contribution margin and the fact that when contribution margin just covers the fixed costs, a company is at the break-even point. However, we will base most of our discussion directly on equation (8-3) because it is more flexible. Equation (8-3) can be expanded to deal with situations in which certain amounts of profit are desired, as follows: S = FC + VC + PBT (8-6) where PBT = profit or income before tax. 311

Example 8.4 The Mudfridge Company plans to sell 30,000 units of its product in year 2 at a price of $20.00. There are no changes in the cost structure planned for year 2. What is the expected net income before taxes for year 2? Solution: S = VC + FC + PBT (8-6) (30,000)(20) = (30,000)(8) + 300,000 + PBT PBT = 60,000 In Example 8.2, Mudfridge planned to sell 30,000 units in year 2. This can be fitted into this framework, as is shown in Example 8.4. The problem in Example 8.4 is rather simple, but a few more examples will indicate the potential of this methodology (Examples 8.5 through 8.7): Example 8.5 What level of sales is necessary for the Mudfridge Company to earn a profit before taxes of $90,000? Solution: S = VC + FC + PBT (8-6) S =.4S + 300,000 + 90,000.6S = 390,000 S = $650,000 The contribution margin approach can also be used to solve the problem. In this case, the CM in dollars must be sufficient to cover fixed costs and provide $90,000 of profit in addition. Thus:.60S = 300,000 + 90,000 S = 390,000/.60 = 650,000 Alternatively, one can concentrate on additional dollars of sales needed above the break-even point to produce $90,000 of profit: S x CM = 90,000 (8-5).60S = 90,000 S = 150,000 of additional sales 312

Cost-Volume-Profit Modelling Total sales = 500,000 (at break even) + 150,000 = 650,000 Example 8.6 What level of sales is necessary for the Mudfridge Company to earn a profit before taxes of 5% of sales? Solution: S = VC + FC + PBT (8-6) S =.4S + 300,000 +.05S S =.45S + 300,000 S = 300,000/.55 S = 545,454, or $545,000 (to nearest $1,000) To use the contribution margin approach, you must note that the total contribution must be enough to cover fixed costs and provide.05s in addition. Thus: S x CM = 300,000 +.05S.60S = 300,000 +.05S.55S = 300,000 S = 545,454 It should be apparent from the preceding three examples that the contribution margin approach and the equation approach are basically the same. In Example 8.7, only the equation (8-3) based modelling approach is used. In this complicated example income taxes are also a factor. Example 8.7 What dollar sales volume does the Mudfridge Company need to yield a net income after taxes of 9% of sales? Assume that an income tax rate of 40% is applied to net income before taxes. The selling price and the cost structure remain the same as before: Solution: Let Y = net income after taxes Let T = income taxes PBT - T = Y (8-7) and T = 0.40 (PBT) Therefore: 313

PBT -.40(PBT) Y = Y =.60(PBT) The profit objective is Y =.09S.60PBT =.09S PBT = 09S/.60 =.15S Substituting into: S = VC + FC + PBT (8-6) S =.40S + 300,000 +.15S S =.55S + 300,000.45S = 300,000 S = $666,667 Check: $666,667 - (.40)(666,667) - 300,000 = PBT 666,667-266,667-300,000 = 100,000 100, 000 - T = Y 100,000-40,000 = 60,000 60,000/666,667= 9% of sales Cost-Volume-Profit Analysis: Graphical Techniques The discussion of CVP analysis relied on simple algebraic techniques. The analysis may be enhanced and clarified for management by using graphs similar to Figure 8.2 to present the same information. Graphical capabilities are now a common feature in most spreadsheet programs. The use of graphs is considered to be a better way to present information to management for clarity and understanding. Figure 8.5 shows this analysis for the Pillgrim Company. The important lines are illustrated in Figure 8.5 as shown in the Excel model depicted in Appendix 8.1. The total sales line is the locus (the intersection) of all values on both axes, since both axes represent sales dollars. The line for fixed costs is a horizontal dashed line with a value of $600,000. Fixed costs remain at this amount for each volume of sales. The graph of total variable costs is a dashed, angled line 314

