Assignment: Brief 2: Portal Corporation Purpose To assess your ability to: define and illustrate a cost object distinguish between direct costs and indirect costs explain variable costs and fixed costs Action Items 1. Read the Problem 3-37. Case Background: You work for an outside consultant hired by the company. The partner (i.e., your instructor) has asked you to provide an analysis of this problem and make a recommendation; therefore, you will address the brief to your instructor. 2. Download the 5-step critical-thinking decision-making matrix. 3. Complete the questions concerning Step 1: Identify the problem(s) and uncertainties based on the assigned problem. 4. Complete the P3-37 template worksheet by filling in the shaded outlined cells; no modifications can be made to the worksheet. This information is one source for completing Step 2: Obtaining Information on the matrix. 5. Complete Step 3: Make predictions about the future on the matrix. 6. Complete Step 4: Make decisions by choosing among the alternatives on the matrix. 7. Review the Sample Business Brief and the grading rubric below for the assignment. 8. Write a one-page analysis according to the Business Brief Guidelines Complete sentences must be used (bullets not acceptable). Your analysis must be written using a concise writing style. Your brief should incorporate all of following instructions: a. An opening paragraph briefly introducing the case situation. Note: The first half of the opening paragraph is to provide a synopsis of the company. The second half of the opening paragraph is state the problem (From Step 1 of the matrix). b. Analysis header - The analytical section should be based on your personal assessment of the financial results from the worksheet. Develop your analysis using percentages and/or relevant dollar totals/balances. This section has the highest point value and should address the following: i. What are the relevant costs that impact the volume production decision(s) at the two locations? ii. Based on the production split for worksheets #2 and #3, what was the contribution margin impact for each location and why? Note: Avoid the inclusion of calculations and/or explaining computations; instead refer to Appendix A. Avoid duplicating information within this section. The information for this section of brief should be derived from Steps 2 and 3 of the matrix. c. i. Based solely on the worksheet information (Appendix A), what production split should the company consider for optimizing plant production and total operating income? (From Step 4 of the matrix) d. 9. Conclusion header - This section should include your opinion based on your analysis of the case information and situation outcome. Your recommendation should address the following question and provide only key relevant information and logical discussion in support of your opinion: APA citation(s) and reference(s). Check your writing style by using the Grammarly app you downloaded. (See instructions under Week 1 Preparation.) Correct your business brief as needed. 10. 11. Submit your business brief to turnitin.com. Read the Originality Report you receive from turnitin.com and make any modifications as needed to your business brief. This may include adding proper citations or better paraphrasing. 12. Attach the appendices to your paper: a. Appendix A containing the P3-37 worksheet. b. Appendix B containing the completed 5-step critical-thinking decision-making matrix. c. Appendix C containing the grading rubric for the assignment. Submission Instructions Upload your analysis using the Submit tool. Grading Criteria See the Grading Rubric for specific details : 0 - 50 points Brief 2 Rubric Portal Corporation Total 50 points Criteria Applies the 5step critical thinking decision making tool (appendix). Develops an opening paragraph that introduces the case. Identifies the relevant costs that impact the volume production decisions(s) at the two locations. Acceptable Proficient Does not accurately complete the problem worksheet. For the most part, accurately completes the problem worksheet and fulfills assignment requirements. Accurately completes the problem worksheet and demonstrates solid ability to accomplish the assignment. (0-3 points) Vaguely applies the 5-step critical thinking decision making tool. (4 points) Applies the 5-step critical thinking decision making tool and, for the most part, fulfills assignment requirements. (5 points) Applies the 5-step critical thinking decision making tool and demonstrates solid ability to accomplish the assignment. (0-3 points) Vaguely develops an opening paragraph that introduces the case or does not have an opening paragraph. (4 points) Develops an opening paragraph that introduces the case and, for the most part, fulfills assignment requirements. (5 points) Develops an opening paragraph that introduces the case and demonstrates solid ability to accomplish the assignment. (4 points) Accurately completes the problem worksheet. Unacceptable (5 points) Identifies the relevant costs that impact the volume production decisions(s) at the two locations and, for the most part, fulfills assignment requirements. Identifies the relevant costs that impact the volume production decisions(s) at the two locations and demonstrates solid ability to accomplish the assignment. (0-3 points) Vaguely identifies the relevant costs that impact the volume production decisions(s) at the two locations or completely off the topic. Student Score and Comments Discusses the contribution margin impact for each location and why. Recommends the production split that the company should consider for optimizing plant production and total operating income. Integrates established accounting principles into the discussion. Synthesizes relevant information and materials to provide evidence of critical thought. (0-3 points) Vaguely discusses the contribution margin impact for each location and why or completely off the topic. (4 points) Discusses the contribution margin impact for each location and why and, for the most part, fulfills assignment requirements. (5 points) Discusses the contribution margin impact for each location and why and demonstrates solid ability to accomplish the assignment. (0-3 points) Vaguely recommends the production split that the company should consider for optimizing plant production and total operating income or completely off the topic. (4 points) Recommends the production split that the company should consider for optimizing plant production and total operating income and, for the most part, fulfills assignment requirements. (5 points) Recommends the production split that the company should consider for optimizing plant production and total operating income and demonstrates solid ability to accomplish the assignment. (0-3 points) Rarely integrates established accounting principles into the discussion. (4 points) For the most part, does a good job of integrating established accounting principles into the discussion. (5 points) Consistently does a good job of integrating established accounting principles into the discussion. (0-3 points) Synthesizes information at a minimal level. (4 points) For the most part, effectively synthesizes information, which supports main ideas. (5 points) Consistently and effectively synthesizes information, which provides strong support to main ideas. (0-3 points) (4 points) (5 points) Uses supporting documentation that has been properly references and cited. Inadequate or minimal use of supporting documentation or not properly referenced or cited. For the most part, uses supporting documentation that is properly referenced and cited. Consistently uses supporting documentation that is properly referenced and cited. Considered holistically, the student demonstrates an inadequate ability to write at the graduate level. (4 points) Considered holistically, the student demonstrates an acceptable ability to write at the graduate level. (5 points) Considered holistically, the student demonstrates a proficient ability to write at the graduate level. (0-3 