CHAPTER COST-VOLUME-PROFIT ANALYSIS LEARNING OBJECTIVES Understand the assumptions underlying cost-volume-profit (CVP) analysis Explain the features of CVP analysis Determine the breakeven point and output level needed to achieve a target operating income using the equation, contribution margin, and graph methods Understand how income taxes affect CVP analysis Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty Use CVP analysis to plan fixed and variable costs Apply CVP analysis to a company producing different products Adapt CVP analysis to situations in which a product has more than one cost driver Distinguish between contribution margin and gross margin CHAPTER OVERVIEW Chapter presents the cost-volume-profit (CVP) analysis model Much “what-if” knowledge may be derived from the use of a model, certainly the case with CVP analysis Models are developed from known relationships and used for forecasting CVP uses one cost driver, volume of units produced and sold, and uses the behavior of costs, variable or fixed, in relation to that cost driver As with all models, a complex situation is simplified The assumptions of CVP analysis identify the simplifications made Throughout the chapter, reference is made to changes in the CVP model to allow for more complexity The complexities not render the model useless, they generally require additional factors be considered for producing better predictions Relevant information for strategic and planning decisions can be made readily available The text focuses on accountants providing value for decision makers CVP analysis is a useful tool for providing cost/beneficial information on a timely basis The basic CVP model deserves careful study The last section of the appendix is noteworthy With the emphasis on decision making in the text, the point made about distinguishing between a good decision and a good outcome and/or a good decision and a bad outcome seems especially relevant TEACHING TIP: An excellent article on the value of models is “Going Forward in Reverse” by Einhorn & Hogarth, Harvard Business Review, Jan./Feb 1987, pp 66-70 Cost-Volume-Profit Analysis 27 CHAPTER OUTLINE I I Basic Cost-Volume-Profit (CVP) model A Definition of CVP analysis: examines the behavior of total revenues, total costs, and operating income as changes occur in output level, selling price, variable cost per unit, and/or fixed costs Learning Objective 1: Understand the assumptions underlying cost-volume-profit (CVP) analysis B Assumptions Simplifications of complex relationships a Number of output units only revenue driver and only cost driver b Total costs can be separated into the primary categories of variable costs and fixed costs c Total revenues and total costs are linear within the relevant range (and time period) d Unit selling price, unit variable costs, and fixed costs known and constant e Single product or constant sales mix f Time value of money effects ignored Complexities noted in chapter that affect basic model a Multiple revenue and multiple cost drivers b Lack of linearity Do multiple choice Assign Exercise 3-16 Learning Objective 2: Explain the features of CVP analysis C Features and terminology Income model: Revenues – Expenses = Income Contribution margin: Total revenues – Total variable costs a Calculated per unit: Selling price/unit – Variable cost/unit [Exhibit 3-1] b Calculated as a percent of sales or ratio: Contribution Margin/Sales c Calculated as a total: Sales (Revenues) – Variable costs Multiple-step-type income statement: Rev – VC = CM – FC = OI 28 Chapter Operating income versus Net income a OI + Nonoperating Rev – Nonoperating Costs – Income Tax = NI b Chapter assumes zero for nonoperating revenues and expenses Do multiple choice Assign Exercises 3-17 and 3-20 II Breakeven concept A Definition of breakeven point: quantity of output sold at which total revenues equal total costs Learning Objective 3: Determine the breakeven point and output level needed to achieve a target operating income using the equation, contribution margin, and graph methods B Contribution margin approach to calculation Equation method: (USP x Q) – (UVC x Q) – FC = OI Contribution margin method a Per unit approach that calculates breakeven in units of output [Use algebraic equation UCM x Q = FC + OI —>UCM x Q = Total CM to calculate Q , units, as FC + OI = CM] b Ratio or percentage approach that calculates breakeven in dollars of revenue [Use equation CM% x Revenues = FC + OI—>CM% x Revenues = Total CM to calculate Revenues by dividing both sides by CM%: CM% = CM/Revenues] Graph method: x-axis output units, y-axis dollars; total revenue and total cost lines intersect at breakeven output quantity [Exhibits 3-2 and 3-3] Do multiple choice Assign Exercises 3-21 and 3-23 and Problem 3-34 TEACHING TIP: Exercise 3-23 is a good example to use before studying sales mix This exercise uses an average revenue amount for the calculations When studying sales mix, referencing an “average sales check per customer” provides an illustration of differing products, from a cup of coffee to a full dinner More sales checks for cups of coffee than for full dinners would change the “average” downward C Useful for target income Operating income: FC + Target OI can be divided by UCM for units of output or divided by CM% for dollars of revenue (sales) Learning Objective 4: Understand how income taxes affect CVP analysis Net income: Target OI must be adjusted by incorporating income tax Target net income/(1 – Tax rate) = Target operating income Cost-Volume-Profit Analysis 29 TEACHING TIP: The use of the income statement format may be helpful to some students, Target Operating Income 100%TOI { $40,000} Tax (Tax Rate x TOI) 35% -35%TOI {.35x40,000 14,000} Target Net Income 65%TOI = $26,000 —> TOI = $26,000 / 0.65 = $40,000 Any of the three approaches for calculating breakeven may be used for target income TEACHING TIP: A caution for students when calculating target income, especially if using total rather than unit costs: variable costs in total are variable with respect to volume and will change if output units change or are expected to change Use of an equation with contribution margin is helpful To calculate revenues use the equation, CM% x Revenues = CM in total dollars, or to calculate output units, UCM x Q = CM in total dollars [CM in total dollars in equal to FC + target OI.] Do multiple choice Assign Problem 3-36 D Effect of income taxes: BEP unaffected by income taxes because no tax is no operating income Do multiple choice Assign Problem 3-39 Learning Objective 5: Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty E Useful for decision making Can incorporate changes in total fixed costs, selling price per unit (changes CM per unit), unit variable cost, and units sold Helps managers by estimating long-term profitability of choices Evaluates risk to operating income if original predicted data not achieved III Sensitivity analysis [Exhibit 3-4] A Definitions Sensitivity analysis: “what-if” technique managers use to examine how a result will change if original predicted data not achieved or if an underlying assumption changes Uncertainty: possibility that an actual amount will deviate from an expected amount B Used before committing costs Analysis of changes in operating income for changes underlying assumptions Systematic and efficient approach Allows for calculation of margin of safety: amount of budgeted revenues over and above breakeven revenues 30 Chapter [Appendix] Probability and expected value incorporated Do multiple choice Assign Problems 3-38, 3-40 and 3-41 Learning Objective 6: Use CVP analysis to plan fixed and variable costs II C Highlights risks and returns Highlights risks and returns as fixed costs are substituted for variable costs in cost structure TEACHING TIP: A section in the chapter appendix references a manager’s attitude toward risk (each decision has its own attitude as well as each manager has such an attitude) Following are descriptive phrases for discussing risk attitudes: (1) risk neutral: decision maker weighs each dollar as a full dollar, no more, no less; (2) risk averse: decision maker weighs loss of dollar as greater than gain of dollar; (3) risk seeking: decision maker weighs gain of dollar as greater than loss of dollar Demand for product or service is variable [Exhibit 3-5] Use of operating leverage: effect fixed costs have on changes in operating income as changes occur in units sold (contribution margin)—degree of operating leverage equals contribution margin divided by operating income [Concepts in Action] Do multiple choice Assign Exercise 3-26 TEACHING TIP: Operating leverage is obviously named for the “lever” effect that comes from the use of fixed costs to generate more profit Costs are incurred to generate revenues If the choice exists to incur fixed or variable cost, and fixed is chosen, then variable cost would be less, yielding a larger contribution margin and the possibility of larger profit Once the fixed costs are recovered, the contribution margin is profit This effect can be seen on a breakeven graph The intersecting revenue and total cost lines create equal and opposite angles at the intersection point One can note that the risk (downside) is equal to the reward (upside) The larger the fixed cost, the wider the intersection angles usually: the greater the opportunity for reward, the greater the possibility of loss Cost labels as fixed or variable a Time frame affects costs: shorter the time frame, more costs fixed b Relevant range assumes limits for constancy of total fixed costs or unit variable costs c Specific question/decision affects relevancy of cost classification IV Products and CVP: A complexity Learning Objective 7: Apply CVP analysis to company producing different products A Sales mix: CVP assumption for one product or a constant mix of different products Cost-Volume-Profit Analysis 31 No unique breakeven point when selling a mix of multiple products: each new mix, a new BEP Profit varies even though same total quantity of units sold: Mix with more units of larger dollar amount of contribution margin per unit yields greater profit{affects BEP} Profit varies even though same total dollars of revenue: Mix with more units of larger contribution margin ratio sold yields greater profit Do multiple choice Assign Exercise 3-28 and Problems 3-44 and 3-46 B Service as a product Define “product” or output unit for measurement Use CVP model for relationship between revenues, variable costs and fixed costs Use CVP analysis for prediction and consideration for adjusting operations Learning Objective 8: Adapt CVP analysis to situations in which a product has more than one cost driver C Multiple cost drivers No unique breakeven point CVP model can be adapted by changes to the variable cost for situation but simple formula cannot be used Do multiple choice Assign Exercise 3-30 and Problem 3-43 Learning Objective 9: Distinguish between contribution