Cost-Volume-Profit Modelling starting at the zero intersection of the two axes. The slope of this line is determined by the relationship of variable costs to sales. In this example, total variable costs are 40% of sales. The line can be drawn by finding one value of variable costs greater than zero and connecting that point with the zero intersection. Thus, when sales volume is $1,500,000, total variable costs are $600,000. This point was connected by a straight line to the zero intersection. The total costs line (variable costs plus fixed costs) is the solid straight line that starts at $600,000 and goes through the point where sales volume is $1,500,000 and total costs are $1,200,000. Every point on the total costs line is the vertical sum of fixed costs and variable costs. The chart in Figure 8.5 of Appendix 8.1 allows the viewer to see all of the combinations of costs and profits for all volumes of sales. So long as the costs, prices, and product composition remain the same, the amount of profit can be read directly from the chart. The shaded area indicates the amount of loss (sales volumes under $1,000,000) or profit (sales volumes above $1,000,000). Thus, if volume of sales were to fall to zero, the net loss would be $600,000, which is the vertical distance in the shaded area labelled net loss. Both of the shaded areas shown in the chart represent the difference between revenue and total costs, which is either profit or loss. Some analysts do not extend the graphs in the chart to zero volume. Rather, they generate graphs for only the relevant volume range. This is the volume range in which the company normally operates. Since the company operates within the relevant range, the cost behaviour patterns in this range are much more reliable. Because of the uncertainty of how costs really behave when volume is below or above this relevant range, these analysts prefer not to extend their graphs outside this range. When graphs extend all the way from zero volume to maximum capacity, it is important to remember that the graph is probably valid only over part of the distance displayed. It is awkward to try to represent too many alternatives on the same chart. If several alternative strategies are being contemplated by management, it is preferable to generate several charts, one for each strategy. Example 8.8 illustrates. Example 8.8 Pillgrim Company management is considering an advertising program that would increase its fixed advertising costs by $100,000. If taken, this action is expected to increase total sales by $200,000. It also would change the variable costs to 38% of sales so that the contribution margin percentage would increase to 62%. The combined effect of this program is shown by means of the cost-volume-profit chart in Figure 8.6 of Appendix 8.1. 315

The solution chart shows that the profit expected from the new program of advertising is $354,000. The company's break-even volume of sales, however, is increased to $1,130,000 by this action. Whether the company's management would implement this program depends on the other alternatives open to it and on the response that the company's competitors might make. These are matters for management judgments. The CVP analysis only portrays probable outcomes of different alternatives. CVP in Multiple Products Companies usually produce and sell more than one product. Cost-volume-profit analysis is still applicable, but the analyst must proceed with caution, since the variable costs and the contribution margin depend on the mix or composition of products sold. The following example shows the break-even calculation for a company with 3 products: Example 8.9. Product Selling Variable Expected Product Expected Expected Expected Line: Price p.u. Costs p.u. Volume Mix Revenue Var.Costs Contribution Prod. A $ 9.00 $ 5.00 1000 33% $ 9,000 $ 5,000 $ 4,000 Prod. B $ 18.00 $ 5.00 500 17% $ 9,000 $ 2,500 $ 6,500 Prod. C $ 24.00 $ 5.00 1500 50% $ 36,000 $ 7,500 $ 28,500 3000 100% $ 54,000 $ 15,000 $ 39,000 Less: Fixed Costs: $ (15,600 ) Net Profit $ 23,400 Standard Mixed Product =.33(A) +.17(B) +.5(C) Price of Standard Product =.33($9) +.17($18) +.5($24) = $ 18 Variable Costs of Standard Product =.33($5) +.17($5) +.5($5) = $ 5 Contribution of Standard Product = ($18 - $5) = $ 13 Break-Even Volume of Standard Product = $ 15,600/$13 = 1,200 units Therefore, assuming product mix remains constant: Break Even Product Expected Expected Expected Volume Mix Revenue Var.Costs Contribution BE Volume of Product A = 400 33% $ 3,600 $ 2,000 $ 1,600 BE Volume of Product B = 200 17% $ 3,600 $ 1,000 $ 2,600 BE Volume of Product C = 600 50% $ 14,400 $ 3,000 $ 11,400 1,200 100% $ 21,600 $ 6,000 $ 15,600 316

