Page 1 of 28 Module 4: Cost behaviour and cost-volume-profit analysis Required reading Chapter 5, pages 187-213 Chapter 6, pages 230-253 Appendix 6A, pages 256-258 Overview The way in which a cost responds to a change in business activity is known as cost behaviour. Cost behaviour is important for prediction purposes in business, where cost prediction is a factor in planning, decision making, and control. In Module 2, cost prediction was required to calculate predetermined overhead. In this module, you will study three types of cost behaviour variable, fixed, and mixed and three methods of separating a mixed cost into its variable and fixed elements. The contribution approach to the income statement will also be described. The second part of this module is devoted to cost volume profit (CVP) analysis, which examines the interrelationship of five key elements that together influence a range of management decisions. These elements are product selling price, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. A major application of CVP analysis is break-even analysis, which is also covered in this module. Computer illustrations 4-1 and 4-2 show how you can use a spreadsheet program to design worksheets for cost-volume-profit analysis and mixed cost analysis using least squares regression. Learning objectives 4.1 Identify examples of variable costs, and explain the effect of a change in activity on both total variable costs and per unit variable costs. (Level 1) 4.2 Identify examples of fixed costs, and explain the effect of a change in activity on both total fixed costs and fixed costs expressed on a per unit basis. (Level 1) 4.3 Analyze a mixed cost using the high-low method and the regression method.(level 1) 4.4 Prepare an income statement using the contribution method. (Level 1) 4.5 Analyze mixed costs using a spreadsheet program.(level 2) 4.6 Explain how changes in activity and changes in variable costs, fixed costs, selling price, and volume affect contribution margin and net income. (Level 1) 4.7 Compute the break-even point by both the equation method and the contribution margin method. (Level 1)
Page 2 of 28 4.8 Use cost-volume-profit formulas to determine the activity level needed to achieve a desired target net profit figure. (Level 1) 4.9 Explain the importance of considering contribution margin when structuring sales commissions. (Level 2) 4.10 Compute the break-even point for a multiple product company, and explain the effects of shifts in the sales mix on contribution margin and the break-even point. (Level 1) 4.11 Explain cost volume profit with uncertainty. (Level 2) 4.12 Design a worksheet to perform a sensitivity analysis on CVP. (Level 2) 4.1 Variable cost behaviour patterns LEVEL 1 Variable and fixed costs represent two types of cost behaviour. Sometimes these two types are mixed together (and may also be termed semivariable costs). Note carefully the specific definitions of variable and fixed costs, both in terms of totals and on a per unit basis. Variable costs A cost is variable if the total cost is expected to vary as a function of output. Accountants often assume that variable costs are linear, as depicted in Exhibit 5-1. This assumption means that variable cost per unit of output is assumed to be constant at all levels of output. The relationship can be expressed in the following mathematical form: where: V = bx V = total variable costs b = unit variable cost (a constant) x = the activity base V = bx is a linear equation that begins at the origin (0,0). The activity base x is called the independent or causal variable. For example, the number of copies of a document that you make will be a causal variable of your total printing costs. Exhibit 5-2 illustrates the types of costs normally classified as variable. However, specific facts can change this classification, and actual behaviour of costs in any circumstance must be determined. Exhibit 5-3 shows a particularly troublesome cost behaviour pattern, the step variable. Step costs are costs that remain constant within a range of activity but are different between ranges of activities. Step costs result from input factors that cannot be increased in very small amounts; they can be increased only in discrete steps. Since step costs cannot be described by a simple algebraic function, for simplicity, if the steps are narrow, the cost is treated as linear (see Exhibit 4-1).