margin and gross margin D CVP uses contribution margin as opposed to gross margin* on financial accounting income statements Service-sector companies a Costs primarily classified as either variable or fixed for calculating contribution margin b Do not have cost of goods sold so cannot use gross margin emphasis Merchandising-sector companies a Costs are primarily classified as either variable or fixed for calculating contribution margin b Costs are primarily classified as either cost of goods sold or operating costs for gross margin emphasis 32 Chapter c If any fixed costs were included in cost of goods sold, they would be reclassified as operating costs for contribution margin emphasis Manufacturing-sector companies a Costs primarily classified as variable or fixed for calculating contribution margin b Costs primarily classified as manufacturing or nonmanufacturing in calculating gross margin c Variable nonmanufacturing costs above the “margin line” for contribution margin calculation but below for gross margin d Fixed manufacturing costs above the “margin line” for gross margin calculation but below for contribution margin e Fixed manufacturing costs used as per unit cost for cost of goods sold (gross margin) but as total cost for contribution margin For statement comparison purposes costs should be classified with both classifications a Variable manufacturing and variable nonmanufacturing b Fixed manufacturing and fixed nonmanufacturing * Gross margin can be expressed as a total, as an amount per unit, or as a percentage If gross margin is expressed as a percentage the basis could be revenue or cost of goods sold Conversion is simple from one base to the other, but the base must be noted for one to know to convert See TEACHING TIP for conversion TEACHING TIP: Quick conversion calculation for GM as a percentage of CGS or revenue: Revenue 125% 100% Revenue 100% 150% CGS 100% 80% CGS 66.7% 100% Gross margin 25% 20% Gross margin 33.3% 50% Conversion: Divide GM (as a percentage of CGS) by revenue (when CGS is 100%) to convert GM to a percentage of revenue: 25%/125% = 20%; a markup of 25% with a margin of 20% or for GM as a percentage of CGS when originally given as percentage of revenue: 33.3%/66.7% = 50%; a margin of 33.3% with a markup of 50% Do multiple choice 10 Assign Exercise 3-31 V Appendix: Decision models and uncertainty [Exhibit 3-6] A Use of a decision model B Identify events (differentiated from actions) C Consider past experience to project probabilities D Incorporate risk attitude E Distinguish between good decision and good outcome CHAPTER QUIZ SOLUTIONS: 1.a 2.c 3.b 4.a 5.c 6.d 7.b 8.c 9.b 10.d Cost-Volume-Profit Analysis 33 CHAPTER QUIZ Which of the following is not an assumption of cost-volume-profit analysis? a b c d The time value of money is incorporated in the analysis Costs can be classified into variable and fixed components The behavior of revenues and expenses is accurately portrayed as linear over the relevant range The number of output units is the only driver Contribution margin is calculated as a b c d total revenue – total fixed costs total revenue – total manufacturing costs (CGS) total revenue – total variable costs operating income + total variable costs Questions 3–5 are based on the following data: Tee Times, Inc., produces and sells the finest quality golf clubs in all of Clay County The company expects the following revenues and costs in 2003 for its Elite Quality golf club sets: Revenues (400 sets sold @ $600 per set) Variable costs Fixed costs How many sets of clubs must be sold for Tee Times, Inc., to reach their breakeven point? a 400 c 200 d 150 b 500 c 400 d 300 What amount of sales must Tee Times, Inc., have to earn a target net income of $63,000 if they have a tax rate of 30%? a $489,000 b 250 How many sets of clubs must be sold to earn a target operating income of $90,000? a 700 $240,000 160,000 50,000 b $429,000 c $420,000 d $300,000 One way for managers to cope with uncertainty in profit planning is to a b c d use CVP analysis because it assumes certainty recommend management hire a futurist whose work it is to predict business trends wait to see what does happen and prepare a report based on actual amounts use sensitivity analysis to explore various what-if scenarios in order to analyze changes in revenues or costs or quantities 34 Chapter The Beta Mu Omega Chi (BMOC) fraternity is looking to contract with a local band to perform at its annual mixer If BMOC expects to sell 250 tickets to the mixer at $10 each, which of the following arrangements with the band will be in the best interest of the fraternity? a b c d Twin Products Company produces and sells two products Product M sells for $12 and has variable costs of $6 Product W sells for $15 and has variable costs of $10 Twin predicted sales of 25,000 units of M and 20,000 of W Fixed costs are $60,000 per month Assume that Twin achieved its sales goal of $600,000 for September, but fell short of its expected operating income of $190,000 Which of the following descriptions best describes the actual results reported of revenue of $600,000 and operating income of less than $190,000? a b c d $2500 fixed fee $1000 fixed fee plus $5 per person attending $10 per person attending $25 per couple attending Twin sold 50,000 of M and no product W Twin sold more of both products M and W than expected Twin sold more of product W and less of product M than expected Twin sold more of product M and less of product