Cost-Volume-Profit Modelling Less: Fixed Costs: $ (15,600) Net Profit $ Nil It must be noted that if the product mix remains the same from one period to the next, the prior period variable-fixed cost relationship can be used without any problems. If the product mix changes, new relationships must be established based on the new mix that is projected. Comments on the Break-Even Volume of Sales Cost-volume-profit analysis sometimes is called break-even analysis. This term probably stems from the graphical analysis. The break-even volume represents the solution of the system of two equations represented by the line for total sales and the line for total costs. The intersection of these two lines is the break-even volume of sales. Even though break-even sales volume does not represent the profit goal of a firm, it is useful information. Some companies view the break-even sales as a goal to be achieved over some fraction of the year. A sales manager might say: "We must have sales of $1,000,000 before we break-even. We plan to reach this volume by the end of July. Our sales in the remaining months following July, will generate our planned profit for the year." This statement is not literally correct, since all sales contribute to any profit made in the year. But viewing the year in this way can provide the sales personnel with a time goal. They realise that if they can reach their break-even volume earlier in the year, the total years net income should be larger than planned. The break-even volume of sales also gives the firm an idea of its sensitivity to economic declines. In general, a company with a relatively low break-even volume in relation to its present or proposed sales is better able to weather economic storms than a firm with a relatively high break-even volume of sales. Figure 8.4 illustrates two companies, each having a planned sales volume of 1,200 units and profit of $200,000 at that level of sales. Figure 8.4 shows that the low break-even company (i.e. Company L) could experience a 50% decrease in sales before incurring a net loss. The high break-even company (i.e. Company H) will incur a loss with only a 20% decrease in sales. The positive difference between planned sales volume and the break-even point is called margin of safety. A large margin of safety is desirable but not always attainable. 317

Several interesting features of Figure 8.4 should be noted. First, the increase in profit for the high breakeven company is much more rapid after the break-even point is reached. Thus, if sales for both companies climb above $1,200,000, company H will show a higher profit than company L. This results from the cost structures of the companies. Company L has low fixed costs (approximately $200,000) and a fairly high variable cost percentage (66.66% of sales). Company H, on the other hand, has high fixed costs (approximately $800,000) and a low variable cost percentage (16.66% of sales). The result is a higher contribution margin percentage for company H, which means higher profits per dollar of sales after the break-even point is reached. Figure 8.4 Break-Even Graphs Company L Company H $ (000s) 1,200 Low Break Even Sales $ (000s) 1,200 High Break Even Sales 1000 Costs 1,000 Costs 800 200 600 1,200 600 960 1,200 Sales Volume Sales Volume The figure also indicates that a high contribution margin percentage is not necessarily the best of all possible worlds. In company H the high CM is accompanied by high fixed costs. If sales drop to $900,000 for both companies, H will show a loss of $50,000, whereas L will still have a profit of $100,000. A high CM that is accompanied by high fixed costs does not allow for much of a downswing 318

Cost-Volume-Profit Modelling in current sales i.e. it provides a low margin of safety. Companies that are capital intensive, such as automobile manufacturers or steel mills, are often faced with this type of situation. Because of high fixed costs, the margin of safety is low. On the other hand, profits can be high when sales are up because of upswings in the business cycle. The best of all possible worlds is low fixed costs and a high CM company. Like most ideals, this situation is probably not attainable. High profits attract competitors, and the result is a situation in which most companies are able to attain some profit; but few can sustain really high levels for an extended period of time. Most companies face trade-offs in their cost structures. A company can reduce variable costs by increasing fixed costs, for example, when it buys labour saving machines; or a company may be able to eliminate some fixed costs but only by increasing variable costs - for example, when a company airplane is sold but the company has to incur increased air fares for company travel. The business cycle, with its swings in business activity, can be weathered much more successfully by a company like company L. On the other hand, company H will have handsome profits in a time of expanding sales, though it may have low profits during a recession. Analysis of company operations should bear these types of consideration in mind. Assumptions of CVP Analysis Now that we have covered the techniques of the CVP analysis and its uses by management, it is important to be reminded of the assumptions that underlie this analysis. Most of the assumptions have been stated or implied in the Topic, so the following serves principally as a summary. The assumptions are: That the cost structure of the enterprise will not change over the period. The pattern of variable, fixed, and semi variable costs will remain about the same over the period. This means that there will be no change in the organisation and methods of production and sales that will lead to significant changes in costs. That the selling price of each product will not change over the period. Furthermore, the selling price will remain fairly constant despite changes in the volume of sales. That all costs can be analysed into fixed and variable components. That variable costs generally will vary proportionally with sales volume, and total fixed costs will be constant over the range of sales volume considered in the analysis. That the prices paid for the resources used by the enterprise will not change over the period. That the product mix will remain constant over the period. 319