Page 3 of 28 Exhibit 4 1 Step variable cost shown as a linear function Where the steps are sufficiently large (Exhibit 5-6), the relevant range concept can be applied to treat the cost as a fixed cost. Exhibit 5-4 shows a curvilinear representation of variable costs that may be more representative of actual cost behaviour. However, because the functional form of a curvilinear relationship is more complex than V = bx, accountants break the curvilinear function into linear pieces using the concept of relevant range. Step-variable (Exhibit 5-3), curvilinear (Exhibit 5-4), and step-fixed (Exhibit 5-6) costs suggest that care must be exercised when predicting costs outside the relevant range. It is important that this aspect be taken into consideration when budgets are being prepared. It is very important that you understand the concept of relevant range and its impact on cost behaviours. 4.2 Fixed costs LEVEL 1 Fixed costs do not vary with changes in activity. In algebraic form, they can be expressed as: where: F = a F = total fixed costs a = constant amount The textbook description of the trend toward fixed costs is particularly interesting because it demonstrates how some of the traditional problems and analyses may not be realistic. For example, recall the explanation in Module 1 of how to treat idle time. Assume a guaranteed employment contract and a decline in production of a short-term nature. Labour in total is a fixed cost because of the guarantee, but direct labour could still be
Page 4 of 28 variable. How? If idle time is treated as overhead, then hours not worked on a job will be deemed overhead, making direct labour variable. A study of the time worked in an administrative office could even make a salaried employee a variable direct labour cost. In summary, while a cost incurred may be fixed, the method of accounting may result in the cost appearing to be variable. Interestingly, the direct labour would be represented as: V = bx while overhead would be: z = b (T x) Total salary would equal: V + z = bx + bt bx = bt If the problem being examined is small enough (for example, costing a product), the cost that is charged may be variable; however, from the whole company's perspective, the cost that is incurred is fixed. The primary difference between committed and discretionary fixed costs relates to the time horizon involved. Committed fixed costs will remain intact for a long time, whereas discretionary fixed costs will remain intact for a much shorter time usually one year. In the long term, all costs are discretionary (for example, you can always sell the equipment). Notice how social responsibility and management philosophy interact. In practice, it is difficult to find a truly variable or truly fixed cost; many costs fall into a semivariable, or mixed, group. The variable element of a mixed cost function may be either linear or curvilinear. If a linear representation is used (Exhibit 5-7), the cost function can be expressed as: where: Y = a + bx This is a very important cost function because it approximates the true cost function (that is, it involves fixed and variable costs) of an organization. The estimation of the total cost function is often fundamental to business planning.
Page 5 of 28 Activity 4 1 Cost behaviour This activity reinforces your understanding of the behaviour of fixed and variable costs. 4.3 Analysis of mixed costs LEVEL 1 Analysis of mixed costs (estimation of fixed and variable costs) can be done in a number of ways. The high low method attempts to segregate total costs by examining two observations: those representing the highest and the lowest costs. Recall that the cost function is: Y = a + bx With two observations, (X 0, Y 0 ) and (X 1, Y 1 ), the slope (the variable cost per unit of activity) and the intercept (the fixed costs) of the cost function can be estimated as: b = (Y 1 Y 0 ) / (X 1 X 0 ) a = Y 0 bx 0 As described in the textbook, the choice of the high Y 1 and the low Y 0 is always based on the level of activity, that is, on the independent variable X. While the high-low method is relatively easy to apply, its major problem lies in the fact that only the two extreme values are used to estimate the total cost line. These two extreme values may not be typical of the relationship between cost and activity. The visual inspection (scattergraph) method entails plotting the relevant observations on a scattergraph and then fitting a line to the data visually. While this method uses all the data, its major drawback is that it is very subjective. A scattergraph is useful not so much as a method of estimating cost but as a way of seeing a behaviour pattern. This is useful when selecting the appropriate approach for determining the cost function. The least squares (linear regression) method is a well-developed statistical technique for the analysis of mixed costs. It permits the cost line, Y = a + bx, to be developed using all observations in the scatter diagrams. It fits a line to the observed relationships between costs and volume, which is known as the best fitted line (minimize the sum of the squares of the vertical distances from the regression line to the plots of the actual observations). It also tells the user how the regression line fits the observed data. Carefully note the formulas for the least squares method on page 212. The solution formulas to calculate the vertical intercept and the slope are given below:
Page 6 of 28 Use of these formulas prevents the need to solve two equations in two unknowns. The formulas are useful in computer spreadsheets where there is no facility to perform regression analysis. Regression analysis using a spreadsheet program will be demonstrated in Computer illustration 4-1. Note: Linear regression and multiple regression concepts and techniques are explained in greater detail in Business Quantitative Analysis [QU1] in the CGA program of professional studies. 4.4 Contribution margin and contribution format income statement LEVEL 1 After management has analyzed fixed and variable costs, the traditional income statement can be reformatted. The new presentation is called the contribution format. This presentation separates income statement costs by their behaviour, not by classifications suggested by generally accepted accounting principles. Exhibit 5-14 compares income statements prepared under both the traditional and contribution approaches. Net income is identical under the two formats. The contribution margin is the difference between sales and total variable costs. By calculating the contribution margin, management knows whether the company will have a net income, a net loss, or break even. In other words: If contribution margin > fixed costs, there is a net income. If contribution margin < fixed costs, there is a net loss. If contribution margin = fixed costs, net income is zero. In the short run, variable costs may be controllable. For example, if net income is falling, management may decide to use less expensive raw materials. However, in the short run, management may not be able to change fixed costs. For example, the company may own or may have a non-cancellable lease on its building. Presenting the income statement in a contribution margin format helps management assess its operating flexibility. Online chapter summary This topic marks the end of the textbook coverage of cost behaviour. To ensure you understand this material and the corresponding terminology, read the summary on page 209, work through the review problem on pages 210-211, and go to the Online Learning Centre, click Contents, click choose Chapter 5, select Chapter Summary and review the material thoroughly. If you are unclear on how to access or use this site, refer to the
Page 7 of 28 Online Learning Centre (OLC) Guide in the course navigation pane. 4.5 Computer illustration 4-1: Regression analysis LEVEL 2 Four worksheets: M4P1A Contains the data for the least squares method of cost analysis M4P1B Contains a partially completed budgeted income statement M4P1AS Solution to Requirement 1 M4P1BS Solution to Requirement 2 Description This illustration is based on Problem P5-22 (page 223). Required Answer Requirements 1 and 2 using the following procedure. Procedure Requirement 1 1. Open the file MA1M4P1 and click the M4P1A sheet tab. 2. Study the layout of the worksheet. Rows 4 to 13 form the data table, and the rest of the worksheet is blank. 3. Perform a least squares regression analysis to derive a cost formula for shipping expense. 4. Choose Tools > Data Analysis in Excel 2003/XP (or choose Data Ribbon in Excel 2007 and select Data Analysis). If this option is not displayed, follow these instructions for installing the Solver Add- In and Analysis ToolPak (To view the content from this link you must go on-line.). 5. Choose Regression and click OK. Type D5:D13 in the Input Y Range text box. This range corresponds to the dependent or "explained" variable (Shipping expense). 6. Click the Input X Range text box and select the range C5:C13, which corresponds to the independent or explanatory variable (Units sold). The column labels are included in the range so that they appear in the regression output when the Labels option is selected see the next step. 7. Select Labels and Output Range. Type the output range A15 in the text box and click OK to place the regression output starting in cell A15. You should obtain the following results:
Page 8 of 28 Intercept (B31) 40,000 Units sold (cell B32)* 7.50 R Squared (B19) 0.993506494 * The value displayed in cell B32 corresponds to the regression coefficient for the explanatory or independent variable. Note also that the value in B32 needs to be divided by 1,000. See the text explanation on page 223, under Requirement 1. The results indicate that the cost formula for shipping expense is: $40,000 + 7.50 X where X is the number of units sold. The high R Squared value indicates that the data fit very closely to the regression line. However, this conclusion can be misleading given the small number of observations. Proceed to Requirement 2. Requirement 2 1. Click the sheet tab M4P1B. Using the relevant information derived from the least squares regression calculations, complete the data table by entering the appropriate cell references in cells C10 and C13 from the worksheet M4P1A. 2. Complete the budgeted income statement in rows 15 to 31. 3. You should obtain a net income figure of $80,000. If you do not obtain this result, print a copy of the formulas of your worksheet M4P1B, and compare your results with the solution worksheet M4P1BS. 4. Click the tab for the solution worksheet M4P1BS and print the formulas. 5. Compare the results obtained in steps 3 and 4 and correct any errors. 4.6 Basics of cost-volume-profit analysis LEVEL 1 Cost-volume-profit (CVP) analysis explores the interrelationship of the five elements listed at the beginning of Chapter 6. As a direct result of CVP analysis, the income statement can be formatted to facilitate profitability analysis. The basic assumption of cost-volume-profit analysis requires that a firm's total costs be separated into fixed and variable components. The definition of contribution margin is important as it is a concept that will be used extensively in this course. Contribution margin is the amount remaining when all the variable costs are deducted from revenue. Once "break-even" is achieved, net income will increase by the contribution margin per unit for each
Page 9 of 28 additional unit sold. The contribution margin ratio (CM ratio) is the contribution margin divided by sales. In simple situations, the CM ratio (really a percentage) multiplied by the change in sales gives the profit change before taxes. The applications of CVP (pages 236-240) show how analysis of various plans can be done quickly. 4.7 Break-even analysis LEVEL 1 A major application of CVP is break-even analysis. Profit is defined as being equal to total revenues less total costs, or in algebraic form: where: P = SPx (FC + VCx) P = profit SP = unit selling price FC = fixed costs VC = unit variable cost x = level of activity (sales volume in units) At break-even sales volume (x), P = 0, so set SPx = FC + VCx and solve for x as follows: SPx VCx = FC x (SP VC) = FC x = FC (SP VC) x = break-even sales volume, and (SP VC) is the contribution margin per unit If VC is given as a percentage of Y (sales in dollars) where Y = SP, then the same concept can be applied after a change in formulation: Y = VCY+ FC (Y VCY) = FC Y (1 VC) = FC Y = FC (1 VC)< /p > (1 VC) is the contribution margin ratio, and Y is the break-even sales dollars. A useful concept of margin of safety is defined on page 244. Margin of safety is total sales break-even sales, or as a percentage, it is margin of safety in dollars total sales.