W than expected In the situation of multiple cost drivers, CVP analysis can be a modified so that the various simple formulas can be used by applying them separately to each cost driver b used with the same formulas as used with a single cost driver c changed by incorporating all of the cost drivers into the breakeven formula to calculate the unique point of output at which the company would break even d adapted by incorporating the cost drivers into the calculation of the variable costs 10 Which of the following statements is true? a “Gross margin” can be used only in financial accounting income statements b “Gross margin” implies a different cost classification usage than the term “contribution margin” when used in income statements c “Contribution margin” can be used in place of “gross margin” if management prefers that terminology in their financial statements d Only manufacturing-sector companies use the term “gross margin” in their income statements Cost-Volume-Profit Analysis 35 WRITING/DISCUSSION EXERCISES Understand the assumptions underlying cost-volume-profit (CVP) analysis How helpful is a model, such as CVP analysis, if the assumptions on which it is based seem too simplistic? Even the simplest models can be helpful Models describe known relationships and their use can prevent errors of omission by focusing on basic concepts and interactions as well as enable learning From a simple checklist to the most sophisticated artificial intelligence program, models force one to take certain steps and combine factors in particular ways Airline pilots, even the most experienced, use a checklist before take-off to insure that they did not forget a key item Models or simulations are also helpful in teaching a person to perform a task The CVP analysis model is a cost-effective tool that managers can use for gathering relevant information in the process of making decisions The simple CVP relationships are helpful in strategic and long-range planning decisions, for example Knowing the assumptions of the basic model, one can incorporate changes to refine or particularize for a given situation The need for a more complex model is recognized after using the basic ideas of the CVP analysis The choice of incurring additional costs is supported for gaining significant benefit of improved decisions with a more complicated and expensive approach Explain the features of CVP analysis Why is contribution margin such an important element in CVP analysis? Contribution margin is an effective summary of the reasons that operating income changes as the number of units sold changes Variable costs increase in total as volume of output units sold increase, the same behavior as revenue Contribution margin is the net or “summary” of those two elements, revenues and variable costs If revenues increase due to volume increases, the contribution margin increases A change in the selling price will change the contribution margin as will a change in variable cost per unit Understanding contribution margin can enable one to quickly note that an increase in selling price without a corresponding change in variable cost will increase the “contribution” to fixed cost and income Or a decrease in variable cost without a corresponding decrease in selling price will “contribute” more to income and/or the coverage of fixed costs Using revenues and variable costs as per unit measures, the “contribution” per unit of product sold can provide a shortcut to breakeven calculations or “what-if” questions Each unit of product sold contributes that amount as it “walks out the door.” Contribution margin is the connecting link between the behavior of variable cost and fixed cost It is the amount that “contributes” to covering total fixed costs and providing income In the calculation of number of output units or total revenues to achieve targeted operating income, contribution margin is the pivot point The total amount of contribution margin, fixed costs in total added to targeted operating income as a total, is equal to an amount of contribution margin per unit multiplied by the number of units needed to be sold to achieve that desired amount of income Contribution margin converts total dollars to units 36 Chapter 3 Determine the breakeven point and output level needed to achieve target operating income using the equation, contribution margin, and graph methods How can a company have more than one breakeven point? CVP analysis suggests only one breakeven point because of its assumptions The authors of the text note that there is no unique breakeven point in the case of multiple products and multiple cost drivers Likewise a curved, rather than a straight line depicting the time value with the compounding of interest allows for more than one breakeven point The CVP analysis assumptions preclude the use of these characteristics Economists note at least two breakeven points in graphing revenues and costs The revenue line is depicted as an upward arcing curve to the right intersecting the straight diagonal line of costs, forming a type of bow (as in archery—the bow frame as revenue and the cost line as its cord) The first or lowest point of intersection is the CVP analysis breakeven point The second or upper point of intersection is determined by the relationship in demand, quantity, and price To keep or increase demand for the product, the economic assumption is that the price must be reduced accordingly Reducing the price will tend to lower total revenue