points) (4 points) (5 points) (0-3 points) Considered holistically, demonstrates the ability to write at the graduate level. SubTotal Points Turnitin.com Did not turn paper into Turnitin.com ---- ---- ---- ---- --- --- Minus 5 points Revisions based on the originality Report Did not revise paper based on the originality report Grammarly Did not revise paper based on the recommendations from Grammarly.com. Minus 5 points Minus 5 points Total Points = 5-Step Critical Thinking Decision-Making Process Matrix Step 1: Identify the problem(s) and uncertainties. What exactly is the problem... (Study the problem to clarify what you need to know to solve it. Distinguish problems over which you have some control from problems over which you have no control. Pay special attention to controversial issues in which it is essential to consider multiple points of view.) The problem is this ... (Write out the problem clearly and precisely, with details. Write the problem in different ways until you get it perfectly clear in your mind.) This is an important problem because... (Remember in business, a problem is important if it affects the bottom line. So how does this problem affect the bottom line (net income). The key question(s) that needs to be answered to solve this problem is... (Every problem has questions connected to it. Here we want you to write out the most important question(s) you need to answer to solve the problem. State it clearly and precisely. Being specific is very important.) Step 2: Obtain information. The following information is needed to answer this question... (Here you are looking for the facts and/or data that help you solve the problem. Actively seek the information most relevant to the question. Include in that information options for action, both short-term and long-term. Recognize limitations in the terms of resources such as money, time, and people.) Some important assumptions I am using in my thinking are... (Figure out what you are taking for granted. Make sure these assumptions are reasonable. Watch out for self - serving or unjustified assumptions.) The points of view relevant to this problem belong to... (Who are your stakeholders? Determine whether the stakeholder's point of view is relevant.) Note: Remember to view the information you have obtained for potential bias. This is from the perspective of your own bias to the research and the bias of the authors who compiled the data and the research you gathered. In other words, do not discount the importance of other's data because of your own bias(is). Step 3: Make predictions about the future. If this problem gets solved, some important implications are... (Evaluate options, taking into account the advantages and disadvantages of possible decisions before acting. What consequences are likely to follow from this or that decision?) If this problem does not get solved, some important implications are... (Evaluate options, taking into account the advantages and disadvantages of possible decisions before acting. What consequences are likely to follow from this or that decision?) The potential alternative solutions to solve the problem are... (If the problem involves multiple conflicting points of view, you will have to assess which solution is the best.) Note: if the problem is one-dimensional, there may be just one correct solution. Step 4: Make decisions by choosing among alternatives. What is the best solution and why... (After following the process above, I think the best solution to the problem is... Defend your recommendation.) Step 5: Implement the decision, evaluate performance, and learn. In business, the fifth step in the decision making process is implementation. In the MBA program, most times you will end with Step 4 since you will not have the opportunity to implement. You may be asked to develop an implementation plan and recommend how you will evaluate performance in some assignments. CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS NOTATIONS USED IN CHAPTER 3 SOLUTIONS SP: VCU: CMU: FC: TOI: 3-1 1. 2. 3. 4. Selling price Variable cost per unit Contribution margin per unit Fixed costs Target operating income The assumptions underlying the CVP analysis outlined in Chapter 3 are Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units sold. Total costs can be separated into a fixed component that does not vary with the units sold and a variable component that changes with respect to the units sold. When represented graphically, the behaviors of total revenues and total costs are linear (represented as a straight line) in relation to units sold within a relevant range and time period. The selling price, variable cost per unit, and fixed costs are known and constant. 3-2 Three methods to express CVP relationships are the equation method, the contribution margin method, and the graph method. The first two methods are most useful for analyzing operating income at a few specific levels of sales. The graph method is useful for visualizing the effect of sales on operating income over a wide range of quantities sold. 3-3 Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the relationship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis because it describes how profits change over many different volume levels. 3-4 CVP certainly is simple, with its assumption of output as the only revenue and cost driver, and linear revenue and cost relationships. Whether these assumptions make it simplistic depends on the decision context. In some cases, these assumptions may be sufficiently accurate for CVP to provide useful insights. The examples in Chapter 3 (the software package context in the text and the travel agency example in the Problem for Self-Study) illustrate how CVP can provide such insights. In more complex cases, the basic ideas of simple CVP analysis can be expanded. 3-5 Sensitivity analysis is a \"what-if\" technique that managers use to examine how an outcome will change if the original predicted data are not achieved or if an underlying assumption changes. The advent of the electronic spreadsheet has greatly increased the ability to explore the effect of alternative assumptions at minimal cost. CVP is one of the most widely used software applications in the management accounting area. 2014 Pearson Education. All rights reserved. 3-1 3-6 Examples include: Manufacturing--substituting a robotic machine for hourly wage workers. Marketing--changing a sales force compensation plan from a percent of sales dollars to a fixed salary. Customer service--hiring a subcontractor to do customer repair visits on an annual retainer basis rather than a per-visit basis. 3-7 Examples include: Manufacturing--subcontracting a component to a supplier on a per-unit basis to avoid purchasing a machine with a high fixed depreciation cost. Marketing--changing a sales compensation plan from a fixed salary to percent of sales dollars basis. Customer service--hiring a subcontractor to do customer service on a per-visit basis rather than an annual retainer basis. 3-8 Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold, and hence, in contribution margin. Knowing the degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes. 3-9 CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time horizon. For example, some vacation cruises offer deep price discounts for people who offer to take any cruise on a day's notice. One day prior to a cruise, most costs are fixed. The other extreme is several years. Here, a much higher percentage of total costs typically is variable. CVP itself is not made any less relevant when the time horizon lengthens. What happens is that many items classified as fixed in the short run may become variable costs with a longer time horizon. 3-10 Yes, gross margin calculations emphasize the distinction between manufacturing and nonmanufacturing costs (gross margins are calculated after subtracting variable and fixed manufacturing costs). Contribution margin calculations emphasize the distinction between fixed and variable costs. Hence, contribution margin is a more useful concept than gross margin in CVP analysis. 