Page 10 of 28 Activity 4 2 Cost-volume-profit (CVP) relationships This activity reinforces your understanding of CVP relationships. 4.8 CVP considerations in choosing a cost structure LEVEL 1 CVP considerations can be used in determining the most favourable combination of variable and fixed costs. The answer usually depends on predictions of future sales and management's attitude toward risk. Operating leverage deals with the risk associated with the fluctuations of sales and cost structures. When a company has a high proportion of fixed costs and a low proportion of variable costs, it is highly leveraged. A small increase in sales volume will significantly increase profits because the contribution margin per unit is substantial (due to low variable costs) and fixed costs do not change. However, if sales are low, the company could suffer losses due to the high level of fixed costs. Therefore, a highly leveraged company has a high risk of losing money when volume is low, but has an opportunity to increase profits substantially if it operates above the break-even level. The increased use of automation has significantly altered the risks and profitability ratios of highly automated organizations. 4.9 Structuring sales commissions LEVEL 2 The observations on how to structure sales commissions are important with respect to guiding employee actions toward the maximization of the organization's profits. This module centers on incentive pay in commission sales. Ethical issues can arise with incentive schemes that encourage deception in sales (for example, hidden fees to financial advisors to pump sales for mediocre mutual funds). While the central ethical concern in this topic and in the accompanying text is with maximization of corporate profits, there is a constraining ethical consideration, namely, honestly and fairly serving the needs of customers. 4.10 Sales mix LEVEL 1 Up to this point, the description of CVP has dealt with one product only. If more than one product exists, the CVP analysis is more complex, as shown by the following formula:
Page 11 of 28 P = SP 1 x 1 + SP 2 x 2 VC 1 x 1 VC 2 x 2 FC where: SP i = Selling price of product i x i = Volume of product i VC i = Variable cost of product i An infinite number of break-even points are possible in this equation because there are two x values. One way to solve this problem is to use a weighted-average (use total sales and variable expenses for an assumed sales mix) and compute an average contribution margin ratio. However, if the mix changes, so will the break-even point. 4.11 Assumptions of CVP analysis LEVEL 2 CVP analysis is a static technique that ignores present values, even though its form of presentation might lead one to believe that it is a dynamic (multiple period) model. The extension of CVP analysis to multiple periods, with present values included, is beyond the scope of this course. However, you should study and understand the limiting assumptions that must be made when using data for this technique. Extending the CVP relationship to a more realistic setting introduces uncertainty. A decision tree quantifies and displays the variables, as can be seen in Exhibits 6-5 and 6-6. Online chapter summary This topic marks the end of the textbook coverage of CVP analysis. To ensure you understand this material and the corresponding terminology, read the summary on page 254, work through the review problem on pages 254-256, and go to the Online Learning Centre, click Contents, choose Chapter 6, select Chapter Summary and review the material thoroughly. If you are unclear on how to access or use this site, refer to the Online Learning Centre (OLC) Guide in the course navigation pane. 4.12 Computer illustration 4-2: CVP sensitivity analysis LEVEL 2 Material provided A prebuilt worksheet M4P2, which you will complete. Three completed solution worksheets, M4P2S, M4P2AS, M4P2BS, to which you can compare your work.