That for manufacturing firms, changes in inventories over the period will not be significant. These basic assumptions appear to severely limit the CVP analysis to problems involving break-even point and profit objectives, given the current cost and revenue structure. However, as we have seen in this Topic, CVP analysis need not be restricted to current cost and revenue data. The analysis can be applied to a wide range of problems by simply changing the cost and revenue data to fit each problem. For each problem a separate CVP analysis can then be made. Thus, we have seen that CVP analysis can be applied to such questions as: Shall we change our product selling price? Shall we introduce labour saving devices that increase our fixed costs? Shall we advertise heavily to increase volume? Income Statements in Contribution Form CVP analysis relies on analysis of planned expenses into their variable and fixed components. Costvolume-profit analysis is firmly anchored in the fact that as sales volume increases total variable expenses increase proportionately with sales volume while total fixed expenses tend to remain at a constant amount. CVP analysis is very useful in estimating the expected profit for different amounts of sales. The analysis may also be used to test the approximate effects on profit of changes in selling price, variable expense, and fixed expense. In CVP analysis we used simple, highly summarised income statements that emphasised the contribution margin. Example 8.10 contrasts the income statement in contribution form with the conventional statement used in financial accounting. The contribution approach to income statements is used by many companies, not only for planning purposes, but also for internal reporting of the results of operations. The argument is simple: If that type of income statement can be modelled to display planned income, why not extend the model to show actual results? Actual income results are then directly comparable with planned income results. Both the contribution and conventional statements for company X give the same net income. This is not necessarily true for a manufacturing enterprise, because some fixed costs of manufacturing may be treated as an expense in the contribution form, whereas they may be treated as part of the cost of inventory in the conventional form. This will be the only reason for a difference (if any) between such statements in the bottom-line profit figure. For merchandising and service enterprises there will generally be no difference between the income amounts shown in the two forms of statement. The difference lies in the way expenses are handled. The conventional form emphasises the various functions of the enterprise and the expenses connected with those functions. The contribution form emphasises cost behaviour and the way costs change when volume changes. The gross margin in conventional statements 320

Cost-Volume-Profit Modelling and the contribution margin in the contribution statements should not be confused. The gross margin is what remains after the cost of buying or producing goods is deducted. The contribution margin is the excess of sales over variable costs. It would be a wild coincidence if these two were equal in amount. The bottom-line net profit, however, will be the same, except for differences in the value of inventory as pointed out earlier. Almost all published reports are in the conventional, functional format. Internally, however, many companies use a contribution format because of its greater usefulness in planning and controlling costs. Example 8.10 INCOME STATEMENTS Contribution and Conventional Form Luke Company Income Statement in Contribution Form Sales $6,000 Less Variable expenses Manufacturing 2,000 Selling 700 Administrative 100 (2,800) Contribution margin 3,200 Fixed expenses Manufacturing 1,600 Selling 500 Administrative 800 (2,900) Income before taxes 300 Corporate taxes (120) Net Profit $180 Luke Company Income Statement in Conventional Form Sales $6,000 Less cost of goods sold (3,600) Gross margin 2,400 Operating expenses Selling 1,200 Administrative 900 (2,100) Income before taxes 300 Corporate taxes (120) Net Profit $180 321