3-11 a. b. c. d. (10 min.) CVP computations. Revenues $2,500 2,000 500 1,600 Variable Costs $ 800 1,500 300 400 Fixed Costs $200 200 200 200 Total Costs $ 1,000 1,700 500 600 Operating Income $1,500 300 0 1,000 Contribution Margin $1,700 500 200 1,200 2014 Pearson Education. All rights reserved. 3-2 Contribution Margin % 68.0% 25.0% 40.0% 75.0% 3-12 (20 min.) CVP exercises. Revenues Orig. 1. 2. 3. 4. 5. 6. 7. 8. Gstands Variable Costs Contribution Margin $10,500,000G 10,500,000 10,500,000 10,500,000 10,500,000 11,235,000e 9,765,000g 11,445,000i 10,500,000 $7,700,000G 7,448,000 7,952,000 7,700,000 7,700,000 8,239,000f 7,161,000h 8,393,000j 7,469,000l $2,800,000 3,052,000a 2,548,000b 2,800,000 2,800,000 2,996,000 2,604,000 3,052,000 3,031,000 Fixed Costs $1,400,000G 1,400,000 1,400,000 1,442,000c 1,358,000d 1,400,000 1,400,000 1,526,000k 1,442,000m Budgeted Operating Income $1,400,000 1,652,000 1,148,000 1,358,000 1,442,000 1,596,000 1,204,000 1,526,000 1,589,000 for given. a$2,800,000 1.09; b$2,800,000 0.91; c$1,400,000 1.03; d$1,400,000 0.97; e$10,500,000 1.07; f$7,700,000 1.07; g$10,500,000 0.93; h$7,700,000 0.93; i$10,500,000 1.09; j$7,700,000 1.09; k$1,400,000 1.09; l$7,700,000 0.97; m$1,400,000 1.03 Alternative 1, a 9% increase in contribution margin holding revenues constant, yields the highest budgeted operating income because it has the highest increase in contribution margin without increasing fixed costs. 3-13 (20 min.) CVP exercises. 1a. [Units sold (Selling price - Variable costs)] - Fixed costs = Operating income [5,400,000 ($0.60 - $0.40)] - $860,000 = $220,000 1b. Fixed costs Contribution margin per unit = Breakeven units $860,000 [($0.60 - $0.40)] = 4,300,000 units Breakeven units Selling price = Breakeven revenues 4,300,000 units $0.60 per unit = $2,580,000 or, Selling price -Variable costs Contribution margin ratio = Selling price $0.60 - $0.40 = = 0.333333 $0.60 Fixed costs Contribution margin ratio = Breakeven revenues $860,000 0.333333 = $2,580,000 2. 5,400,000 ($0.60 - $0.46) - $860,000 = $ (104,000) 3. [5,400,000 (1.20) ($0.60 - $0.40)] - [$860,000 (1.20)] = $ 264,000 4. [5,400,000 (1.35) ($0.36a - $0.28)] - [$860,000 (0.6)] = $ 67,200 5. $860,000 (1.20) ($0.60 - $0.40) = 5,160,000 units 2014 Pearson Education. All rights reserved. 3-3 6. ($860,000 + $20,000) ($0.72 - $0.40) = 2,750,000 units a$0.60 0.60; b$0.40 0.70 3-14 (10 min.) CVP analysis, income taxes. 1. Monthly fixed costs = $55,000 + $75,000 + $14,000 = $144,000 Contribution margin per unit = $30,000 - $26,000 - $800 = $ 3,200 Monthly fixed costs $144,000 Breakeven units per month = = = 45 cars Contribution margin per unit $3,200 per car 2. Tax rate Target net income 40% $59,250 Target operating income = Target net income 59, 250 59,520 1 tax rate (1 0.40) 0.60 Quantity of output units required to be sold = Fixed costs Target operating income $144, 000 $99, 2000 76 cars Contribution margin per unit $3, 200 3-15 (30 min.) CVP analysis, sensitivity analysis. 1. SP = $35.00 (1 - 0.30 margin to bookstore) = $35.00 0.70 = $24.50 VCU = $4.50 variable production and marketing cost 2.45 variable author royalty cost (0.10 $24.50) $6.95 CMU = $24.50 - $6.95 = $17.55 per copy FC = $ 575,000 fixed production and marketing cost 2,500,000 up-front payment to Tomas $3,075,000 2014 Pearson Education. All rights reserved. 3-4 = $99,200 Solution Exhibit 3-15A shows the PV graph. SOLUTION EXHIBIT 3-15A PV Graph for SingleDay Publishers FC = $3,075,000 $4,000 CMU = $17.55 per book sold 3,000 Operating income (000's) 2,000 1,000 Units sold 0 100,000 -1,000 200,000 300,000 400,000 175,214 units -2,000 -3,000 $3.075 million -4,000 2a. Breakeven FC number of units = CMU = $3,075,000 $17.55 = 175,214 copies sold (rounded up) 2b. Target OI = FC OI CMU $3,075,000 + $850,000 $17.55 $3,925,000 = $17.55 = 2014 Pearson Education. All rights reserved. 3-5 500,000 = 223,647 copies sold (rounded up) 3a. Increasing the normal royalty to 12% of the net sales price of each book SP = $35.00 (1 - 0.30) = $35.00 0.7 = $24.50 VCU = $4.50 variable production and marketing cost +2.94 variable author royalty cost (0.12 $24.50) $7.44 CMU = $24.50 - $7.44 = $17.06 per copy Breakeven FC = number of units CMU $3,075,000 = $17.06 = 180,246 copies sold (rounded up) The breakeven point increases from 175,214 copies in requirement 2 to 180,246 copies. 3b. Increasing the listed bookstore price to $40 while keeping the royalty at 10% of the net sales price has the following effects: = $40.00 (1 - 0.30) = $40.00 0.70 = $28.00 VCU = $ 4.50 variable production and marketing cost + 2.80 variable author royalty cost (0.10 $28.00) $ 7.30 SP CMU= $28.00 - $7.30 = $20.70 per copy Breakeven $3,075,000 = number of units $20.70 = 148,551 copies sold (rounded up) The breakeven point decreases from 175,214 copies in requirement 2 to 148,551 copies. 3c. Increasing the royalty percentage increases the breakeven point. The breakeven point increases since the variable cost per book increases. Increasing the sales price decreases the breakeven point since contribution margin per book increases. In negotiations with Tomas, if SingleDay publishing increased the selling price of the book, the royalty per book would increase from $2.45 ($24.50 10%) to $2.80 ($28 10%). This is preferable for both Tomas and SingleDay Publishing. This assumes, of course, that overall sales would not be affected if the sales price is increased to $40. Regardless of the effect on the breakeven point, SingleDay should choose the selling price that will maximize operating income. 2014 Pearson Education. All rights reserved. 3-6 3-16 (10 min.) CVP analysis, margin of safety. 1. Breakeven point revenues = Fixed costs Contribution margin percentage Contribution margin percentage = $720,000 0.48 or 48% $1,500,000 Selling price Variable cost per unit Selling price SP - $13 0.48 = SP 0.48 SP = SP - $13 0.52 SP = $13 SP = $13 0.52 = $25 3. Breakeven sales in units = Revenues Selling price = $1,500,000 $25 = 60,000 units Margin of safety in units = Sales in units - Breakeven sales in units = 85,000 - 60,000 = 25,000 units 2. Contribution margin percentage = Revenues, 85,000 units $25 Breakeven revenues Margin of safety $2,125,000 1,500,000 $ 625,000 4. The risk of making a loss is low. Sales would need to decrease by 25,000 units 85,000 units = 29.4% before McKnight Corp. will make a loss. The most likely reasons for this risk to increase is greater competition, weakness in the economy, or bad management. 3-17 (25 min.) Operating leverage. 1a. Let Q denote the quantity of carpets sold Breakeven point under Option 1 $850Q $340Q = $18,870 $510Q = $18,870 Q = $18,870 $510 = 37 carpets 1b. 2. Breakeven point under Option 2 $850Q $340Q (0.20 $850Q) = 0 340Q = 0 Q = 0 Operating income under Option 1 = $510Q $18,870 Operating income under Option 2 = $340Q Find Q such that $510Q $18,870 = $340Q $170Q = $18,870 Q = $18,870 $170 = 111 carpets 2014 Pearson Education. All rights reserved. 3-7 Revenues = $850 111 carpets = $94,350 For Q = 111 carpets, operating income under both Option 1 ($510 111 - $18,870) and Option 2 ($340 111) = $37,740 For Q > 111, say, 115 carpets, Option 1 gives operating income Option 2 gives operating income So Curt Rugs will prefer Option 1. For Q < 111, say, 105 carpets, Option 1 gives operating income Option 2 gives operating income So Curt Rugs will prefer Option 2. 3. = ($510 115) $18,870 = $39,780 = $340 115 = $39,100 = ($510 105) $18,870 = $34,680 = $340 105 = $35,700 Contribution margin Operating income Contribution margin per unit Quantity of carpets sold Operating income Under Option 1, contribution margin per unit = $850 - $340 = 510 Contribution margin = $510 185 = $94,350 Operating income = Contribution margin - Fixed costs = $94,350 - $18,870 = $75,480 Degree of operating leverage = Degree of operating leverage = $94,350 = 1. 