Page 12 of 28 Description This problem is a variation of Case 6-29 of the text. You will complete Requirements 1 and 2 in this illustration using a spreadsheet program. Required Complete Requirements 1 and 2 of Case C6-29 using the following procedure. Procedure 1. Open the file MA1M4P2. 2. Click the sheet tab M4P2 and study the layout of the worksheet. The data table in the range A6 to G28 contains the per unit variable costs and the fixed costs for Alpine Inc. Rows 22 to 27 contain the base data required to complete an income statement in the contribution format. 3. Move to row 29. Rows 29 to 52 contain a partially completed income statement. Requirement 1 1. Enter the necessary formulas to complete the 2005 contribution income statement on a total basis (column F) and on a per unit basis (column G) using the data from the data table. The formulas in rows 43, 44, 50, and 51 have been pre-entered to save you time. 2. Save your worksheet. Rows 22 to 27 contain the base data required to complete an income statement in the contribution format. 3. Observe in cell F51 the net loss for 1996. You should obtain a net loss of $46,200. If you do not obtain this result, follow the next steps. If you have obtained the correct answer, proceed to Requirement 2. 4. Print a copy of your formulas in the range F33 to G51. 5. Click the sheet tab M4P2S and compare the solution formulas with your printout from step 4. 6. Correct any errors. Requirement 2a 1. With your completed worksheet from Requirement 1 or the solution worksheet M4P2S on-screen, modify the data table to reflect the sales manager's proposal as described in the case in Requirement 2a. 2. Save your worksheet. 3. Observe the effect of these changes on the bottom line. The net loss is now $75,300.
Page 13 of 28 If you do not obtain this result, print your worksheet. Click the sheet tab M4P2AS and compare the solution with your printout. Requirement 2b 4. With the base case income statement or the solution worksheet M4P2S on-screen, make the necessary changes to the data table to reflect the vice president's proposal. 5. Save your worksheet. 6. You should obtain a net income of $102,800. If you do not obtain this result, compare your worksheet with the solution worksheet M4P2BS. Note the ease with which you can make changes to the different cost and revenue elements and see the effects on net income. Sensitivity analyses are relatively easy to perform on computers and therefore allow management to deal with the dynamics of CVP more efficiently. Module 4 summary This module consists of two related parts: cost behaviour and cost-volume-profit (CVP) analysis. In order to make decisions, control operations, and evaluate performance, managers need to predict how costs behave with changes in activity. Topics 4.1, 4.2, and 4.3 deal respectively with the analyses of variable, fixed, and mixed costs behaviour patterns. Topic 4.4 introduces the contribution format income statement as a basic tool for many decisions. Topic 4.5 conducts a regression analysis for a mixed cost, the result of which is incorporated in a contribution format income statement. The CVP analysis, introduced in Topic 4.6, builds on the knowledge acquired in previous topics. The CVP model allows the identification of courses of actions for profitability improvement programs. Topic 4.7 offers a direct application of the CVP model with the break-even point analysis. CVP model is also used in decisions involving the choice of cost structure for a business as well as in the structuring of sales commissions that are dealt with respectively in Topics 4.8 and 4.9. The applicability of CVP analysis extends also to multiproduct and multiservice companies. Topic 4.10
Page 14 of 28 addresses the issues such companies must cope with. The CVP model was criticized for its simplified assumptions, namely the degree of certainty associated with the analysis. Topic 4.11 responds by introducing probability theory in the model to address uncertainty. Finally, Topic 4.12 shows, through the use of a computer illustration, how dynamic and powerful the CVP model can be when used for sensitivity analysis. Module 4 self-test Question 1 Computer question Detmer Holdings AG of Zurich, Switzerland, has just introduced a new fashion watch for which the company is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each 2.5 per unit reduction in the selling price. The company s present selling price is 78 per unit, and variable expenses are 53 per unit. Fixed expenses are 784,300 per year. The present annual sales volume (at the 78 selling price) is 41,000 units. Required Use the procedure described below to complete worksheet M4Q3. From this worksheet, answer the following questions: 1. What is the present yearly net income or loss? 2. What is the present break-even point in units and in Euro sales? 3. Assuming that the marketing studies are correct, what is the maximum profit that the company can earn yearly? At how many units and at what selling price per unit would the company generate this profit? Fixed expenses will not change over the range of sales volume to be considered. 4. What would be the break-even point in units and in Euro sales using the selling price you determined in (3) above (for example, the selling price at the level of maximum profits)? Why is this break-even point different from the break-even point you computed in (1) above? Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Managerial Accounting, Sixth Canadian Edition, Problem 6-13, pages 264-265. Copyright 2004, by McGraw-Hill Ryerson Limited. Adapted with permission. Procedure 1. Open the file MA1M4Q1. 2. Observe the layout of the worksheet. In particular, notice that cells A4 to E15 contain a data table. 3. Complete the income statement in rows 19 to 23, using the values in the data table to calculate the net income.
