To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter Cost-Volume-Profit Analysis LEARNING OBJECTIVES Chapter addresses the following questions: Q1 Q2 Q3 Q4 Q5 Q6 What is cost-volume-profit (CVP) analysis, and how is it used for decision making? How are CVP calculations performed for a single product? How are CVP calculations performed for multiple products? What is the breakeven point? What assumptions and limitations should managers consider when using CVP analysis? How are margin of safety and operating leverage used to assess operational risk? These learning questions (Q1 through Q6) are cross-referenced in the textbook to individual exercises and problems COMPLEXITY SYMBOLS The textbook uses a coding system to identify the complexity of individual requirements in the exercises and problems Questions Having a Single Correct Answer: No Symbol This question requires students to recall or apply knowledge as shown in the textbook This question requires students to extend knowledge beyond the applications e shown in the textbook Open-ended questions are coded according to the skills described in Steps for Better Thinking (Exhibit 1.10):  Step skills (Identifying)  Step skills (Exploring)  Step skills (Prioritizing)  Step skills (Envisioning) To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-2 Cost Management QUESTIONS 3.1 A mixed cost function includes both fixed and variable costs If there are fixed costs in the cost function, then total costs will increase at a smaller rate than the increase in total sales volume If there are variable costs in the cost function, then total costs will increase with total sales volume When there is a combination of fixed and variable costs, a 10% volume increase will increase total costs by less than 10% because only the increase in variable cost is proportionate to volume; the fixed cost does not change with volume 3.2 The weighted average contribution margin per unit is calculated only when performing CVP analysis for multiple products There are two ways to calculate it: (1) Calculate the total contribution of all products by subtracting total variable costs from total revenues Then calculate the weighted average contribution margin per unit by dividing the total contribution margin by the total number of units (the sum of units for all products) (2) Calculate the sales mix for each product by dividing the number of units sold for that product by the total number of units sold for all products Calculate the contribution margin per unit for each product by subtracting that product’s variable cost from its revenues and dividing the result by that product’s number of units sold Then calculate the weighted average contribution margin per unit by summing the following computation for all products: Each product’s sales mix percentage times its contribution margin per unit 3.3 The firm has only variable costs and no fixed costs If there were fixed costs, income would increase by more than 20% when sales increase by 20% 3.4 None The firm does not pay income taxes at the breakeven point 3.5 Assumptions: Fixed costs remain fixed, variable costs per unit or as a percentage of revenue remain constant, selling prices per unit remain constant, the sales mix remains constant, and operations are within a relevant range where all of these assumptions are met These are very strong assumptions There is always some variation in fixed costs because they include costs such as electricity that varies with weather In addition, organizations often get or give volume discounts, so variable costs and prices per unit may change at high volumes However, results using these assumptions are accurate enough for general planning and decision making purposes 3.6 The margin of safety percentage and degree of operating leverage are related as follows Margin of Safety Percentage Degree of Operating Leverage Degree of Operating Leverage Margin of Safety Percentage To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-3 As the degree of operating leverage gets larger (a higher proportion of fixed costs), the margin of safety percentage gets smaller, and vice versa 3.7 The cost function is assumed to be linear over a relevant range If there are volume discounts, the cost function becomes piece-wise linear and the range of operations within which the organization is performing must be taken into account in CVP analysis The level of operations must be matched with the appropriate part of the function Each piece can be considered as a separate relevant range, and the estimated level of activity needs to be matched with the appropriate relevant range Otherwise, the analysis will either understate or overstate variable costs 3.8 Sales mix is the specific proportion of total sales of each type of good or service that is sold A simple example was presented in the chapter for an ice cream store Usually about 15% of revenue was from beverages and the rest from ice cream products As the proportion of specific products sold changes, the contribution margin ratio changes because the contribution per unit is different for the different products in the sales mix 3.9 CVP refers to changes in income over the relevant range of activity; as such, it includes the notion of breakeven Breakeven is more narrowly constructed; it focuses on only one outcome—the single point at which total revenue equals total cost 3.10 By definition, the margin of safety is the difference between expected unit sales and breakeven unit sales If expected unit sales are below breakeven unit sales, the margin of safety will be negative 3.11 CVP analysis can be used for planning purposes such as