25 $75,480 Under Option 2, contribution margin per unit = $850 - $340 - 0.20 $850 = $340 Contribution margin = $340 185 units = $62,900 = Operating margin $62,900 Degree of operating leverage = = 1.0 $62,900 4. The calculations in requirement 3 indicate that when sales are 185 units, a percentage change in sales and contribution margin will result in 1.25 times that percentage change in operating income for Option 1, but the same percentage change in operating income for Option 2. The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes. 2014 Pearson Education. All rights reserved. 3-8 3-18 (30 min.) Sales mix, new and upgrade customers. 1. SP VCU CMU New Customers $195 65 $130 Upgrade Customers $115 35 $ 80 The 60%/40% sales mix implies that, in each bundle, 3 units are sold to new customers and 2 units are sold to upgrade customers. Contribution margin of the bundle = 3 $130 + 2 $80 = $390 + $160 = $550 $16, 500, 000 = 30,000 bundles Breakeven point in bundles = $550 Breakeven point in units is: 90,000 units Sales to new customers: 30,000 bundles 3 units per bundle Sales to upgrade customers: 30,000 bundles 2 units per bundle 60,000 units Total number of units to breakeven 150,000 units Alternatively, Let S = Number of units sold to upgrade customers 1.5S = Number of units sold to new customers Revenues - Variable costs - Fixed costs = Operating income [$195 (1.5S) + $115S] - [$65 (1.5S) + $35S] - $16,500,000 = OI $407.5S - $132.5S - $16,500,000 = OI Breakeven point is 120,000 units when OI = $0 because $275.5S S 1.5S BEP = $16,500,000 = 60,000 units sold to upgrade customers = 90,000 units sold to new customers = 150,000 units Check Revenues ($195 90,000) + ($115 60,000) Variable costs ($65 90,000) + ($35 60,000) Contribution margin Fixed costs Operating income $24,450,000 7,950,000 16,500,000 16,500,000 $ 0 2014 Pearson Education. All rights reserved. 3-9 2. When 220,000 units are sold, mix is: Units sold to new customers (60% 220,000) Units sold to upgrade customers (40% 220,000) Revenues ($195 132,000) + ($115 88,000) Variable costs ($65 132,000) + ($35 88,000) Contribution margin Fixed costs Operating income 3a. 132,000 88,000 $35,860,000 11,660,000 24,200,000 16,500,000 $ 7,700,000 At New 40%/Upgrade 60% mix, each bundle contains 2 units sold to new customers and 3 units sold to upgrade customers. Contribution margin of the bundle = 2 $130 + 3 $80 = $260 + $240 = $500 $16,500, 000 = 33,000 bundles Breakeven point in bundles = $500 Breakeven point in units is: Sales to new customers: 33,000 bundles 2 unit per bundle 66,000 units Sales to upgrade customers: 33,000 bundles 3 unit per bundle 99,000 units Total number of units to breakeven 165,000 units Alternatively, Let S = Number of units sold to new customers then 1.5S = Number of units sold to upgrade customers [$195S + $115 (1.5S)] - [$65S + $35 (1.5S)] - $16,500,000 = OI 367.5S - 117.5S = $16,500,000 250S = $16,500,000 S = 66,000 units sold to new customers 1.5S = 99,000 units sold to upgrade customers BEP = 165,000 units Check Revenues ($195 66,000) + ($115 99,000) $24,255,000 Variable costs ($65 66,000) + ($35 99,000) 7,755,000 Contribution margin 16,500,000 Fixed costs 16,500,000 Operating income $ 0 3b. At New 80%/ Upgrade 20% mix, each bundle contains 4 units sold to new customers and 1 unit sold to upgrade customers. Contribution margin of the bundle = 4 $130 + 1 $80 = $520 + $80 = $600 $16,500, 000 = 27,500 bundles Breakeven point in bundles = $600 Breakeven point in units is: Sales to new customers: 110,000 units 27,500 bundles 4 units per bundle Sales to upgrade customers: 27,500 bundles 1 unit per bundle 27,500 units Total number of units to breakeven 137,500 units 2014 Pearson Education. All rights reserved. 3-10 Alternatively, Let S = Number of units sold to upgrade customers then 4S= Number of units sold to new customers [$195 (4S) + $110S] - [$65 (4S) + $35S] - $16,500,000 = OI 895S - 295S = $16,500,000 600S = $16,500,000 S = 27,500 units sold to upgrade customers 4S = 110,000 units sold to new customers 137,500 units Check Revenues ($195 110,000) + ($115 27,500) Variable costs ($65 110,000) + ($35 27,500) Contribution margin Fixed costs Operating income $24,612,500 8,112,500 16,500,000 16,500,000 $ 0 3c. As Data increases its percentage of new customers, which have a higher contribution margin per unit than upgrade customers, the number of units required to break even decreases: Requirement 3(a) Requirement 1 Requirement 3(b) New Customers 40% 60 80 Upgrade Customers 60% 40 20 Breakeven Point 165,000 150,000 137,500 It is not always better to choose the sales mix that yields lower breakeven point, because this calculation ignores the demand for the new product and the upgrade product. The company should look to sell as much of the product to new customers and to upgrade customers to maximize operating income even if this means that the sales mix results in a higher breakeven point. 2014 Pearson Education. All rights reserved. 3-11 3-19 (15-25 min.) Sales mix, three products. 1. Sales of A, B, and C are in ratio 24,000 : 96,000 : 48,000. So for every 1 unit of A, 4 (96,000 24,000) units of B are sold, and 2 (48,000 24,000) units of C are sold. Contribution margin of the bundle = 1 $5 + 4 $4 + 2 $3 = $5 + $16 + $6 = $27 $405,000 = 15,000 bundles Breakeven point in bundles = $27 Breakeven point in units is: Product A: 15,000 bundles 1 unit per bundle 15,000 units Product B: 15,000 bundles 4 units per bundle 60,000 units Product C: 15,000 bundles 2 units per bundle 30,000 units Total number of units to breakeven 105,000 units Alternatively, Let Q = Number of units of A to break even 4Q = Number of units of B to break even 2Q = Number of units of C to break even Contribution margin - Fixed costs = Zero operating income $5Q + $4(4Q) + $3(2Q) - $405,000 $27Q Q 4Q 2Q Total 2. Contribution margin: A: 24,000 $5 B: 96,000 $4 C: 48,000 $3 Contribution margin Fixed costs Operating income = 0 = $405,000 = 15,000 ($405,000 $27) units of A = 60,000 units of B = 30,000 units of C = 105,000 units $120,000 384,000 144,000 $648,000 405,000 $243,000 2014 Pearson Education. All rights reserved. 3-12 3. Contribution margin A: 24,000 $5 B: 48,000 $4 C: 96,000 $3 Contribution margin Fixed costs Operating income $120,000 192,000 288,000 $600,000 405,000 $195,000 Sales of A, B, and C are in ratio 24,000 : 48,000 : 96,000. So for every 1 unit of A, 2 (48,000 24,000) units of B and 4 (96,000 24,000) units of C are sold. Contribution margin of the bundle = 1 $5 + 2 $4 + 4 $3 = $5 + $8 + $12 = $25 $405,000 = 16,200 bundles Breakeven point in bundles = $25 Breakeven point in units is: Product A: 16,200 bundles 1 unit per bundle 16,200 units Product B: 16,200 bundles 2 units per bundle 32,400 units Product C: 16,200 bundles 4 units per bundle 64,800 units Total number of units to breakeven 113,400 units Alternatively, Let Q = Number of units of A to break even 2Q = Number of units of B to break even 4Q = Number of units of C to break even Contribution margin - Fixed costs = Breakeven point $5Q + $4(2Q) + $3(4Q) - $405,000 $25Q Q 2Q 4Q Total = 0 = $405,000 = 16,200 ($405,000 $25) units of A = 32,400 units of B = 64,800 units of C = 113,400 units Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C. 4. No, it is not always better to choose the sales mix with the lowest breakeven point because this calculation ignores the demand for the various products. The company should look to and sell as much of each of the 3 products as it can to maximize operating income even if this means that this sales mix results in a higher breakeven point. 2014 Pearson Education. All rights reserved. 3-13 3-20 (30 min.) CVP, Not for profit 1. Ticket sales per concert Variable costs per concert: Guest performers Marketing and advertising Total variable costs per concert Contribution margin per concert Fixed costs Salaries Lease payments ($4,000 12) Total fixed costs Less donations Net fixed costs Breakeven point in units = $ 4,500 $ 1,500 1,600 3,100 $ 1,400 $30,000 48,000 $78,000 29,000 $49,000 Net fixed costs $49,000 = 35 concerts = $1,400 Contribution margin per concert Check Donations Revenue ($4,500 35) Total revenue $ 29,000 157,500 186,500 Less variable costs Guest performers ($1,500 35) Marketing and advertising ($1,600 35) Total variable costs Less fixed costs Salaries Lease payments Total fixed costs Operating income 2. $52,500 56,000 108,500 $30,000 48,000 $ Ticket sales per concert Variable costs per concert: Guest performers Marketing and advertising Total variable costs per concert Contribution margin per concert Fixed costs Salaries ($30,000 + $28,000) Lease payments ($4,000 12) Total fixed costs Less donations Net fixed costs $ 4,500 $1,500 1,600 3,100 $ 1,400 $58,000 48,000 2014 Pearson Education. All rights reserved. 