Page 15 of 28 4. Complete the break-even analysis for requirement 2 by entering appropriate formulas in cells E28 and E30. 5. As part of the solution to requirement 3, complete the income-volume sensitivity analysis table in rows 38 to 46. Note that you should enter formulas rather than actual values in these cells. 6. Save a copy of your completed worksheet. Solution Question 2 Textbook, Case 5-23, page 224. Solution Question 3 Textbook, Exercise 6-1, page 259-260. Solution Question 4 Textbook, Problem 6-19, page 267. Solution Question 5 Textbook, Problem 6-17, Requirements 1, 2, 3, and 4 only, pages 266-267. Solution Question 6 Textbook, Problem 6-11, Requirements 1 and 2 only, pages 263-264. Solution Self-test - Content Links
Page 16 of 28 Solution 1 Requirement 1 The present net income is Є 240,700. Requirement 2 The break-even point in units is 31,372 and Є 2,447,016. Requirement 3 The maximum profit is Є 250,700, generated by selling 46,000 units at Є 75.5 per unit. Requirement 4 At a selling price of Є 75.5 per unit, the contribution margin is Є 22.5 per unit. Therefore: The breakeven point in units = 784,300 22.5 = 34,858 units 34,858 units Є 75.5 = Є 2,631,779 to break even The break-even point is different from the break-even point in requirement 2 because of the change in selling price. With the change in selling price, the unit contribution margin drops from Є 25 to Є 22.5, thereby driving up the break-even point. Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Solutions Manual to accompany Managerial Accounting, Sixth Edition. Copyright 2004, by McGraw-Hill Ryerson Limited. Adapted with permission.
Page 17 of 28 Solution printout
Page 18 of 28 Solution 2 Case 5-23 This case requires the ability to build on concepts that are introduced only briefly in the text. To some degree, this case anticipates issues that will be covered in more depth in later chapters. 1. In order to estimate the contribution to profit of the charity event, it is first necessary to estimate the variable costs of catering the event. The costs of food and beverages and labour are all apparently variable with respect to the number of guests. However, the situation with respect overhead expenses is less clear. A good first step is to plot the labour hour and overhead expense data in a scattergraph as
Page 19 of 28 shown below. This scattergraph reveals several interesting points about the behaviour of overhead costs: The relation between overhead expense and labour hours is approximated reasonably well by a straight line. (However, there appears to be a slight downward bend in the plot as the labour hours increase evidence of increasing returns to scale. This is a common occurrence in practice. See Noreen & Soderstrom, Are overhead costs strictly proportional to activity? Journal of Accounting and Economics, vol. 17, 1994, pp. 255-278.) The data points are all fairly close to the straight line. This indicates that most of the variation in overhead expenses is explained by labour hours. As a consequence, there probably wouldn t be much benefit to investigating other possible cost drivers for the overhead expenses. Most of the overhead expense appears to be fixed. Jasmine should ask herself if this is reasonable. Does the company have large fixed expenses such as rent, depreciation, and salaries? The overhead expenses can be decomposed into fixed and variable elements using the high-low method, least-squares regression method, or even the quick method based on the scattergraph. The high-low method throws away most of the data and bases the estimates of variable and fixed costs on data for only two months. For that reason, it is a decidedly inferior method in this situation.
Page 20 of 28 Nevertheless, if the high-low method were used, the estimates would be computed as follows: Labour Hours Overhead Expense High level of activity 4,500 $61,600 Low level of activity 1,500 44,000 Change 3,000 17,600 Variable cost = Change in cost Change in activity = $17,600 3,000 labour hours = $5.87 per labour hour Fixed cost element = Total cost Variable cost element = $61,600 ($5.87 4,500) = $35,185 In contrast, the least-squares regression method yields estimates of $5.27 per labour hour for the variable cost and $38,501 per month for the fixed cost using statistical software. (The adjusted R 2 is 96%.) To obtain these estimates, use a statistical software package or a spreadsheet application such as Excel. Using the least-squares regression estimates of the variable overhead cost, the total variable cost per guest is computed as follows: Food and beverages $17.00 Labour (0.5 hour @ $10 per hour) 5.00 Overhead (0.5 hour @ $5.27 per hour) 2.64 Total variable cost per guest $24.64 The total contribution from 120 guests paying $45 each is computed as follows: Revenue (120 guests @ $45.00 per guest) $5,400.00 Variable cost (120 guests @ $24.64 per guest) 2,956.80 Contribution to profit $2,443.20 Fixed costs are not included in the above computation because there is no indication that any additional fixed costs would be incurred as a consequence of catering the cocktail party. If additional fixed costs were incurred, they should also be subtracted from revenue. 