budgets, product emphasis, setting prices, setting activity levels, setting work schedules, purchasing raw materials, setting levels for discretionary costs such as advertising and research and development It can also help with monitoring operations, and analyzing the operating leverage of an organization 3.12 To make decisions about advertising costs, accountants predict the amount of cost to be incurred and predict the increase in sales CVP analysis is then used to determine whether the increase in cost is equal to or greater than the increase in contribution margin from additional units sold 3.13 Good managers are likely to always ask for sensitivity analysis because uncertainty about sales volumes and other factors always exists However, when unanticipated changes in the business environment or consumer preferences arise, managers will be even more interested in sensitivity analysis By analyzing a variety of scenarios, managers can respond more quickly to unanticipated changes To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-4 Cost Management EXERCISES 3.14 Target Profit, Not-For-Profit Breakeven A Information is given on a per unit basis, so use the following equation: profit = (p-v)q – F $1,000 = ($7 per gift basket – $2 per gift basket)*Q - $5,000 $6,000 = ($5 per gift basket)*Q Q = $6,000/$5 per gift basket = 1,200 gift baskets B This problem is about a not-for-profit organization Many not-for-profit organizations provide services or sell products at a loss and use donations or grants to cover the losses As students approach problems in this textbook, they should think briefly about the type of organization in the problem to help them solve it This problem is a breakeven problem with a unit cost of $7.64 and unit revenue of $4.64, or a unit contribution margin (loss) of $(3.00) In a for-profit organization, these numbers would indicate that the company loses money on each unit it sells In a not-for-profit, it may be appropriate to sell services at a loss, as long as another source of funds covers the loss In this problem, the clinic receives a grant from the city, so there is ―fixed‖ revenue in addition to the fees collected Taking the grant into account, the breakeven is: = ($4.64 - $7.64)*Q + $460,000 grant - $236,000 fixed cost = $-3*Q +$224,000 Solving for Q: 3Q = $224,000 Q = 74,667 patients To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-5 3.15 CVP Graph A CVP Graph 3.15(A) Total Revenue Total Cost $15,000 Dollars $12,000 $9,000 $6,000 $3,000 $0 500 1,000 1,500 2,000 Number of Gift Baskets The revenue line is $7 times number of baskets and represents total revenue from units sold The cost line intersects the intercept at $5,000 reflecting the fixed cost The slope is 2, which represents the variable cost The breakeven occurs at 1,000 gift baskets Total revenues exceed total costs by $1,000 at 1,200 gift baskets B CVP Graph 3.15(B) Total Revenue Total Cost $1,600,000 Dollars $1,200,000 $800,000 $400,000 $0 37,500 75,000 112,500 150,000 Number of Patient Visits Total revenue is the sum of the grant plus patient fees Unlike most CVP graphs, the breakeven point is the maximum volume before the clinic incurs a loss The grant To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-6 Cost Management exceeds fixed costs, so the clinic has a surplus up the breakeven point Because the clinic’s contribution margin is negative, the surplus decreases by $3 per patient visit After the breakeven point of 74,667 patient visits, the clinic incurs losses 3.16 Cost Function, Breakeven A This problem gives information in units, so use the formula TC = v*q + F to determine variable cost The average cost must first be turned into total cost: Total cost for 1,200 units is $234*1,200 = $280,800 Total cost for 1,400 units is $205*1,400 = $287,000 Use the two-point method (change in cost divided by change in volume) to determine the variable cost: Variable cost = (287,000 – 280,800)/(1,400 – 1,200) V = $31 Notice that the information about profit is not used because it is irrelevant for this problem Recognizing and discarding irrelevant information is an important skill B Turn sales into units and use profit = (P-V)*Q – F Calculate the number of units sold: Revenue / Selling price per unit = Number of units $10,600/$0.25 per unit =42,400 units Variable cost is $0.12 plus selling costs of $0.02 = $0.14 per unit Use the breakeven equation, and then solve for the unknown amount of fixed costs: = ($0.25 - $0.14)*42,400 – F = $4,664 – F F = $4,664 C There can only be one breakeven point within the relevant range, so the breakeven point is first calculated for the first range If the result is within that range, no additional calculations are needed However, if the breakeven point is not in the first range, then calculations must be made for the next range In the relevant range < Q < 200, the breakeven point is calculated as: = ($300 - $200)*Q - $24,000 Q = 240 units This result is outside of the relevant range, so it is not a feasible solution To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-7 In the relevant range 200 < Q, the breakeven point is calculated as: = $100*Q - $36,000 Q = 360 units This result is in the relevant range, so it is the breakeven point 3.17 The Martell Company A Profit (loss) before taxes is: $5(1,000,000) - $4.50(1,000,000) -$ 600,000 = $500,000 - $600,000 = $(100,000) B Solving for price at target profit of $25,000: 1,000,000*P - $4.50(1,000,000) - $600,000 = $25,000 1,000,000*P = $5,125,000 P = $5.125 The firm needs to have an average selling price of $5.125 to earn $25,000 on sales of 1,000,000 units This problem can be used to raise the issue