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Cost-Volume-Profit Modelling Summary Once behaviour of costs has been ascertained, cost-volume-profit (CVP) analysis becomes a powerful tool for analysis. CVP analysis is a technique for analysing the effect on profit of changes in a company's revenue and cost structures. Given the assumptions that underlie the analysis, much useful information can be developed. Of course, the user must be aware of the uncritical use of the analysis in situations that do not match the assumptions. The following summarises the principal uses of CVP analysis: Testing the profit effect of a sales forecast. The analysis can give a rough approximation of the expected profit from a given sales forecast. Finding the break-even volume of sales. The analysis can yield the estimated break-even point from which one can estimate the margin of safety. Determining the volume of sales required to meet certain profit goals. For example, what sales are required to generate a profit after taxes of 5% of sales? Estimating the effect on the break-even point and on profits of changes in the firm's cost structure and revenue structure. For example, what will happen to profits and the break-even point if labour saving machines are introduced with the-result that fixed costs are increased and variable costs are reduced? In each particular use of the analysis, it must be remembered that factors not explicitly included in the problem are assumed to remain the same. The contribution form of the income statement utilises the breakdown of costs into variable and fixed elements in the income statement itself. A statement that emphasises cost behaviour can help management in understanding effects of changes in selling price and cost factors. 323

Appendix 8.1 A B C D E F G 1 Topic 8 CVP Analysis 2 3 4 Cost-Volume-Profit Graph 5 6 Company Pilgrim Company 7 8 Sales 1500000 9 Variable costs as a percent of sales 40% 10 Fixed costs 600000 11 12 13 Sales Sales Variable costs Fixed costs Total costs 14 0 0 0 0 600000 600000 15 1 150000 150000 60000 600000 660000 16 2 300000 300000 120000 600000 720000 17 3 450000 450000 180000 600000 780000 18 4 600000 600000 240000 600000 840000 19 5 750000 750000 300000 600000 900000 20 6 900000 900000 360000 600000 960000 21 7 1050000 1050000 420000 600000 1020000 22 8 1200000 1200000 480000 600000 1080000 23 9 1350000 1350000 540000 600000 1140000 24 10 1500000 1500000 600000 600000 1200000 25 324

Cost-Volume-Profit Modelling Appendix 8.1 (Cont) Figure 8.5 Pilgrim Company Cost-Volume-Profit Graph $1400 $1200 Sales Costs $000s $1000 $800 $600 Sales Variable costs Fixed costs Total costs $400 $200 $ $ $150 $300 $450 $600 $750 $900 $1050 $1200 $1350 $1500 Sales Volume in $000s 325

Appendix 8.1 (Cont) A B C D E F G H 1 Topic 8 CVP Analysis 2 3 4 Cost-Volume-Profit Graph 5 6 Company Pilgrim Company (Advertising Alternative) 7 8 Sales 1700000 9 Variable costs as a percent of sales 38% 10 Fixed costs 700000 11 12 13 14 Sales Sales Variable costs Fixed costs Total costs 15 0 0 0 0 700000 700000 16 1 170000 170000 64600 700000 764600 17 2 340000 340000 129200 700000 829200 18 3 510000 510000 193800 700000 893800 19 4 680000 680000 258400 700000 958400 20 5 850000 850000 323000 700000 1023000 21 6 1020000 1020000 387600 700000 1087600 22 7 1190000 1190000 452200 700000 1152200 23 8 1360000 1360000 516800 700000 1216800 24 9 1530000 1530000 581400 700000 1281400 25 10 1700000 1700000 646000 700000 1346000 26 326

Cost-Volume-Profit Modelling Appendix 8.1 (Cont) Figure 8.6 $1800 Pilgrim Company Cost-Volume-Profit Graph Increased Advertising Alternative $1600 $1400 Sales Costs $000s $1200 $1000 $800 $600 Sales Variable costs Fixed costs Total costs $400 $200 $ $ $170 $340 $510 $680 $850 $1020 $1190 $1360 $1530 $1700 Sales Volum e in $000s 327