2. Assuming that no additional fixed costs are incurred as a result of catering the charity event, any price greater than the variable cost per guest of $24.64 would contribute to profits. 3. We would favour bidding slightly less than $42 to get the contract. Any bid above $24.64 would
Page 21 of 28 contribute to profits, and a bid at the normal price of $45 is unlikely to land the contract. And apart from the contribution to profit, catering the event would show off the company s capabilities to potential clients. The danger is that a price that is lower than the normal bid of $45 might set a precedent for the future, or it might initiate a price war among caterers. However, the price need not be publicized, and the lower price could be justified to future clients because this is a charity event. Another possibility would be for Jasmine to maintain her normal price but throw in additional services at no cost to the customer. Whether to compete on price or service is a delicate issue that Jasmine will have to decide after getting to know the personality and preferences of the customer. Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Solutions Manual to accompany Managerial Accounting, Sixth Canadian Edition. Copyright 2004, by McGraw-Hill Ryerson Limited. Reproduced with permission. Solution 3 Exercise 6-1 Total Per Unit 1. Sales (30,000 units 1.15 = 34,500 units) $172,500 $5.00 Less variable expenses 103,500 3.00 Contribution margin 69,000 $2.00 Less fixed expenses 50,000 Net operating income $ 19,000 Total Per Unit 2. Sales (30,000 units 1.20 = 36,000 units) $162,000 $4.50 Less variable expenses 108,000 3.00 Contribution margin 54,000 $1.50 Less fixed expenses 50,000 Net operating income $ 4,000 Total Per Unit 3. Sales (30,000 units 0.95 = 28,500 units) $156,750 $5.50 Less variable expenses 85,500 3.00 Contribution margin 71,250 $2.50 Less fixed expenses ($50,000 + $10,000) 60,000 Net operating income $ 11,250 Total Per Unit 4. Sales (30,000 units 0.90 = 27,000 units) $151,200 $5.60 Less variable expenses 86,400 3.20 Contribution margin 64,800 $2.40 Less fixed expenses 50,000 Net operating income $ 14,800
Page 22 of 28 Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Solutions Manual to accompany Managerial Accounting, Sixth Canadian Edition. Copyright 2004, by McGraw-Hill Ryerson Limited. Reproduced with permission. Solution 4 Problem 6-19 1. a. Selling price $37.50 100% Less variable expenses 22.50 60 Contribution margin $15.00 40% Sales = Variable expenses + Fixed expenses + Profits $37.50Q = $22.50Q + $480,000 + $0 $15.00Q = $480,000 Q = $480,000 $15.00 per skateboard Q = 32,000 skateboards Alternative solution: b. The degree of operating leverage would be: 2. The new CM ratio will be: Selling price $37.50 100% Less variable expenses 25.50 68 Contribution margin $12.00 32%
Page 23 of 28 The new break-even point will be: Sales = Variable expenses + Fixed expenses + Profits $37.50Q = $25.50Q + $480,000 + $0 $12.00Q = $480,000 Q = $480,000 $12.00 per skateboard Q = 40,000 skateboards Alternative solution: Break-even point in unit sales = Fixed expenses CM per unit = $480,000 $12 per skateboard = 40,000 skateboards 3. Sales = Variable expenses + Fixed expenses + Profits $37.50Q = $25.50Q + $480,000 + $120,000 $12.00Q = $600,000 Q = $600,000 $12.00 per skateboard Q = 50,000 skateboards Alternative solution: Unit sales to attain target profit = = Fixed expenses + Target profit CM per unit $480,000 + $120,000 $12 per skateboard = 50,000 skateboards Thus, sales will have to increase by 10,000 skateboards (50,000 skateboards, less 40,000 skateboards currently being sold) to earn the same amount of net operating income as earned last year. The computations above and in part (2) show quite clearly the dramatic effect that increases in variable costs can have on an organization. These effects from a $3 per unit increase in labour costs for Tyrene Company are summarized below: Present Expected Break-even point (in skateboards) 32,000 40,000 Sales (in skateboards) needed to earn net operating income of $120,000 40,000 50,000 Note particularly that if variable costs do increase next year, then the company will just break even if it sells the same number of skateboards (40,000) as it did last year.