of predatory pricing versus aggressive competition 3.18 RainBeau Salon A Cost Hair dresser salaries Manicurist salaries Supplies Utilities Rent Miscellaneous Total Fixed $18,000 16,000 400 1,000 2,963 $38,363 Variable $0.500 0.325 $0.825 TC = $38,363 + $0.825*appointments Explanations: Salaries: The amount of salaries in May is used to predict the next month because there was a cost-of-living increase To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-8 Cost Management Supplies: An examination of the pattern in supplies costs reveals that for April and May supply cost was $0.50 per appointment The cost was higher in March, but it is best to use the most current information Students may have averaged the three months for $0.52 per month, or they could have used the high-low method which gives $0.50 with no fixed costs Utilities: Because weather probably drives most of utilities cost for this business, this solution uses the prior month’s utilities to predict next month’s cost Miscellaneous: An examination of miscellaneous costs reveals that while it increases as volumes increase, it does not so proportionately (as did supplies) For this solution the high-low method is used Variable cost = $0.325 [($3,580 - $3,450)/(1,900 – 1,500)] Using TC = F +VC*Q and solving for F gives a fixed cost of $2,963 [$3,450 = F + ($0.325*1,500)] B = ($25.00 - $0.825)Q - $38,363 = $24.175*Q - $38,363 Q = 1,587 appointments 3.19 Madden Company A Divide sales and variable costs by 160,000 to get the per-unit selling price of $50 and the variable cost per unit of $12.50 Then breakeven formula is $50*Q - $12.50*Q - $3,000,000 = $0 $37.5*Q = $3,000,000 Q = 80,000 units B Variable costs are $12.50 per unit/$50.00 per unit = 25% of revenue Breakeven in sales, where TR = total revenue: TR - 0.25*TR - $3,000,000 = $4,500,000 0.75*TR= $7,500,000 TR = $10,000,000 C Target after-tax profit 0.10*$36,000,000 = $3,600,000 After-tax income = (1-0.40)*before tax income To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-9 Combining these calculations: $3,600,000 = 0.60*before tax income Before-tax income = $6,000,000 CVP calculation: TR- 0.25*TR - $3,000,000 = $6,000,000 0.75*TR = $9,000,000 TR = $12,000,000 3.20 Laraby Company A Selling price per unit = $625,000/25,000 units= $25/unit Variable cost per unit = $375,000/25,000 units= $15/unit Breakeven point $25*Q – $15*Q - $150,000 = $0 Q = 15,000 units B Adjust the after-tax income target to a before-tax income target Income before tax*(1 - 45) = $77,000 Income before tax*0.55 = $77,000 Income before tax = $140,000 Then solve for units at target profit: $25Q- 15Q - 150,000 = $140,000 Q = 29,000 units C Current variable cost Less old component Plus new component New variable cost $15.00 (2.50) 4.50 $17.00 Solve for breakeven where $25*Q – $17*Q - $153,000 = $0 Q = 19,125 units Current fixed cost Plus depreciation on new machine $18,000/6 New fixed cost $150,000 3,000 $153,000 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-10 Cost Management D Solve for target profit where: $25*Q – $17*Q - $153,000 = $100,000 (before tax) Q = 31,625 units E Current contribution margin ratio = ($25 – $15)/$25 = 40% New price: P - $17 = 0.40*P Rearrange terms: 0.60*P = $17 P = $28.33 3.21 Dalton Brothers A First determine the pretax income necessary to obtain the $150,000 target net income The company is subject to two income tax rates The first $40,000 of taxable income is taxed at 15%, and income over that amount is taxed at 40% Thus, after-tax income is calculated after subtracting two tax amounts Assume π = Target pretax income π - [0.15 x $40,000 + 0.40*(π - $40,000)] = $150,000 π - (6,000 + 0.4 π - 16,000) = $150,000 0.6 π + 10,000 = $150,000 π = $233,333.33 Now total revenue (TR) can be calculated: TR - 0.60*TR - $250,000 = $233,333.33 0.40*TR = $483,333.33 TR = $1,208,333.33 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-28 Cost Management It is likely that Joe may need to advertise He also may need a receptionist in the office during business hours He has not included regulatory costs such as business licenses, employment and property taxes, and any local fees for services Joe has not considered insurance or employee benefit costs Students may have identified other costs as well Joe cannot be certain that his estimated sales volume is correct because he does not know what the local and regional competition might be, and he does not know whether most of his sales will happen during holiday seasons Unanticipated fluctuations are also likely to occur for discretionary products such as clocks Furthermore, he does not have experience selling the clocks full time, so he might be overestimating demand for the clocks C Because Joe likes to make the clocks, he is biased toward starting this business Therefore, he is likely to overestimate revenues and underestimate costs Part B.2 above already identified a number of costs that he has overlooked D Uncertainties and potential biases reduce the quality of the information used as inputs for the CVP analysis, thus reducing the quality of the CVP information As a result, an objective person would be skeptical of the CVP results and would potentially seek higher quality information For example, market research might be used to increase the quality of revenue estimates E There is no one answer to this part Sample solutions and a discussion of typical student responses will be included in assessment guidance on the Instructor’s web site for the textbook (available at www.wiley.com/college/eldenburg) 3.35 Jasmine Krishnan A Usually, sensitivity analysis is performed to determine how sensitive profits are to changes