3-14 78,000 0 $106,000 29,000 $ 77,000 Breakeven point in units = Net fixed costs $77,000 = 55 concerts = $1,400 Contribution margin per concert Check Donations Revenue ($4,500 55) Total revenue $ 29,000 247,500 276,500 Less variable costs Guest performers ($1,500 55) Marketing and advertising ($1,600 55) Total variable costs Less fixed costs Salaries Lease payments Total fixed costs Operating income $82,500 88,000 170,500 $58,000 48,000 106,000 $ 0 Operating Income if 53 concerts are held Donations Revenue ($4,500 53) Total revenue $ 29,000 238,500 267,500 Less variable costs Guest performers ($1,500 53) Marketing and advertising ($1,600 53) Total variable costs Less fixed costs Salaries Lease payments Total fixed costs Operating income (loss) $79,500 84,800 164,300 $58,000 48,000 106,000 $ (2,800) The Music Society would not be able to afford the new marketing director if the number of concerts were to increase to only 53 events. The addition of the new marketing director would require the Music Society to hold at least 55 concerts in order to breakeven. If only 53 concerts were held, the organization would lose $2,800 annually. The Music Society could look for other contributions to support the new marketing director's salary or perhaps increase the number of attendees per concert if the number of concerts could not be increased beyond 53. 2014 Pearson Education. All rights reserved. 3-15 3. Ticket sales per concert Variable costs per concert: Guest performers Marketing and advertising Total variable costs per concert Contribution margin per concert Fixed costs Salaries ($30,000 + $28,000) Lease payments ($4,000 12) Total fixed costs Deduct donations ($29,000 + $14,000) Net fixed costs Breakeven point in units = $ 4,500 $ 1,500 1,600 3,100 $ 1,400 $58,000 48,000 $106,000 43,000 $ 63,000 Net fixed costs $63,000 = = 45 concerts Contribution margin per concert $1,400 Check Donations Revenue ($4,500 45) Total revenue $ 43,000 202,500 245,500 Less variable costs Guest performers ($1,500 45) Marketing and advertising ($1,600 45) Total variable costs Less fixed costs Salaries Lease payments Total fixed costs Operating income $67,500 72,000 139,500 $58,000 48,000 106,000 $ 0 2014 Pearson Education. All rights reserved. 3-16 3-21 (15 min.) Contribution margin, decision making. 1. Revenues Deduct variable costs: Cost of goods sold Sales commissions Other operating costs Contribution margin $500,000 $200,000 55,000 25,000 280,000 $220,000 $220,000 = 44% $500,000 2. Contribution margin percentage = 3. Incremental revenue (25% $500,000) = $125,000 Incremental contribution margin (44% $125,000) Incremental fixed costs (advertising) Incremental operating income $55,000 15,000 $40,000 If Mr. Wharton spends $15,000 more on advertising, the operating income will increase by $40,000, decreasing the operating loss from $54,000 to an operating loss of $14,000. Proof (Optional): Revenues (125% $500,000) Cost of goods sold (40% of sales) Gross margin $625,000 250,000 375,000 Operating costs: Salaries Sales commissions (11% of sales) Depreciation of equipment and fixtures Store rent Advertising Other operating costs: $25,000 Variable $625,000 $500,000 Fixed Operating income 4. $190,000 68,750 14,000 60,000 15,000 31,250 10,000 389,000 $(14,000) To improve operating income, Mr Wharton must find ways to decrease variable costs, decrease fixed costs, or increase selling prices. 2014 Pearson Education. All rights reserved. 3-17 3-22 (25min.) Contribution margin, gross margin and margin of safety. 1. Sweet Aroma Operating Income Statement, November 2012 Units sold Revenues Variable costs Variable manufacturing costs Variable marketing costs Total variable costs Contribution margin Fixed costs Fixed manufacturing costs Fixed marketing & administration costs Total fixed costs Operating income 2. 8,000 $64,000 $ 43,200 1,600 44,800 19,200 $12,000 3,000 15,000 $ 4,200 $19,200 $2.40 per unit 8,000 units Fixed costs $15,000 Breakeven quantity = 6,250 units Contribution margin per unit $2.40 per unit Revenues $64,000 Selling price = $8 per unit Units sold 8,000 units Breakeven revenues = 6,250 units $8 per unit = $50,000 Contribution margin per unit = Alternatively, Contribution margin percentage = Breakeven revenues = Contribution margin $19,200 30% Revenues $64,000 Fixed costs $15,000 $50,000 Contribution margin percentage 0.30 3. Margin of safety (in units) = Units sold - Breakeven quantity = 8,000 units - 6,250 units = 1,750 units 4. Units sold Revenues (Units sold Selling price = 7,500 $8) Contribution margin (Revenues CM percentage = $60,000 30%) Fixed costs Operating income Taxes (30% $3,000) Net income 2014 Pearson Education. All rights reserved. 3-18 7,500 $60,000 $18,000 15,000 3,000 900 $ 2,100 3-23 (30 min.) Uncertainty and expected costs. 1. Monthly Number of Orders 400,000 500,000 600,000 700,000 800,000 Cost of Current System $1,000,000 + $45(400,000) = $19,000,000 $1,000,000 + $45(500,000) = $23,500,000 $1,000,000 + $45(600,000) = $28,000,000 $1,000,000 + $45(700,000) = $32,500,000 $1,000,000 + $45(800,000) = $37,000,000 Monthly Number of Orders 400,000 500,000 600,000 700,000 800,000 Cost of Partially Automated System $11,000,000 + $25(400,000) = $21,000,000 $11,000,000 + $25(500,000) = $23,500,000 $11,000,000 + $25(600,000) = $26,000,000 $11,000,000 + $25(700,000) = $28,500,000 $11,000,000 + $25(800,000) = $31,000,000 Monthly Number of Orders 400,000 500,000 600,000 700,000 800,000 Cost of Fully Automated System $19,000,000 + $10(400,000) = $23,000,000 $19,000,000 + $10(500,000) = $24,000,000 $19,000,000 + $10(600,000) = $25,000,000 $19,000,000 + $10(700,000) = $26,000,000 $19,000,000 + $10(800,000) = $27,000,000 2. Current System Expected Cost: $19,000,000 0.10 = $ 1,900,000 23,500,000 0.25 = 5,875,000 28,000,000 0.45 = 12,600,000 32,500,000 0.15 = 4,875,000 37,000,000 0.05 = 1,850,000 $27,100,000 Partially Automated System Expected Cost: $21,000,000 0.10 = $ 2,100,000 23,500,000 0.25 = 5,875,000 26,000,000 0.45 = 11,700,000 28,500,000 0.15 = 4,275,000 31,000,000 0.05 = 1,550,000 $25,500,000 Fully Automated System Expected Cost: $23,000,000 0.10 = $ 2,300,000 24,000,000 0.25 = 6,000,000 25,000,000 0.45 = 11,250,000 26,000,000 0.15 = 3,900,000 27,000,000 0.05 = 1,350,000 $24,800,000 2014 Pearson Education. All rights reserved. 3-19 The fully automated system has the lowest expected cost. It has high costs for low numbers of orders and low costs if the numbers of orders are high. Given the probabilities that Dawnmart assesses, it should implement the fully automated system. 3. Dawmart should consider the impact of the different systems on its relationship with suppliers. The interface with Dawmart's system may require that suppliers also update their systems. This could cause some suppliers to raise the cost of their merchandise. It could force other suppliers to drop out of Dawmart's supply chain because the cost of the system change would be prohibitive. Dawmart may also want to consider other factors such as the reliability of different systems and the effect on employee morale if employees have to be laid off as it automates its systems. 3-24 (15-20 min.) CVP analysis, service firm. 1. Revenue per package Variable cost per package Contribution margin per package $7,500 6,300 $1,200 Breakeven (packages) = Fixed costs Contribution margin per package $570,000 = = 475 tour packages $1,200 per package 2. Contribution margin ratio = $1, 200 Contribution margin per package = 16% = Selling price $7,500 Revenue to achieve target income = (Fixed costs + target OI) Contribution margin ratio = Number of tour packages to earn $102,000 operating income $570,000 $102,000 = $4,200,000, or 0.16 $570,000 $102,000 560 tour packages $1, 200 Revenues to earn $102,000 OI = 560 tour packages $7,500 = $4,200,000. 