even though output quantity (supply) is increasing, which concurrently causes increasing costs CVP analysis recognizes these assumptions by imposing the relevant range and time period constraints The question may be how can a company calculate only one breakeven point when realistically the point at which loss becomes profit, or vice versa, can exist at many turns The value of examining the relationships between revenues and costs enables managers to avoid pitfalls A simple or basic calculation is a good starting point to understanding the complex interactions Understand how income taxes affect CVP analysis What changes to CVP analysis would have to be made if a company did have nonoperating revenues and expenses? The presence of nonoperating revenues and expenses would not change CVP analysis CVP analysis is an operations concept and accordingly uses operating income Tax effects on operating decisions are important information for managers and can be incorporated by using net income The text assumes the nonoperating items to be zero for ease of computation Most nonoperating items are noted net of tax, causing no change to the income tax on operations The use of the subtotal “Income before income taxes” is used to compute the amount of income taxes in arriving at net income “Income before income taxes” would be defined as target operating income + nonoperating revenues – nonoperating expenses Target net income = (Income before income taxes) – [(Income before income taxes) x (Tax rate)] Target operating income +Nonoperating revenue −Nonoperating expense Income before income tax Income tax expense (30%) Net income (targeted) $440,000 80,000 20,000 $500,000 150,000 $350,000 100% 30% 70% Cost-Volume-Profit Analysis 37 Explain CVP analysis in decision making and how sensitivity analysis can help managers cope with uncertainty What ethical guidelines require a management cost accountant to use sensitivity analysis when supplying a decision maker with information obtained from CVP analysis? The following statements taken from the IMA Standards of Ethical Conduct for Management Accountants may be used as discussion points: Competence Prepare complete and clear reports and recommendations after appropriate analysis of relevant and reliable information Integrity Communicate unfavorable as well as favorable information and professional judgments or opinions Objectivity Communicate information fairly and objectively Disclose fully all relevant information that could reasonably be expected to influence an intended user’s understanding of the reports, comments, and recommendations presented Use CVP analysis to plan fixed and variable costs Can the use of CVP analysis change a cost from variable to fixed or vice versa? The use of CVP analysis can cause a manager to consider alternative cost structures The analysis does not change the cost classification for that is based upon the total cost behavior in proportion to the volume of cost driver, a causal relationship However, from working through several scenarios of volume levels and the impact each would have on revenues and cost within the existing company cost structure, a manager might make specific choices to incur costs in such a way as to change the company’s cost structures The cost structure could be changed from predominantly variable costs to more fixed costs, for example One industry, in particular, has become even better known because of its accounting practices: Hollywood Movies that seemingly are box office hits, grossing fabulous sums of money, fail to show any net profit Movies such as “Forrest Gump,” “Coming to America,” and “Batman” are a few that represents “net profits” accounting Popular actors and actresses along with directors and producers receive a percentage of the movies’ gross receipts [variable costs before contribution margin] and then have other large costs, such as production, distribution and marketing, and interest, to deduct after that After all of those deductions, even with the highest-grossing films, net profit is nonexistent or the film shows a loss Those who are able to get a share of the gross receipts find the pictures to be highly profitable, but those who are to share in the net profit often end up with nothing 38 Chapter Apply CVP analysis to a company producing different products In his story of Don Quixote, Cervantes stated “Forewarned forearmed.” How is this quote applicable to CVP analysis? With the help of CVP analysis, a manager can develop an understanding of trade-offs when dealing with multiple products or sales mix The manager can be “forewarned” that the downturn in sales of one product in favor of another would have unfavorable consequences on income Through CVP analysis the manager can know to work to boost sales of the products with the higher contribution margins as well as work to make each product more profitable The manager can also consider combinations of big sale products with lesser contribution margins teamed with products that have greater margins but not sell as well Perhaps as a pair or group (and higher selling price), more amount of margin could be made with the same level of sales Being “armed” with a variety of options helps the manager to make better decisions Adapt CVP analysis to situations in which a product has more than one cost driver Does a company have multiple cost drivers because they have multiple products? Multiple products could create the need to recognize multiple cost drivers