in assumptions such as estimated prices, costs and volumes of sales Sensitivity analysis helps decision makers understand the range of operations that could be expected, both under normal conditions and under best and worst case scenarios B Jasmine is excited about her idea She probably also believes that setting up these trips would be quite a lot of fun Therefore, she may be over-optimistic in her beliefs about future operations When people find an alternative in which they are highly interested, they become biased toward that alternative and choose assumptions that are likely to lead to a positive decision about that alternative In addition, they may interpret results more positively than if they were not biased Jasmine would need to underestimate insurance or other costs or overestimate sales for this business venture to be attractive to investors If she does this, she is biasing the information C If the brochure contains biased information, the quality of information is low Potential investors who rely on the brochure would be given misleading information Thus, the To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-29 quality of potential investor decisions would be low unless they seek and obtain more objective sources of information D The ethical problem is that the biased information misleads potential investors to believe that the new venture has a higher probability of success than it actually has Some investors may rely on Jasmine to return their investments in the future, but she may not succeed and may not be able to return the investment or any return on it Most investors have a range of choices and consider both the investment return and risk as they compare their choices By biasing the information, Jasmine would also bias the decision making process for her potential investors; they may invest in a project that is more risky than their other investments without realizing the potential consequences of this decision This is unfair to them and unethical E Jasmine needs to present the most objective set of assumptions possible in her calculations so that her investors can make the best decisions for their own welfare Sensitivity analysis showing realistic best and worst case scenarios will help investors identify more accurately the risk they are undertaking by investing in this venture The quality of their decision making will be greatly improved 3.36 Small Business Owners A Many small business owners have no business experience or education They not know any of the techniques needed for high quality decisions B Because risk of loss for small businesses is the risk of loss of their personal cash flows, owners need to fully understand the consequences of their choices on profits In addition, a large proportion of new businesses fail Therefore, CVP analysis is highly useful CVP analysis can help owners more thoroughly consider the quality of information they use to estimate future results and recognize the risks of their decisions They are also able to perform sensitivity analysis to reduce elements of surprise from changes in future plans and results They can respond more quickly to changes in their operating environment, increasing their chances of success C Student answers to this question will vary depending on the web sites they locate and explore D Student memos will vary, but they should include the following in simple, clear language: Developing CVP analysis forces decision makers to estimate future revenues, costs, and volumes, which is good for small businesses because of the uncertainty in their operating environments Using sensitivity analysis increases the ability of owners to identify risk and respond to changes in their operating environment To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-30 Cost Management CVP analysis also acts as a budget or plan for future operations Small business owners may not believe they need a plan, but most businesses need to plan Provide an overview of the process of using CVP analysis, including identification of the estimates that must be developed, the formulas used, and the types of sensitivity analysis that could be performed Recommendations for setting up a spreadsheet to perform CVP analysis 3.37 Wildcat Lair [Note: This problem contains the same data is problem 2.28 in Chapter 2, which requires students to determine a cost function The cost function computations shown in Part A below are identical to the solution for problem 2.28.] A Before calculating the breakeven points and degree of operating leverage, it is first necessary to create the cost function The Lair’s costs are categorized as follows: Fixed Purchases of prepared food Serving personnel Cashier Administration University surcharge Utilities Totals $ Variable $21,000 30,000 5,500 10,000 1,500 $47,000 7,000 _ $28,000 Total revenue is the most likely cost driver for both variable costs Food costs are likely to vary proportionately with sales, and the University surcharge is specifically based on sales Because revenue is the cost driver for both variable costs, total revenue (TR) instead of quantity (Q) can be used in the cost function: Variable cost = $28,000/$70,000 = 0.40, or 40% or revenue Combining fixed and variable costs, the cost function is: TC = $47,000 + 40%*Total revenue Given the cost function, the university’s breakeven point is: $47,000/($42,000/$70,000) = $47,000/0.6 = $78,333 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-31 Wildcat Lair’s breakeven point is: $47,000/(49,000/$70,000) = $47,000/0.7 = $67,143 B For July, the degree of operating leverage (without the University surcharge) is: F Profit = [$47,000/($-5,000 + $7,000)] + = 24.5 C The university surcharge is irrelevant If the university closes the restaurant it will lose $2,000, which is the current contribution margin (–$5,000 + $7,000) D The fixed costs consist mostly of serving personnel and cashiers Personnel could work on a more variable basis, with more employees scheduled for busier times Employees could be called in or sent home when volumes fluctuate During slow periods, serving personnel could also serve as cashiers E Reducing the reliance on fixed costs reduces the risk of losses during periods when volume is low When volumes decrease, for example between semesters and through the summer, the fixed costs would be lower and easier to cover F There is no one answer to this part Sample solutions and a discussion of typical student responses will be included in assessment guidance on the Instructor’s web site for the textbook (available at www.wiley.com/college/eldenburg) Following is a brief summary of some pros and cons: If the club is closed, the university foregoes $2,000 current contribution In addition, students may leave campus for food that is now prepared on campus, and it is likely that there are economies of scale at food services, so food for other outlets could increase in cost On the other hand, the facility currently being used by the Lair could potentially be used for some other purpose If the Lair is not widely used, then it might not provide an important service to the university community G There is no one answer to this part Sample solutions and a discussion of typical student responses will be included in assessment guidance on the Instructor’s web site for the textbook (available at www.wiley.com/college/eldenburg) 3.38 The Elder Clinic A The cost function is: TC = $19,736 + $6.07*patient-visits For more details about developing the cost function, see problem 2.36 in Chapter To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-32 Cost Management Breakeven, solving for price: $0 = (P - $6.29) * 940 patient-visits - $19,285 940*P = $25,197.6 P = $26.81 per patient-visit The average patient fee during March-July was: $16,545/3,290 patient-visits = $5.03 per patient-visit The actual fees charged are far below the levels needed to break even B Many patients may not be able to afford this fee Since many of elderly patients are on fixed incomes, they may have to make trade-offs between other living expenses and their medical expenses They may also forego needed medical services C If the fee is raised, volumes are likely to go down That means that fees may need to be raised again, causing further declines in volume This is called the ―Death Spiral‖ (this topic is explicitly addressed in Chapter 13) D If possible, the clinic could try to substitute cheaper labor for expensive labor If a physician’s assistant or specially trained nurse can see some portion of patients instead of a physician, this would reduce some of the fixed cost Analysis of other costs that can be reduced is needed There may be grants that would offset some fixed costs, or it is possible that donors can be found to offset some costs An annual fund raising event might be held 3.39 Elina’s Stained Glass A spreadsheet showing the solution for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/college/eldenburg) A Below is one solution for the cost function This solution involves a number of judgments about cost classification and choice of estimation methods Other reasonable solutions are possible, particularly for ―raw materials and supplies‖ and ―miscellaneous.‖ Labor and rent costs are most likely fixed Rent is usually a fixed cost, and labor appears to be fixed for this company because the employees work regular schedules Both of these costs are estimated based on the most recent month’s information This procedure will incorporate the apparent rent increase that took place in September and the most recent employee schedules and pay rates Therefore, the rent cost is estimated at €2,200, and the labor cost is estimated at €4,282 Raw materials and supplies for a manufacturing organization are most likely to be variable No information is provided about alternative cost drivers, so this solution estimates raw materials and supplies as a percentage of revenue This treatment is reasonable because these types of costs and revenues both tend to vary with the size of To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-33 window If raw material and supply costs change over time, then it is best to use the most recent information available Therefore, this variable cost is estimated using the most recent month’s data: €4,029/€16,116 = 25% of revenue No information is provided about the nature of the miscellaneous cost Miscellaneous might include direct costs such as packing materials for the windows and indirect costs for supplies used in the office Also, this cost appears to have increased along with the increases in revenues over the four months presented The scatter plot shown below is used to further analyze the relationship Miscellaneous Costs Scatter Plot 3.39(A) $900 $800 $700 $600 $500 $400 $300 $200 $100 $0 $0 $5,000 $10,000 $15,000 $20,000 Revenues The scatter plot seems to confirm a positive relationship between miscellaneous costs and revenues Therefore, regression analysis will be used to estimate the cost function for miscellaneous costs, with revenues as the independent variable Portions of the regression output are shown below Regression Statistics Multiple R 0.93615673 R Square 0.876389423 Adjusted R Square 0.814584134 Standard Error 50.45858562 Observations Intercept X Variable Coefficients 334.0982722 0.030302406 