Self Assessment Questions Q8.1 What is meant by the break-even point? Q8.2 What are the assumptions that underlie cost-volume-profit analysis? Q8.3 Is the corporate income tax a variable cost? Explain. Q8.4 Is it possible to do a break-even analysis if some costs are not clearly either fixed or variable? Explain. Q8.5 The Chairman of a company claims that break-even analysis is useless because his company needs to make a substantial profit and not just break even. Explain the usefulness of this type of analysis to the Chairman. Q8.6 What is the significance of the relevant range in break-even analysis? Q8.7 In CVP analysis cost relationships are assumed to be linear with respect to volume. Economists usually draw curvilinear relationships. How can these two different approaches be reconciled? Q8.8 What is the significance of the contribution margin percentage in CVP analysis? Q8.9 Variable costs are fixed per unit of product. On the other hand, fixed costs vary because the cost per unit goes down as volume increases. Discuss. Q8.10 What is the margin of safety? Which is likely to have a higher margin of safety, a profitable company with high fixed costs and a high contribution margin or a profitable company with low fixed costs and a low contribution margin? Self Assessment Answers Q8.1 The breakeven point is the point (measured in sales volume or unit volume) at which the revenues exactly equal the total costs and no profit or loss results. Q8.2 There are a number of assumptions of breakeven analysis, including the assumption that selling and cost prices remain unchanged, that fixed costs and variable costs are completely fixed and variable, respectively, that cost relationships are linear, that product mix will remain constant, that changes in inventories will not be significant, and that the basic cost structure will not change. 328

Cost-Volume-Profit Modelling Q8.3 The income tax varies with income before tax, not with total revenue; therefore it is not really a variable cost. Since it is not fixed in amount, it must be handled separately in C-V-P analysis. Q8.4 Yes. Costs that are neither fixed nor variable are analysed into fixed and variable components for breakeven analysis purposes. It is true that the analysis sometimes proceeds on somewhat shaky foundations because the components are somewhat arbitrary and the fit is not perfect but the benefits of the analysis tend to outweigh this type of shortcoming. Q8.5 Breakeven analysis is helpful in determining the cost behaviour in a particular company. A knowledge of cost behaviour is helpful at any level of activity - even well above the breakeven point. Q8.6 The relevant range is the range of activity within which the company usually operates. Assumptions about cost and sales behaviour are only accurate within this range. If operations fall outside of the range, a whole new study must be made of cost behaviour. The production report should concentrate on the relationship between budgeted and actual costs. Q8.7 Within the relevant range assumed as part of breakeven analysis in accounting the cost and sales lines are fairly straight. Extending these lines beyond the relevant range would also involve some change in the slope of the lines - they would become curvilinear. Thus the accountants and the economists are not really as far apart as it might seem. Studies of actual cost behaviour have shown that many costs are straight-line in nature within a fairly wide range. The practice of extending cost lines all the way to zero activity in breakeven charts is of course erroneous. Q8.8 The contribution margin idea is of vital importance. The contribution margin indicates how much of each sales dollar is available for covering fixed costs and providing profits. The percentage itself can be used for determining the breakeven point, determining the effect of changes in volume on profit, etc. Q8.9 This question emphasizes the importance of choosing an appropriate point of reference. Variable costs vary with volume. When related to units, variable costs are the same per unit. Fixed costs do not change as volume changes. However, it fixed costs are divided by the total number of units produced, the fixed costs per unit decline as more units are produced. In general, fixed unit costs are treacherous. Q8.10 The margin of safety is the amount by which budgeted or actual sales exceed the breakeven point. The company with a low contribution margin is likely to have the highest margin of safety. For each dollar of sales lost, the low contribution margin company will lose less profit. Thus sales volume can decline quite a bit before the breakeven point is reached. Of course, it may be harder for a low contribution margin company to attain a high level of profits in the first place. 329

Self Assessment Exercises E8.1 Break even. The Clinton Division of the Lewinsky Company had the following results last year: Sales $130,000 Variable costs 52,000 Contribution margin $ 78,000 Fixed costs 70,000 income before taxes $ 8,000 Income taxes (40%) 3,200 Net income $ 4,800 Required: Compute the break-even volume of sales for the Clinton Division. E8.2 CVP analysis. Refer to Problem E8.1. Required: (a) If sales are expected to increase 20% next year and all cost relations are expected to stay the same, what is the expected net income for the year? (b) Compute the rate of return on sales for last year and for part a. Explain why the rate of return changed. E8.3 CVP analysis. Starr Corporation and Tripp Corporation both have sales of $1,000,000, and total costs of $800,000. Starr's costs are 80% fixed and 20% variable. Tripp's costs are 20% fixed and 80% variable. Required: (a) Compute the break-even point for both companies. Explain why one break-even point is higher than the other. (b) Compute the income before taxes for both companies if sales increase to $1,200,000. Explain your results. E8.4 CVP analysis. Last year the Hillary Company sold 40,000 units of product. The contribution margin of 40% amounted to $3.20 per unit. Fixed costs were $89,600. Required: a. What is the selling price per unit? b. What was the profit last year? c. What was the break-even point in dollars of sales and in units last year? 330