but production is not the sole determinant of the need for multiple cost drivers Cost-volume-profit analysis is primarily focused on operating income Any costs are candidates for analysis and the cause of what “drives” them Distinguish between contribution margin and gross margin Is breakeven point calculation exclusive of the contribution margin approach to calculating income? (See Appendix to Chapter 9) Breakeven point calculations are easier from the perspective of classifying costs as either fixed or variable rather than mixing those behaviors through the manufacturing/nonmanufacturing classification of the gross margin approach of cost of goods sold The changing of the fixed manufacturing costs from a per unit (product) cost under gross margin emphasis to a total cost for contribution margin emphasis means that a fixed manufacturing cost changes from a product cost to a “period” cost Fixed costs as a product unit cost means that if the amount of product inventory (work in process and finished goods) changes within a time period, the amount of fixed cost considered an expense (CGS) would differ based on the level of inventory Using fixed manufacturing costs as a total for the contribution approach, and therefore unchanging, means breakeven analysis does not need to factor in changes in product inventory This differentiation of how to account for fixed costs is a major difference between the gross margin and contribution margin approaches to calculating operating income If production is different than sales, the income amount differs from income statement to income statement If absorption costing is used, income is a function of both sales and production Therefore, changes in inventory levels can dramatically affect income The breakeven point is not unique There may be several combinations of sales and production that produce an income of zero The breakeven formula for absorption costing is: BEP in units Q= Total FC incurred during period + Fixed Overhead Rates (BEP in units Q – Units Produced) Unit Contribution Margin If all units produced are sold, the amount of fixed cost included in inventory is equal to the total fixed cost incurred The total fixed cost incurred would then be written off as cost of goods sold for gross margin emphasis as well as written off as total fixed manufacturing cost for contribution margin emphasis If some units produced are not sold, then some of the fixed manufacturing costs would be housed with the unsold inventory for gross margin emphasis The contribution margin emphasis would write off all of the cost Cost-Volume-Profit Analysis 39 DEMONSTRATION PROBLEM Dey and Knight are the owners of the Modern Processing Company and the Oldway Manufacturing Company, respectively These companies manufacture and sell the same product, and competition between the two owners has always been friendly Cost and profit data have been freely exchanged Uniform selling prices have been set by market conditions Dey and Knight differ markedly in their management thinking Operations at Modern are highly mechanized, and the direct labor force is paid on a fixed-salary basis Oldway uses manual hourly paid labor for the most part and pays incentive bonuses Modern’s salesmen are paid a fixed salary, whereas Oldway’s salesmen are paid small salaries plus commissions Mr Knight takes pride in his ability to adapt his costs to fluctuations in sales volume and has frequently chided Mr Dey on Modern’s “inflexible overhead.” During 2002, both firms reported the same profit on sales of $100,000 However, when comparing results at the end of 2003, Mr Knight was startled by the following results: MODERN Sales revenue Costs and expenses Net income Return on sales 2002 $100,000 90,000 $ 10,000 10% OLDWAY 2003 $120,000 94,000 $ 26,000 21 2/3% 2002 $100,000 90,000 $ 10,000 10% 2003 $150,000 130,000 $ 20,000 13 ½% On the assumption that operating inefficiencies must have existed, Knight and his accountant made a thorough investigation of costs but could not uncover any evidence of costs that were out of line At a loss to explain the lower increase in profits on a much higher increase in sales volume, they have asked you to prepare an explanation You find that fixed costs and expenses recorded over the two-year period were as follows: Modern Oldway $70,000 each year $10,000 each year REQUIRED Prepare an explanation for Mr Knight showing why Oldway’s profits for 2003 were lower than those reported by Modern despite the fact that Oldway’s sales had been higher Redo the income statements emphasizing contribution margin Calculate breakeven point for each company Calculate operating leverage at revenue level of $100,000 Calculate the volume of sales that Oldway would have to have had in 2003 to achieve the profit of $26,000 realized by Modern in 2003 Comment on the relative future positions of the two companies when there are reductions as well as increases in sales volume [SEE PAGE AFTER SOLUTION FOR GRAPH OF TWO COMPANIES] 40 Chapter SOLUTION FOR DEMONSTRATION PROBLEM: Redo the income statements emphasizing contribution margin MODERN Sales revenue Variable costs Contribution margin Fixed costs Operating income OLDWAY 2003 $120,000 24,000 $ 96,000 70,000 $ 26,000 2002 $100,000 80,000 $ 20,000 10,000 $ 10,000 2003 $150,000 120,000 $ 30,000 10,000 $ 20,000 Calculate breakeven point for each company Fixed costs/CM ratio = 2002 $100,000 20,000 $ 80,000 70,000 $ 10,000 Modern: $70,000/80% = $87,500 Oldway: $10,000/20% = $50,000 Calculate operating leverage at revenue level of $100,000, the point of indifference (either approach gives same income) Contribution margin Operating income Degree of operating leverage MODERN OLDWAY $80,000 $10,000 $80,000/$10,000 = $20,000 $10,000 $20,000/$10,000 = An increase of 20% in sales ($20,000) and contribution margin ($16,000) for Modern results in an 8.0 times that percentage change in operating income, an increase of 160% or $16,000 increase For Oldway, an increase of 50% in sales ($50,000) and contribution margin ($40,000) results in a 2.0 times that percentage change in operating income, an increase of 100% or $10,000 Calculate the volume of sales that Oldway would have to have had in 2003 to achieve the profit of $26,000 realized by Modern in 2003 Sales – Variable costs – Fixed costs = $26,000 Sales - 80(Sales) - $10,000 = $26,000 20 Sales = $36,000 Sales = $180,000 100% Sales 80% Variable costs 20% Contribution margin Fixed costs Operating income $180,000 144,000 $ 36,000 10,000 $ 26,000 Comment on the relative future positions of the two companies when there are reductions as well as increases in sales volume If the companies experience reductions in sales volume, Modern will suffer loss when the sales volume drops below $87,500, whereas Oldway will remain profitable until sales drop below $50,000 Modern’s loss will be larger in absolute amount of dollars than Oldway’s Oldway has a greater margin of safety than Modern for Oldway can watch sales drop further before experiencing a loss situation However, if sales volume continues to increase, Modern can use its fixed costs to “leverage” income to higher levels than Oldway If sales volume does increase by 80% to $180,000, Modern can use the fixed cost “lever” to raise income by (80% x = 640%) $64,000 to $74,000 As shown in #4 above, Oldway would gain only $16,000 of income (80% x = 160%) for income of $26,000 Each company equalizes risk with reward Modern has taken a riskier approach by investing more money in fixed cost-type items but can experience the possibility of higher reward Oldway, on the other hand, has selected to take less risk and therefore forgo the possibility of greater reward [See graphs for angles at intersection of cost and revenue lines.] Cost-Volume-Profit Analysis 41 Operating Leverage $ Profit opens up Revenues BEPs OLDWAY costs MODERN costs Fixed costs as lever to change angle at BEP Point of Indifference Volume “The use of fixed costs to lever open profit & expose loss possibilities” 42 Chapter COMPARING INCOME STATEMENTS USING TWO DIFFERENT COSTING METHODS Variable Costing compared to Traditional For each of the following independent cases, find the unknowns designated by the capital letters Case Direct materials used Direct manufacturing labor Variable marketing, distribution, and customer-service costs Fixed manufacturing overhead Fixed marketing, distribution, and customer-service costs Gross margin Finished goods inventory, January 1, 2002 Finished goods inventory, December 31, 2002 Contribution margin (dollars) Revenues Direct materials inventory, January 1, 2002 Direct materials inventory, December 31, 2002 Variable manufacturing overhead Work-in-process inventory, January 1, 2002 Work-in-process inventory, December 31, 2002 Purchases of direct materials Breakeven point (in revenues) Cost of goods manufactured Operating income (loss) $ H H 30,000 K I J 25,000 0 30,000 100,000 12,000 5,000 5,000 0 15,000 66,667 G L Case $ 40,000 15,000 T 20,000 10,000 20,000 5,000 5,000 V 100,000 20,000 W X 9,000 9,000 50,000 Y U (5,000) Note to instructor [solution next page]: This problem provides a review of Chapters and by comparing the traditional income statement used for financial accounting (Chapter 2) with the variable costing income statement introduced in Chapter Because there are no changes in the amounts of beginning to ending inventory for Work-in-Process Inventory and for Finished Goods Inventory, the amount of Cost of Goods Manufactured is the same as the Cost of Goods Sold The change in amount from beginning to ending of Direct Materials Inventory affects the Direct Materials Used, a component of the manufacturing costs, but it is also a variable cost so the total of manufacturing costs is unchanged by the change in inventory amount Problem 9-33 provides insight for consideration of changes in the WIP and FG inventories and the problem of building inventory to manufacture profit under absorption (traditional) costing A similar problem is included in Chapter of this manual, The B.E Company Cost-Volume-Profit Analysis 43 Solution to Cases and Comparing income statements using two different costing methods Case illustrated [“Given” numbers from problem in bold] Revenues $100,000 Revenues $100,000 Variable manufacturing costs: §Cost of goods sold: *Direct materials 22,000 *Direct materials 22,000 Direct mfg labor 30,000 Direct mfg labor 30,000 57,000 Var indirect mfg 5,000 Var indirect mfg 5,000 Fixed indirect mfg.*** 18,000 _ Total var mfg costs 57,000 §Cost of goods sold 75,000 [G] Var nonmfg costs:** 13,000 [K] Total variable costs 70,000 Contribution margin 30,000 Gross margin 25,000 Fixed costs: Nonmanufacturing costs: Fixed indirect mfg.*** 18,000 [I] Var nonmfg.