Standard Error 98.20792106 0.008047137 t Stat 3.401948 3.765614 P-value 0.076609 0.063843 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-34 Cost Management Based on the regression results, the miscellaneous cost function is estimated as: TC = €334 + 3% of revenues Given the following summary of individual cost functions, the total cost function for Elina's is TC = €6,816 + 28% of total revenue Cost Category Raw materials and supplies Labor Rent Miscellaneous Total Fixed € Variable 25% of total revenue 4,282 2,200 334 3% of total revenue €6,816 28% of total revenue B The monthly amount of revenues needed to generate profit of $10,000 per month is: Revenue F Profit CMR 6,816 10,000 0.28 23,356 C The degree of operating leverage for September was: [€16,116*(1-0.28)]/€4,813 = 2.41 D If sales decrease by 10%, profit decreases by about 24% (10% * 2.41) Elina’s cost structure includes a large proportion of fixed costs E Total Revenue CVP Graph 3.39(E) Total Cost $30,000 $25,000 Breakeven Point Target Profit Dollars $20,000 $15,000 $10,000 Margin of Safety $5,000 $0 $0 $5,372 $10,744 $16,116 Revenues $21,488 $26,860 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-35 F There are many different ways to write a memo to Elina Following are points that should be covered in the memo The CVP analysis indicates that Elina must achieve a substantial increase in revenues to achieve targeted profit of €10,000 per month Revenue would have to increase by €7,240 over September's level, or 45% (€23,356-€16,116)/€16,116 = 0.45) The CVP graph and degree of operating leverage indicate that fixed costs are a large portion of total costs If Elina believes that this is too much risk, she will need to find a way to increase revenue without increasing fixed costs Here are a few possible recommendations for increasing revenues, students may have thought of others She could offer classes in the evening to develop a larger clientele for her work She could sell stained glass pieces and supplies to people taking classes and to others who produce stained glass for hobby purposes Both of these plans are unlikely to increase fixed costs by much since employees are currently idle part of the time (However, she would need to invest in higher inventories.) 3.40 Toddler Toy Company A sample spreadsheet for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/college/eldenburg) A See the sample spreadsheet B When the volume of doll sales increases to 225,000, total company profit increases from $347,500 to $383,750 Manual check: The profit should have increased by the contribution margin for dolls times the increase in volume of doll sales: (225,000 dolls – 200,000 dolls) x ($3.50 price per doll - $2.05 variable cost per doll) = 25,000 dolls x $1.45 per doll = $36,250 The profit increase is added to the original profit, and the revised profit agrees with the spreadsheet: Original profit Increase in profit (calculated above) Revised profit C The expected pretax profit decreases from $347,500 to $288,500 $347,500 36,250 $383,750 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-36 Cost Management D The expected pretax profit would increase from $347,500 to $375,000 Note about rounding in the following solutions The spreadsheet template available on the Web for this problem does not include any rounding—i.e., the spreadsheet allows partial units of product and prices with more than decimal places Because CVP is an estimation technique involving uncertain future revenues and costs, the authors not believe that it would be useful for the spreadsheet to round units to whole numbers or to round prices to decimal places Additional precision in the calculations would not improve decision making E The new breakeven point is a total of 668,919 units (243,243 dolls, 152,027 bears, and 273,649 cars) and revenue of $1,705,135 F The expected pretax profit is $485,363 G The spreadsheet shows total units as follows for different levels of target income: Target Income $100,000 $150,000 $2,000,000 x 10% = $200,000 Total Units 239,050 275,827 312,604 H All of these cash flows and quantities are subject to change depending on things like consumer preferences, the economic environment, capacity constrains, unusual situations like electricity disruptions due to weather, labor strikes, and other factors that are not predictable Sensitivity analysis provides managers a model best-case, worst-case, and average scenarios This can help them reduce risk in operations as they make decisions For example, if there is a down turn in the economy, sales are likely to be affected Sensitivity analysis can help managers determine whether the organization will profit even if sales decrease In addition, each product can be analyzed separately to determine which product is most profitable and should be emphasized Managers are often biased toward an optimistic view of the future They may believe that their decisions will always turn out well, or they may wish to report favorable expectations to superiors They may support one particular product based on their own preferences They may favor a product designed or manufactured by employees who are also good friends These types of biases often cause them to overestimate sales volumes and prices and to underestimate costs Alternatively, they may be biased against products because they not like them or because someone they not like developed or manufactures them These types of biases cause managers to underestimate sales volumes and prices and to overestimate costs To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-37 3.41 Pet Palace A sample spreadsheet