3. Fixed costs = $570,000 + $19,000 = $589,000 Breakeven (packages) = Fixed costs Contribution margin per package Contribution margin per package = = Fixed costs Breakeven (packages) $589,000 = $1,240 per tour package 475 tour packages Desired variable cost per tour package = $7,500 - $1,240 = $6,260 Because the current variable cost per unit is $6,300, the unit variable cost will need to be reduced by $40 to achieve the breakeven point calculated in requirement 1. 2014 Pearson Education. All rights reserved. 3-20 Alternate Method: If fixed cost increases by $19,000, then total variable costs must be reduced by $19,000 to keep the breakeven point of 475 tour packages. Therefore, the variable cost per unit reduction = $19,000 475 = $40 per tour package. Contribution margin per package = $8,200 $6,300 = $1,900 4. Breakeven (packages) = Fixed costs Contribution margin per package = $570,000 $1,900 per tour package = 300 tour packages The key question for the general manager is: Can Outback Escapes sell enough packages at $8,200 per package to earn more total operating income than when selling packages at $7,500. Lowering the breakeven point per se is not the objective. 3-25 (20 min.) CVP analysis, margin of safety. 1. Selling price Variable costs per unit: Production costs $100 Shipping and handling 20 Contribution margin per unit (CMU) $2,000,000 Fixed costs = Breakeven point in units = Contribution margin per unit $200 Margin of safety (units) = 12,000 - 10,000 = 2,000 units 2. 3. $320 120 $200 = 10,000 units Selling price per unit $320 Variable costs: Production costs $100 120% $120 Shipping and handling ($20 90%) 18 138 Contribution margin per unit $182 (Total) contribution margin = $182 12,000 units = $2,184,000 Operating income = Contribution margin - Fixed costs = $2,184,000 - $2,000,000 = $184,000 $2,000,000 = 10,990 units $182 Margin of safety = 12,000 - 10,990 = 1,010 units Breakeven point in units = The change in variable costs decreases the margin of safety from 2,000 units to 1,010. This means that the company's sales units can drop by only 1,010 before the company begins reporting an operating loss. 4. Margin of safety is smaller, so there is some concern of losses if sales drop. To reduce risk, the manager should try to reduce fixed costs and variable costs or increase price. $2,000,000 $400,000 FC TOI Target sales in units = = = 13,187 units CMU $182 Target sales in dollars = $320 13,187 = $4,219,840 2014 Pearson Education. All rights reserved. 3-21 3-26 (30-40 min.) CVP analysis, income taxes. 1. Revenues - Variable costs - Fixed costs = Target net income 1 Tax rate Let X = Net income for 2012 20,000($24.00) - 20,000($13.50) - $147,000 = $480,000 - $270,000 - $147,000 = X 1 0.40 X 0.60 X = $63,000 0.6 = $37,800 Alternatively, Operating income = Revenues - Variable costs - Fixed costs = $480,000 - $270,000 - $147,000 = $63,000 Income taxes = 0.40 $63,000 = $25,200 Net income = Operating income - Income taxes = $63,000 - $25,200 = $37,800 2. Let Q = Number of units to break even $24.00Q - $13.50Q - $147,000 = 0 Q = $147,000 $10.50 = 14,000 units 3. Let X = Net income for 2013 22,500($24.00) - 22,500($13.50) - ($147,000 + $10,500) $540,000 - $303,750 - $157,500 = $78,750 4. = = 1 0.40 X 0.60 X 0.60 X = $47,250 Let Q = Number of units to break even with new fixed costs of $157,500 $24.00Q - $13.50Q - $157,500 Q = $157,500 $10.50 Breakeven revenues = 15,000 $24.00 5. X = 0 = 15,000 units = $360,000 Let S = Required sales units to equal 2012 net income $24.00S - $13.50S - $157,500 = $37,800 0.60 $10.50S = $63,000 + $157,500 = $220,500 S = 21,000 units Revenues = 21,000 units $24 = $504,000 2014 Pearson Education. All rights reserved. 3-22 6. Let A = Amount spent for advertising in 2012 $24 = 22,500 - $13.50 22,500 - ($147,000 + A) = $47,100 0.60 $540,000 - $303,750 - $147,000 - A = 78,500 $89,200 - A = $78,500 A = $89,250 - $78,500 = $10,750 3-27 (25 min.) CVP, sensitivity analysis. Contribution margin per pair of shoes = $70 - $30 = $40 Fixed costs = $80,000 Units sold = Total sales Selling price = $280,000 $70 per pair= 4,000 pairs of shoes 1. Variable costs decrease by 15%; Fixed costs increase by 10% Sales revenues 4,000 $70 $280,000 Variable costs 4,000 $30 (1 - 0.15) 102,000 Contribution margin 178,000 Fixed costs $80,000 1.10 88,000 Operating income $ 90,000 2. Increase advertising (fixed costs) by $20,000; Increase sales 40% Sales revenues 4,000 1.40 $70.00 $392,000 1.40 $30.00 Variable costs 4,000 168,000 Contribution margin 224,000 Fixed costs ($80,000 + $20,000) 100,000 Operating income $124,000 3. Increase selling price by $10.00; Sales decrease 15%; Variable costs increase by $8 Sales revenues 4,000 0.85 ($70 + $10) $272,000 0.85 ($30 + $8) Variable costs 4,000 129,200 Contribution margin 142,800 Fixed costs 80,000 Operating income $ 62,800 4. Double fixed costs; Increase sales by 60% Sales revenues 4,000 1.60 $70 Variable costs 4,000 1.60 $30 Contribution margin Fixed costs $80,000 2 Operating income $448,000 192,000 256,000 160,000 $ 96,000 Alternative 2 yields the highest operating income. Choosing alternative 2 will give Derby a 55% increase in operating income [($124,000 - $80,000) $80,000 = 55%], which is greater than the company's 25% targeted increase. Alternatives 1 and 4 also generate more operating income for Derby, but they too do not meet Derby's target of 25% increase in operating income. Alternative 3 actually results in lower operating income than under Derby's current cost structure. There is no reason, however, for Derby to think of these alternatives as being mutually 2014 Pearson Education. All rights reserved. 3-23 exclusive. For example, Derby can combine actions 1 and 2, automate the machining process and advertise. This will result in an even greater increase in operating income. The point of this problem is that managers always need to consider broader rather than narrower alternatives to meet ambitious or stretch goals. 3-28 (30 min.) CVP analysis, clothing store. 1. CMU (SP - VCU = $160 - $128) a. Breakeven units (FC CMU = $320,000 $32 per unit) b. Breakeven revenues (Breakeven units SP = 10,000 units $160 per unit) $ 2. Suits sold Revenues, 8,000 $160 Total cost of suit, 8,000 $120 Total sales commissions, 8,000 $8 Total variable costs Contribution margin Fixed costs Operating income (loss) 8,000 $1,280,000 960,000 64,000 1,024,000 256,000 320,000 $ (64,000) 3. Unit variable data (per suit) Selling price Cost of suits Sales commissions Variable cost per unit Annual fixed costs Rent Salaries, $200,000 + $90,000 Advertising Other fixed costs Total fixed costs 32.00 10,000 $1,600,000 $ $ 160.00 120.00 0 120.00 $ 45,000 290,000 50,000 25,000 $ 410,000 CMU, $160 - $120 a. Breakeven units, $410,000 $40 per unit b. Breakeven revenues, 10,250 units $160 per unit 2014 Pearson Education. All rights reserved. 3-24 $ 40.00 10,250 $1,640,000 4. Unit variable data (per suit) Selling price Cost of suits Sales commissions Variable cost per unit Total fixed costs $ 160.00 120.00 8.75 $ 128.75 $ 320,000 CMU, $160 - $128.75 a. Break even units = $320,000 $31.25 per unit b. Break even revenues = 10,240 units $160 per unit 5. Suits sold Revenues (15,000 suits $160 per suit) Total cost of suits (15,000 suits $120 per suit) Sales commissions on first 10,000 suits (10,000 suits $8.00 per suit) Sales commissions on additional 5,000 suits [5,000 pairs ($8.00 + $0.75 per suit)] Total variable costs Contribution margin Fixed costs Operating income $ 31.25 10,240 (rounded up) $1,638,400 15,000 $2,400,000 $1,800,000 80,000 43,750 $1,923,750 $ 476,250 320,000 $ 156,250 Alternative approach: Breakeven point in units = 10,000 suits Store manager receives commission of $0.75 on 5,000 (15,000 - 10,000) suits. Contribution margin per suit beyond breakeven point of 10,000 suits = $31.25 ($160 - $120 - $8.75) per suit. Operating income = 5,000 suits $31.25 contribution margin per suit = $156,250. 