E8.5 CVP analysis. Last year s results for Jordan Company were as follows: Sales $120,000 Variable expenses 54,000 Contribution margin 66,000 Fixed expenses 52,000 Income before taxes $ 14,000 Required: a. What was the break-even point last year? b. If sales are expected to increase by 10%, prepare a budgeted income statement for the current year. c. Assume that an increase of $6,000 in advertising will increase sales by 12%. Prepare a budgeted income statement under these assumptions. E8.6 Profit-volume graph. Refer to Problem E8.5. Cost-Volume-Profit Modelling Required: construct a profit-volume graph for Jordan Company, assuming no change in cost relationships from last year. E8.7 Costs, prices, and profits. ConFess Company sets selling prices at l20% of costs. The company's fixed costs are $800,000. Variable costs are $50 per unit. Three operating levels are under consideration: 40,000 units, 50,000 units, and 60,000 units. Required: a. What would selling price per unit be at each of the contemplated operating levels? b. Determine the net profit before taxes at each contemplated operating level. c. Comment on your results. E8.8 Effects of changes in costs. The Paula Company sells its one product at $l0 per unit. Variable costs are $4 per unit. Fixed costs are $180,000. Required: Determine break-even point in dollars and units in each of the following situations: a. No change in present conditions. b. Variable costs per unit increase 1 0%. c. Fixed costs increase 10%. d. Sales price increases 1 0%. e. Variable costs per unit decrease 1 0%. f. Fixed costs decrease 1 0%. g. Sales price decreases 1 0%. 331

E8.9 Break even, profit. The Oval Company has purchased the franchise for selling Coca Cola at White University s rugby games. The franchise fee is $8,000. Equipment to sell coke can be rented for $1,400 for the season. Coke will be sold for $.50 a cup. Variable costs, including labour, are $.22 per cup. The manager of the operation at the rugby game will be paid $800 for the season. Required: a. Determine the break-even point in dollars of sales and in cups of coca cola. b. What will dollar sales have to be to make a profit of $2,000? c. What will dollar sales have to be to make a profit of 1 0% on sales (before taxes)? E8.10 Break even, profit. Sales this year for Currie Ltd. are budgeted at $40,000,000. Fixed costs are budgeted at $6,000,000. Variable costs are budgeted at 70% of sales. Required: a. What is the budgeted break-even point? b. What sales volume would be necessary to increase budgeted profit40%? c. Would it be profitable for the company to increase budgeted sales by 30%, without changing prices, by means of increasing quality and thus raising variable costs by 4% of sales? E8.11 Break even, government operations. The city of Whitewater police department is considering hiring another pair of police officers and leasing another police car for traffic control duty. The salary of a beginning police officer is $18,000 a year including all benefits. The car could be leased for $2,600 a year. Tickets written by police officers provide average revenue of $40 each. Variable costs (paperwork, car operating costs) are expected to average $8 a ticket. Required: a. How many tickets must the new police officers write for the city to break even for the year? b. How many tickets would have to be written to return net profits of $4,000 to the city? E8.12 New program, break even. The Chelsea Company has a new product, electronically locked zippers that can be unzipped only by the fingerprints of authorized persons. The product had sales of $2,000,000 last year. The company is planning a big promotion for the current year. Advertising costs will be $250,000, and a premium offer will cost $.15 per additional uint of zipper. Zippers sells for $1.00 per unit and variable costs are $.38 per unit. the Required: a. How much will dollar sales have to increase over last year s total to breakeven on the promotion? b. How much will sales have to increase over last year s total to make a 30% rate of return on increased sales from the promotion? 332