for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/college/eldenburg) A See the sample spreadsheet B The breakeven point is revenue of $900,442 Revenue needed for an after-tax target income of $100,000 is $1,118,732 C Expected after-tax income under the original assumptions is $11,250 Below is a summary of the expected after-tax income if each product were emphasized in an advertising campaign: Product Emphasized Pets Food Toys Other After-Tax Profit $ 4,875 26,250 11,250 15,000 This answer contradicts the previous answer Based on the expected after-tax profit, the company would benefit most from emphasizing Food in an advertising campaign Other products have the highest contribution margin; each additional dollar of revenue for Other products contributes more to profits than an additional dollar of revenue for Food, Toys, or Pets products However, estimated revenues for Food are much higher than for the other products Therefore, a 10% increase in revenue for Food has a much larger positive effect on profit than a 10% increase in revenue for any of the other products D There are many possible answers to this question Managers may increase advertising to increase brand recognition If some products are unique to a particular outlet, managers may want to promote them because there is no competition for those products Managers may also choose to advertise products that are on sale to bring customers into the store To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-38 Cost Management BUILD YOUR PROFESSIONAL COMPETENCIES 3.42 Focus on Professional Competency: Decision Modeling A Chapter addressed any type of decision that might be affected by the relationships between a company’s revenues and costs The chapter included examples of the following types of decisions: Which products or services to emphasize, the amount to budget for revenues or costs, and whether to incur a discretionary cost such as advertising Additional examples are provided in Exhibit 3.6 The quantitative analyses in Chapter address decisions including calculation of: Breakeven point in number of units or revenues Volume of units or revenues needed to achieve a targeted level of pretax or after-tax income Sensitivity of results to changes in assumptions about volumes, prices, and costs Development of a cost function, including techniques such as analysis at the account level, regression, and the high-low method Quantitative results were not the only information used by decision makers in Chapter They also used several qualitative (i.e., non-quantitative) factors For example, the store manager of The Spotted Cow Creamery considered the effects of weather on ice cream sales The Spotted Cow Creamery owner considered ways to motivate employee work effort In the Small Animal Clinic example, the manager was concerned about the risk of loss if she increased the clinic’s fixed costs Qualitative factors are useful in decision making because some relevant information cannot be quantified Following is one example from Chapter where data, knowledge, and insights were linked together; students may think of others In The Spotted Cow Creamery (Part 2), the owner knew that beverages had a much higher contribution margin than ice cream The owner combined this knowledge with insight to hypothesize that differences in profitability between store locations might be driven by differences in sales mix The owner then obtained data about the sales mix at the different stores to evaluate whether his hypothesis was true Following is one example from Chapter where improvement in analysis led to improved decision making; students may think of others In The Spotted Cow Creamery (Parts and 2), the store manager (Holger) originally believed that his store sales would increase the following month However, he did not have any reasonable evidence to suggest how or why profits would improve After the owner provided the store manager with information about the sales mix and its effect on profitability at other stores, Holger performed CVP analysis and began to investigate specific ways to achieve higher profits These new analyses were more focused on relevant information and were less biased, leading to higher quality decisions To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-39 B CVP analysis is a method to calculate quantitative information; it is used to estimate profit and also to estimate activity levels that would lead to targeted income Solutions are tested with CVP analysis through calculations of expected outcomes For example, CVP analysis reveals the profit effects of an advertising expenditure In addition, CVP sensitivity analyses helps decision makers identify the assumptions that are the most influential to the quantitative results, or determine the effects of fluctuations in volumes, revenues, and costs on profitability C CVP sensitivity analysis is the use of quantitative and qualitative information to study how volumes, revenues, costs, and profits would change with changes in various assumptions If profitability changes little as changes in assumptions are made, managers have more confidence in the likelihood that outcomes will be similar to plans However, if profitability changes a great deal with small changes in assumptions, managers have less confidence that outcomes will be similar to plans The degree of operating leverage is an index of the extent to which the cost function includes fixed costs Organizations having a higher degree of operating leverage have greater volatility in earnings from changes in sales volumes than companies having a lower degree of operating leverage Thus, the degree of operating leverage is a quantitative