3-29 (25 min.) CVP analysis, clothing store. 1. The new store will have the same operating income under either compensation plan when the volume of sales is 11,250 suits. This can be calculated as the unit sales level at which both compensation plans result in the same total costs: Let Q = unit sales level at which total costs are same for both plans $120Q + $320,000 + $90,000 = $128Q + $320,000 $8 Q = $90,000 Q = 11,250 suits 2. When sales volume is above 11,250 suits, the higher-fixed-salaries plan results in lower costs and higher operating incomes than the salary-plus-commission plan. So, for an expected volume of 12,000 suits, the owner would be inclined to choose the higher-fixed-salaries-only plan. Operating income with no sales commission = $40 12,000 $410,000 = $70,000 Operating income with sales commission = $32 12,000 $320,000 = $64,000 2014 Pearson Education. All rights reserved. 3-25 But it is likely that sales volume itself is determined by the nature of the compensation plan. The salary-plus-commission plan provides a greater motivation to the salespeople, and it may well be that for the same amount of money paid to salespeople, the salary-plus-commission plan generates a higher volume of sales than the fixed-salary plan. 3. Let Q = Target number of units For the salary-only plan, $160Q - $120Q - $410,000 $40Q Q Q For the salary-plus-commission plan, $160Q - $128Q - $320,000 $32Q Q Q 4. = $180,000 = $590,000 = $590,000 $40 = 14,750 units = $180,000 = $500,000 = $500,000 $32 = 15,625 units Dress4Less Company Operating Income Statement, 2013 Revenues (18,000 suits $160) + (2,000 suits $100) Cost of suits, 20,000 suits $120 Commissions = Revenues 5% = $3,080,000 0.05 Contribution margin Fixed costs Operating income 3-30 $3,080,000 2,400,000 154,000 526,000 320,000 $ 206,000 (40 min.) Alternative cost structures, uncertainty, and sensitivity analysis. 1. Contribution margin per page assuming current fixed leasing agreement = $0.15 - $0.04 - $0.05 = $0.06 per page Fixed costs = $1,200 Breakeven point = Fixed costs $1,200 20,000 pages Contribution margin per page $0.06 per page Contribution margin per page assuming $20 per 500 page = $0.15-$0.04a - $0.04 - $.05 = $0.02 per page commission agreement Fixed costs = $0 2014 Pearson Education. All rights reserved. 3-26 Breakeven point = Fixed costs $0 0 pages Contribution margin per page $0.02 per page (i.e., Integral makes a profit no matter how few pages it sells) $20 500 pages = $0.04 per page a 2. Let x denote the number of pages Integral must sell for it to be indifferent between the fixed leasing agreement and commission based agreement. To calculate x we solve the following equation. $0.15 x - $0.04 x - $0.05 x - $1,200 = $0.15 x - $0.04 x - $0.04 x - $.05 x $0.06 x - $1,200 = $0.02 x $0.04 x = $1,200 x = $1,200 $0.04 = 30,000 pages For sales between 0 to 30,000 pages, Integral prefers the commission-based agreement because in this range, $0.02 x > $0.06 x - $1,200. For sales greater than 30,000 pages, Integral prefers the fixed leasing agreement because in this range, $0.06 x - $1,200 > $.02 x . 3. Fixed leasing agreement Pages Variable Revenue Sold Costs (1) (2) (3) 20,000 $.09=$1,800 20,000 20,000 $.15=$ 3,000 30,000 30,000 $.15=$ 4,500 30,000 $.09=$2,700 40,000 $.09=$3,600 40,000 40,000 $.15=$ 6,000 50,000 $.09=$4,500 40,000 50,000 $.15=$ 7,500 60,000 $.09=$5,400 60,000 60,000 $.15=$ 9,000 Expected value of fixed leasing agreement Fixed Costs (4) $1,200 $1,200 $1,200 $1,200 $1,200 Operating Income (Loss) (5)=(2)-(3)-(4) $ 0 $ 600 $1,200 $1,800 $2,400 Probability (6) 0.20 0.20 0.20 0.20 0.20 Expected Operating Income (7)=(5) (6) $ 0 120 240 360 480 $1,200 Commission-based leasing agreement: Pages Variable Sold Revenue Costs (1) (2) (3) 20,000 $.13=$2,600 20,000 20,000 $.15=$ 3,000 30,000 30,000 $.15=$ 4,500 30,000 $.13=$3,900 40,000 $.13=$5,200 40,000 40,000 $.15=$ 6,000 50,000 $.13=$6,500 50,000 50,000 $.15=$ 7,500 60,000 $.13=$7,800 60,000 60,000 $.15=$ 9,000 Expected value of commission based agreement Operating Income (4)=(2)-(3) $400 $600 $800 $1,000 $1,200 Probability (5) 0.20 0.20 0.20 0.20 0.20 Expected Operating Income (6)=(4) (5) $ 80 120 160 200 240 $800 Integral should choose the fixed cost leasing agreement because the expected value is higher than under the commission-based leasing agreement. The range of sales is high enough to make the fixed leasing agreement more attractive. 2014 Pearson Education. All rights reserved. 3-27 3-31 (25 min.) CVP, alternative cost structures. 1. Contribution margin per phone = Selling price -Variable cost per phone = $150 - $55 - $45= $50 Breakeven point = Fixed costs Contribution margin per phone = $5,000 $50 = 100 phones (per month) 2. Target number of phones = = 3. $5,000 + $4,000 180 phones $50 Contribution margin per phone = Selling price - Variable cost per phone = $150 - $77.50 - $10 = $62.50 Fixed costs = $5,000 Fixed costs Breakeven point = Contribution margin per phone 4. Fixed costs + Target operating income Contribution margin per phone $5, 000 80 phones $62.50 Let x be the number of phones for which Crabapple is indifferent between paying a monthly rental fee for the retail space and paying a 20% commission on sales. Crabapple will be indifferent when the profits under the two alternatives are equal. $150 x - $100 x - $5,000 = $150 x - $100 x - $150 (0.20) x $50 x - $5,000 = $20 x $30 x = $5,000 x = 167 phones (rounded up) For sales between 0 and 166 phones, Crabapple prefers to pay the 20% commission because in this range, $20 x > $50 x -$5,000. For sales greater than 167 phones, the company prefers to pay the monthly fixed rent of $5,000 because $50 x -$5,000 > $20 x 5. The company would need to consider the forecasted sales since this will determine cost under each alternative. The company would also need to consider any potential price increases, as this would affect the rent cost under the commission alternative. 2014 Pearson Education. All rights reserved. 3-28 3-32 (25 min.) CVP analysis, income taxes, sensitivity. 1a. To breakeven, Skudder Inc must sell 1,875 units. This amount represents the point where revenues equal total costs. Let Q denote the quantity of engines sold. Revenue = Variable costs + Fixed costs $750Q = $350Q + $750,000 $400Q = $750,000 Q = 1,875 units Breakeven can also be calculated using contribution margin per unit. Contribution margin per unit = Selling price - Variable cost per unit = $750 - $350 = $400 Breakeven = Fixed Costs Contribution margin per unit = $750,000 $400 = 1,875 units 1b. To achieve its net income objective, Skudder Inc must sell 2,375 units. This amount represents the point where revenues equal total costs plus the corresponding operating income objective to achieve net income of $150,000. Revenue = Variable costs + Fixed costs + [Net income (1 - Tax rate)] $750Q = $350Q + $750,000 + [$150,000 (1 0.25)] $750Q = $350Q + $750,000 + $200,000 $400Q = $950,000 Q = 2,375 units 2. To achieve its net income objective, Skudder should select alternative c, where fixed costs are reduced by 20% and selling price is reduced by 10% resulting in 2,100 additional units being sold through the end of the year. This alternative results in the highest net income and is the only alternative that equals or exceeds the company's net income objective of $150,000. Calculations for the three alternatives are shown below. Alternative a Revenues Variable costs Operating income Net income = = = = ($750 500) + ($750 0.80 2,800) $350 (500 + 2,800) $2,055,000 $1,155,000 $750,000 $150,000 (1 0.25) = = = = $2,055,000 $1,155,000 $ 150,000 $ 112,500 2014 Pearson Education. All rights reserved. 3-29 Alternative b Revenues = Variable costs = Operating income= Net income = ($750 500) + [($750 $100) 2,300)] ($350 500) + [($350 $15) 2,300) $1,870,000 $945,500 $750,000 $174,500 (1 0.25) Alternative c Revenues Variable costs Fixed costs Operating income Net income = = = = = 3-33 = $1,870,000 = $ 945,500 = $ 174,500 = $ 130,875 ($750 500) + ($750 0.90 2,100 = $1,792,500 $350 (500 + 2,100) = $ 910,000 $750,000 0.80 = $ 600,000 $1,792,500 $910,000 $600,000 = $ 282,500 $282,500 (1 0.25) = $211,875 (30 40 min.) Choosing between compensation plans, operating leverage. 