Page 24 of 28 4. The contribution margin ratio last year was 40%. If we let P equal the new selling price, then: P = $25.50 + 0.40P 0.60P = $25.50 P = $25.50 0.60 P = $42.50 To verify: Selling price $42.50 100 % Less variable expenses 25.50 60 Contribution margin $17.00 40 % Therefore, to maintain a 40% CM ratio, a $3 increase in variable costs would require a $5 increase in the selling price. 5. The new CM ratio would be: Selling price $37.50 100 % Less variable expenses 13.50 * 36 Contribution margin $24.00 64 % *$22.50 ($22.50 40%) = $13.50 The new break-even point would be: Sales = Variable expenses + Fixed expenses + Profits $37.50Q = $13.50Q + $912,000* + $0 $24.00Q = $912,000 Q = $912,000 $24.00 per skateboard Q = 38,000 skateboards *$480,000 1.9 = $912,000 Alternative solution: Break-even point in unit sales = Fixed expenses CM per unit = $912,000 $24 per skateboard = 38,000 skateboards Although this break-even figure is greater than the company's present break-even figure of 32,000 skateboards [see part (1) above], it is less than the break-even point will be if the company does not automate and variable labour costs rise next year [see part (2) above].
Page 25 of 28 6. a. Sales = Variable expenses + Fixed expenses + Profits $37.50Q = $13.50Q + $912,000* + $120,000 $24.00Q = $1,032,000 Q = $1,032,000 $24.00 per skateboard Q = 43,000 skateboards *480,000 1.9 = $912,000 Alternative solution: Unit sales to attain target profit = = Fixed expenses + Target profit CM per unit $912,000 + $120,000 $24 per skateboard = 43,000 skateboards Thus, the company will have to sell 3,000 more skateboards (43,000-40,000 = 3,000) than now being sold to earn a profit of $120,000 each year. However, this is still far less than the 50,000 skateboards that would have to be sold to earn a $120,000 profit if the plant is not automated and variable labour costs rise next year [see part (3) above]. b. The contribution income statement would be: Sales (40,000 skateboards $37.50 per skateboard) $1,500,000 Less variable expenses (40,000 skateboards $13.50 per skateboard) 540,000 Contribution margin 960,000 Less fixed expenses 912,000 Net operating income $ 48,000 Degree of operating leverage = Contribution margin Net operating income = $960,000 $48,000 = 20 c. This problem shows the difficulty faced by many firms today. Variable costs for labour are rising, yet because of competitive pressures it is often difficult to pass these cost increases along in the form of a higher price for products. Thus, firms are forced to automate (to some degree) resulting in higher operating leverage, often a higher break-even point, and greater risk for the company.
Page 26 of 28 There is no clear answer as to whether one should have been in favour of constructing the new plant. However, this question provides an opportunity to bring out points such as in the preceding paragraph and it forces students to think about the issues. Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Solutions Manual to accompany Managerial Accounting, Sixth Canadian Edition. Copyright 2004, by McGraw-Hill Ryerson Limited. Reproduced with permission. Solution 5 Problem 6-17 Requirement 1 1. The break-even point in units: SP $ 25 ($625,000 25,000) VC 15 ($375,000 25,000) CM $ 10 Requirement 2 Requirement 3 Break-even ($) = 15,000 units $25 = $375,000 sales 2. Margin of safety = Sales break-even sales = $625,000 $375,000 = $250,000 3. Targeted net income before taxes is equal to the net income after taxes divided by (1- tax rate). The pretax income is then added to fixed costs and divided by the UCM to find the necessary number of units. $66,000 0.55 = $120,000 net income before taxes Alternative solution: X = number of units to sell
Page 27 of 28 [SP(X) - VC(X) - FC] (1 - T) = NIAT [25X - 15X - 150,000] (1-0.45) = 66,000 Divide both sides by 0.55 10X - 150,000 = 120,000 X = 27,000 units Requirement 4 4. The break-even point is 19,250 units given increases FC and VC. The UCM would decrease to $8 ($25 sales price $17), and FC would increase by $4,000, next year's portion of depreciation ($20,000/5 years). New FC would be $154,000. Alternative solution: 25X 17X 150,000 4,000 = 0 X = 19,250 units Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Solutions Manual to accompany Managerial Accounting, Sixth Canadian Edition. Copyright 2004, by McGraw-Hill Ryerson Limited. Reproduced with permission. Solution 6 Problem 6-11 Requirement 1 1. *$215,000 $500,000 = 43%. 2.
Page 28 of 28 Source: Ray H. Garrison, Eric W. Noreen, G.R. Chesley, and Raymond F. Carroll, Solutions Manual to accompany Managerial Accounting, Sixth Canadian Edition. Copyright 2004, by McGraw-Hill Ryerson Limited. Reproduced with permission.