measure of how profitability is likely to change under different scenarios It can also be used as a measure of risk The higher the operating leverage, the more risky operations are, from a financial perspective D CVP analysis requires the following types of data: volumes, revenues, cost function (fixed and variable costs), target profit, income tax rate For CVP analysis of multiple products, volume, revenue, and cost data are also needed for each product Knowledge about the organization improves the abilities to develop reasonable CVP assumptions, perform meaningful sensitivity analyses, and appropriately interpret the results Many types of organizational knowledge are useful for CVP analysis, including knowledge about individual products and product lines, cost behavior, relationships between selling prices and volumes, and income tax rates 3.43 Integrating Across the Curriculum: Economics and Marketing [Note: This problem requires familiarity with elementary microeconomics and the ability to differentiate a simple function.] A Recall the equation for total revenue: TR = P*Q Substituting the demand function (1,000 – 2*P) for Q: TR = P*(1,000 – 2*P) TR = 1,000*P – 2*P2 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-40 Cost Management B Total cost = TC = ($24,000 + $6,000) + ($75 + $25)*Q = $30,000 + $100*Q Substituting the demand function (1,000 – 2*P) for Q: TC = $30,000+$100*(1,000–2*P) = $30,000+$100,000-$200*P TC = $130,000-$200*P C First set the revenue function equal to the cost function and algebraically convert the equation to quadratic form (AP2 + BP + C = 0): TR = TC 1,000*P – 2*P2 = 130,000 - 200*P 2*P2 - 1,200*P + 130,000 = Using a quadratic equation calculator, there are two values of P that solve this equation (i.e., there are two breakeven points): P1 = $458.12 (rounded up) P2 = $141.89 (rounded up) Note: The above solution was obtained using the quadratic equation calculators at www.1728.com/quadratc.htm and www.math.com/students/calculators/source/quadratic.htm These calculators were located by entering ―quadratic equation calculator‖ in the Google search engine The results can be double-checked by verifying that profit is zero at the two breakeven points: Total revenue (1,000*P – 2*P2) Total cost ($130,000-$200*P) Profit Breakeven Point _ P=$458.12 P=$141.89 $38,372.14 $101,624.46 38,376.00 101,622.00 $ (3.86) $ 2.46 (nonzero profits due to rounding) D Because the revenue and cost functions both depend on the selling price (P), it is necessary to calculate price before a graph can be created The demand function can be used to solve for P: Q = 1,000 – 2*P P = (1,000 – Q) / To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 3: Cost-Volume-Profit Analysis 3-41 Now a hypothetical data table can be created for units, price, revenues, and costs The data table is used to create a CVP graph for Q between zero and 1,000 units Units 125 250 375 500 625 750 875 1,000 Price $500 438 375 313 250 188 125 63 Revenues $ 54,688 93,750 117,188 125,000 117,188 93,750 54,688 Costs $ 30,000 42,500 55,000 67,500 80,000 92,500 105,000 117,500 130,000 Total Revenue CVP Graph 3.43(D) Total Cost $140,000 $120,000 Dollars $100,000 $80,000 $60,000 $40,000 Breakeven Point $20,000 $0 125 250 375 500 625 750 875 1,000 Number of Units Break even occurs at the following two points: Q1 = 1,000 – 2*P1 = 1,000 – 2*458.12 = 83.76 units Q2 = 1,000 – 2*P2 = 1,000 – 2*141.89 = 716.22 units E Profit is maximized at the selling price where marginal revenue equals marginal cost Marginal revenue and marginal cost are calculated by differentiating each function with respect to price: Marginal revenue: TR = 1,000*P – 2*P2 First derivative of TR = 1,000 – 4*P To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-42 Cost Management Marginal cost: TC = 130,000 - 200*P First derivative of TC = -200 Set marginal revenue equal to marginal cost and solve for P: 1,000 – 4*P = -200 4*P = 1,200 P = $300 per unit Based on a selling price of $300 per regulator, the company should sell all of the regulators that are demanded at that price: 1,000 – 2*P = 1,000 – 2*300 = 1,000 – 600 = 400 regulators F In this situation, total revenue is a nonlinear function; the selling price does not remain constant at different levels of activity The total revenue function is consistent with microeconomic theory, which assumes that quantities sold (i.e., the quantity demanded) will decline as the price increases G If the company’s sales have varied between 375 and 425 regulators per year at a price of $300, then this range of activity can is assumed to be a relevant range of operations In turn, this means that it is reasonable to assume that the selling price will remain constant in the future within this range of operations (assuming there are no other factors that might influence the price)—i.e., the total revenue function is approximately linear within the range of 375 to 425 regulators per year Given this assumption, it would be appropriate to use CVP analysis to estimate profits within the relevant range of 375 to 425 regulators per year ... ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-2 Cost Management QUESTIONS 3.1 A mixed cost function includes both fixed and variable costs If there are fixed costs... ebook, solutions and test bank, visit http://downloadslide.blogspot.com 3-26 Cost Management D The managers assume that their cost function is linear (fixed costs remain fixed and variable costs... proportion of fixed costs because salaries for staff and supervisors would be much higher per hour than the cost of supplies and snacks C The marginal cost is the variable cost (supplies and snacks)