1. Recast Diem's income statement to emphasize contribution margin, and then use it to compute the required CVP parameters. Diem Corporation Income Statement For the Year Ended December 31, 2012 Revenues Variable Costs Cost of goods soldvariable Marketing commissions Contribution margin Fixed Costs Cost of goods soldfixed Marketingfixed Operating income Using Sales Agents $35,000,000 $19,250,000 7,000,000 4,750,000 1,450,000 Contribution margin percentage ($8,750,000 35,000,000; $10,500,000 $35,000,000) Breakeven revenues ($6,200,000 0.25; $7,950,000 0.30) Degree of operating leverage ($8,750,000 $2,550,000; $10,500,000 $2,550,000) 26,250,000 8,750,000 6,200,000 $ 2,550,000 Using Own Sales Force $35,000,000 $19,250,000 5,250,000 4,750,000 3,200,000 24,500,000 10,500,000 7,950,000 $ 2,550,000 25% 30% $24,800,000 $26,500,000 3.43 4.12 2. The calculations indicate that at sales of $35,000,000, a percentage change in sales and contribution margin will result in 3.43 times that percentage change in operating income if Diem continues to use sales agents and 4.12 times that percentage change in operating income if Diem employs its own sales force. The higher contribution margin per dollar of sales and higher fixed costs by using own sales force gives Diem more operating leverage, that is, greater benefits 2014 Pearson Education. All rights reserved. 3-30 (increases in operating income) if revenues increase but greater risks (decreases in operating income) if revenues decrease. Diem also needs to consider the skill levels and incentives under the two alternatives. Sales agents have more incentive compensation and hence may be more motivated to increase sales. On the other hand, Diem's own sales force may be more knowledgeable and skilled in selling the company's products. Using its own sales force gives Diem direct access to its customers and better information about their needs. That is, the sales volume itself will be affected by who sells and by the nature of the compensation plan. 3. Variable costs of marketing = 18% of Revenues Fixed marketing costs = $3,200,000 Variable manufacturing costs per dollar of revenue = $19,250,000 $35,000,000 = 0.55 Variable Fixed Fixed marketing marketing Operating income = Revenues Variable manuf. costs manuf. costs costs costs Denote the revenues required to earn $2,550,000 of operating income by R, then R 0.55R $4,750,000 0.18R $3,200,000 = $2,550,000 R 0.55R 0.18R = $2,550,000 + $4,750,000 + $3,200,000 0.27R = $10,500,000 R = $10,500,000 0.27 = $38,888,889 3-34 (45 min.) Multi-product CVP and decision making. 1. Small trampoline: Selling price Variable cost per unit Contribution margin per unit $200 120 $ 80 Large trampoline: Selling price Variable cost per unit Contribution margin per unit $600 420 $180 Each bundle contains 4 small trampolines and 1 larger trampoline. So contribution margin of a bundle = 4 $80 + 1 $180 = $500 Breakeven Fixed costs $1,250,000 point in = 2,500 bundles Contribution margin per bundle $500 bundles Breakeven point in units of small trampolines and large trampolines is: Small trampolines: 2,500 bundles 4 units per bundle = 10,000 units Large trampolines: 2,500 bundles 1 units per bundle = 2,500 units Total number of units to breakeven 12,500 units 2014 Pearson Education. All rights reserved. 3-31 Breakeven point in dollars for small trampolines and large trampolines is: Small trampolines: 10,000 units $200 per unit = $2,000,000 Large trampolines: 2,500 units $600 per unit = 1,500,000 Breakeven revenues $3,500,000 Alternatively, weighted average contribution margin per unit = Breakeven point = $1,250,000 12,500 units $100 (4 $80) + (1 $180) = $100 5 4 12,500 units = 10,000 units 5 1 Large: 12,500 units 2,500 units 5 Small: Breakeven point in dollars Small trampolines: 10,000 units $200 per unit = $2,000,000 Large trampolines: 2,500 units $600 per unit = $1,500,000 2. Small trampolines: Selling price Variable cost per unit Contribution margin per unit $200 105 $ 95 Large trampolines: Selling price Variable cost per unit Contribution margin per unit $600 375 $225 Each bundle contains 4 small trampolines and 1 large trampoline. So contribution margin of a bundle = 4 $95 + 1 $225 = $605 Breakeven Fixed costs $1,250,000 $202,000 point in = 2,400 bundles Contribution margin per bundle $605 bundles Breakeven point in units of small trampolines and large trampolines is: Small trampolines: 2,400 bundles 4 units per bundle = 9,600 units Large trampolines: 2,400 bundles 1 units per bundle = 2,400 units Total number of units to breakeven 12,000 units Breakeven point in dollars for small trampolines and large trampolines is: Small trampolines: 9,600 units $200 per unit = $1,920,000 Large trampolines: 2,400 units $600 per unit = 1,440,000 Breakeven revenues $3,360,000 2014 Pearson Education. All rights reserved. 3-32 Alternatively, weighted average contribution margin per unit = Breakeven point = $1,250,000 + $202,000 12,000 units $121 (4 $95) + (1 $225) = $121 5 4 12,000 units = 9,600 units 5 1 Large: 12,000 units 2,400 units 5 Small: 3. Let x be the number of bundles for JumpUP to be indifferent between the old and new production equipment. Operating income using old equipment = $500 x - $1,250,000 Operating income using new equipment = $605 x - $1,250,000 - $202,000 At point of indifference: $500 x - $1,250,000 = $605 x - $1,452,000 $605 x - $500 x = $1,452,000 - $1,250,000 $105 x = $202,000 x = $202,000 $105 = 1,924 bundles (rounded up) Small trampolines = 1,924 bundles 4 units per bundle = 7,696 units Large trampolines = 1,924 bundles 1 units per bundle = 1,924 units Total number of units 9,620 units Note that at sales of 9,620 units, JumpUP will make a loss ($288,000) whether it uses old or new production equipment, because 9,620 units is lower than the breakeven points calculated in requirements 1 and 2. Let x be the number of bundles, When total sales are less than 9,620 units (1,924 bundles), $500x $1,250,000 > $605x $1,452,000 so JumpUP is better off with the old equipment. When total sales are greater than 9,620 units (1,924 bundles), $605x $1,452,000 > $500x $1,250,000, so JumpUP is better off buying the new equipment. At total sales of 13,000 units (2,600 bundles), JumpUP should buy the new production equipment. Proof: With old equipment, Operating income = $500 2,600 $250,000 = $50,000 With new equipment, Operating income = $605 2,600 $1,452,000 = $121,000 2014 Pearson Education. All rights reserved. 3-33 3-35 (20-25 min.) Sales mix, two products. 1. Sales of standard and deluxe carriers are in the ratio of 180,000 : 60,000. So for every 1 unit of deluxe, 3 (180,000 60,000) units of standard are sold. Contribution margin of the bundle = 3 $6 + 1 $10 = $18 + $10 = $28 $1,050,000 = 37,500 bundles Breakeven point in bundles = $28 Breakeven point in units is: Standard carrier: 37,500 bundles 3 units per bundle 112,500 units Deluxe carrier: 37,500 bundles 1 unit per bundle 37,500 units Total number of units to breakeven 150,000 units Alternatively, Let Q = Number of units of Deluxe carrier to break even 3Q = Number of units of Standard carrier to break even Revenues - Variable costs - Fixed costs = Zero operating income $30(3Q) + $28Q - $24(3Q) - $28Q - $1,050,000 = $90Q + $38Q - $72Q - $28Q = $28Q = Q = 3Q = 0 $1,050,000 $1,050,000 37,500 units of Deluxe 112,500 units of Standard The breakeven point is 112,500 Standard units plus 37,500 Deluxe units, a total of 150,000 units. 2a. 2b. Unit contribution margins are: Standard: $30 - $24 = $6; Deluxe: $38 - $28 = $10 If only Standard carriers were sold, the breakeven point would be: $1,050,000 $6 = 175,000 units. If only Deluxe carriers were sold, the breakeven point would be: $1,050,000 $10 = 105,000 units 3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe - Fixed costs = 200,000($6) + 40,0