** 13,000 Fixed nonmfg †† 2,000 [J] Fixed nonmfg †† 2,000 Total fixed costs† 20,000 Total nonmfg costs 15,000 Operating income $ 10,000 [L] Operating income $ 10,000 Breakeven point =Fixed Costs ÷ CM% of Rev Schedule of Cost of Goods Manuf & Sold 66,667 = FC / 66,667 * 0.3 = 20,000 = FC† *Direct materials inventory: Total FC = 20,000 – Mfg 18,000 = 2,000 Nonmfg †† Beg $12 + Purch $15 – End $5 = Used $22 [H] § No change in WIP inventory and finished goods inventory, Cost of Goods Manufactured = Cost of Goods Sold Case illustrated [“Given” numbers from problem in bold] Revenues $100,000 Revenues $100,000 Variable manufacturing costs: Cost of goods sold: Direct materials 40,000 Direct materials 40,000 Direct mfg labor 15,000 Direct mfg labor 15,000 Var indirect mfg 5,000* [X] Var indirect mfg 5,000* 75,000 Fixed indirect mfg 20,000 Total var mfg costs 60,000 Cost of goods sold 80,000 [U] § Var nonmfg costs: 15,000** [T] Total variable costs 75,000 Contribution margin 25,000 † [V] Gross margin 20,000 Fixed costs: Nonmanufacturing costs: Fixed indirect mfg 20,000 Var nonmfg 15,000** Fixed nonmfg 10,000 Fixed nonmfg 10,000 Total fixed costs 30,000 Total nonmfg costs 25,000 Operating income $ (5,000) Operating income $ (5,000) Breakeven point =Fixed Costs ÷ CM% of Rev Schedule of Cost of Goods Manuf & Sold BEP = 30,000 /CM% 120,000 = 30,000/0.25 †[Y] DM: Beg20 + Purch50 – Used40 =End30[W] § No change in WIP inventory and finished goods inventory, Cost of Goods Manufactured = Cost of Goods Sold 44 Chapter Chapter Worksheet for Comparing Income Statements (Note the primary cost classifications used in each income statement) Variable or Fixed Costs Manufacturing or Nonmanufacturing Contribution Income Statement Emphasizing Contribution Margin Revenues Financial Accounting Income Statement Emphasizing Gross Margin Revenues Variable manufacturing costs: Cost of goods sold: Direct materials Direct materials Direct manufacturing labor Direct manufacturing labor Variable indirect manufacturing Variable indirect manufacturing Fixed indirect manufacturing Total variable manufacturing costs Cost of goods sold Variable nonmanufacturing costs: Total variable costs Contribution margin Gross margin Fixed costs: Nonmanufacturing costs: Fixed indirect manufacturing Variable nonmanufacturing Fixed nonmanufacturing Fixed nonmanufacturing Operating income Operating income Breakeven point =Fixed Costs ÷ CM% of Rev Schedule of Cost of Goods Manuf & Sold (Note the relationship of fixed indirect manufacturing costs in calculating the margins.) Cost-Volume-Profit Analysis 45 Additional Considerations for Problem 3-28: Zapo 1-2-3 Problem 3-28 in the text asks only about units of product sold for calculating the breakeven point The “New Customers” group returns 57.14% on sales dollar ($120/$210) whereas the “Upgrade Customers” group returns 66.67% on each sales dollar ($80/$120) The return on sales dollar is maximized by selling the upgrades rather than to new customers Many questions arise in this situation: Can only a certain number of units be sold—market constraint? Can only a certain number of units be produced—capacity constraint? How is sales performance measured—number of units sold, amount of revenue dollars, amount of contribution dollars? Why is variable advertising so high for new customers compared to upgrade customers—when it is essentially the same product? What is the size of the upgrade group, and what is needed in terms of new customers to maintain a profitable base of customers? What is the relationship with upgrade customers? Can the same type of relationship with upgrade customers be maintained if new customers outnumber them—jeopardizing all customer relationships? If the problem is recast to look at sales dollars rather than units, some thought-provoking information is available See accompanying spreadsheet analysis of comparison of units and sales dollars For every “New Customer” unit lost or not sold, one and three-fourths units need to be sold to “Upgrade Customers” to maintain the same dollars of sales This requires more units to be sold If this is possible for the company to do, then more profit is realized [Obviously, the company would not intentionally forgo a sale to a new customer if such a sale were possible.] The “Upgrade” sold in replacement of a “New” is calculated as shown: New Sales $210 V.C 90 C M $120 100.00% 42.86% 57.14% Upgrade replacement $120 + $90 = $210 100.00% 40 + 30 = 70 33.33% $ 80 + $60 = $140 66.67% The difference of $20 more for the “75% replacement” ($210/$120 = 1.75%) equates to $26.67 per full replacement unit If the company sells one unit more than the total sold using the unitsbasis, then their profit is $26.67 more than it would have been under the units-basis The accompanying spreadsheet shows this relationship A company would want to not only get the most sales dollars but also the most profit from each of those sales dollars Noting the relationship of margin per sales dollar for products can be meaningful 46 Chapter Spreadsheet for Problem 3-28 –Excel spreadsheet in separate file Cost-Volume-Profit Analysis 47 SUGGESTED READINGS Huka, S., Luft, J & Ballow, B., “Second-Order Uncertainty in Accounting Information and Bilateral Bargaining Costs,” Journal of Management Accounting Research (2000) p.115 [25p] Maher, M., “Management Accounting Education at the Millennium,” Issues in Accounting Education (May 2000) p.335 [12p] Tambrino, P., “Contribution Margin Budgeting,” Community College Journal of Research and Practice (January 2001) p.29 [8p] Yunker, J., “Stochastic CVP Analysis with Economic Demand and Cost Function,” Review of Quantitative Finance and Accounting (September 2001) p.127 [23p] 48 Chapter