Cost Volume Profit Analysis Solutions Part 6

EA 2. The club committee is considering expanding this year’s magic show invitation list to include volunteer members (in addition to its contributing members). If the club committee expands the magic show invitation list, it expects an 80% increase in attendance. Calculate the effect this will have on the profitability of the show assuming that fixed costs will be the same as last year. SOLUTION (20 min.) Gross margin and contribution margin. 1. Ticket sales ($30 600 attendees) $18,000 Variable cost of magic show ($20a 600 attendees) $12,000 Variable printing, invitations and paperwork ($1.5b 600) 90,012,900 Contribution margin 5,100 Fixed cost of magic show 8,000 Fixed cost of printing, invitations and paperwork 900 8,900 Operating profit (loss) $ (3,800) a ($20,000 60%)/600 attendees = $20/attendee ($1,800 50%)/600 attendees = $1.50/attendee b 2. Ticket sales ($30 600 attendees  180%) $32,400 Variable cost of magic show ($20  1,080 attendees) $21,600 Variable printing, invitations and paperwork ($1.50 1,080) 1,620 23,220 Contribution margin 9,180 Fixed cost of magic show 8,000 Fixed cost of printing, invitations and paperwork 900 8,900 Operating profit (loss) $ 280 3-53 Ethics, CVP analysis. Megaphone Corporation produces a molded plastic casing, M&M101, for many cell phones currently on the market. Summary data from its 2017 income statement are as follows: Joshua Kirby, Megaphone’s president, is very concerned about Megaphone Corporation’s poor profitability. He asks Leroy Gibbs, production manager, and Tony DiNunzo, controller, to see if there are ways to reduce costs. After 2 weeks, Leroy returns with a proposal to reduce variable costs to 55% of revenues by reducing the costs Megaphone currently incurs for safe disposal of wasted plastic. Tony is concerned that this would expose the company to potential environmental liabilities. He tells Leroy, ―We would need to estimate some of these potential environmental costs and include them in our analysis.‖ ―You can’t do that,‖ Leroy replies. ―We are not violating any laws. There is some possibility that we may have to incur environmental costs in the future, but if we bring it up now, this proposal will not go through because our senior management always assumes these 3-61 EA costs to be larger than they turn out to be. The market is very tough, and we are in danger of shutting down the company and costing all of us our jobs. The only reason our competitors are making money is because they are doing exactly what I am proposing.‖ Required: 1. Calculate Megaphone Corporation’s breakeven revenues for 2017. 2. Calculate Megaphone Corporation’s breakeven revenues if variable costs are 55% of revenues. 3. Calculate Megaphone Corporation’s operating income for 2017 if variable costs had been 55% of revenues. 4. Given Leroy Gibbs’s comments, what should Tony DiNunzo do? SOLUTION (30 min.) 1. Ethics, CVP analysis. Contribution margin percentage = = = Breakeven revenues = = 2. If variable costs are 55% of revenues, contribution margin percentage equals 45% (100%  55%) Breakeven revenues = = 3. Revenues  Variable costs Revenues $5, 000,000 $3, 250,000 $5,000,000 $1,750,000 = 35% $5,000,000 Fixed costs Contribution margin percentage $1,890,000 = $5,400,000 0.35 Fixed costs Contribution margin percentage $1,890,000 = $4,200,000 0.45 Revenues Variable costs (0.55  $5,000,000) Fixed costs Operating income $5,000,000 2,750,000 1,890,000 $ 360,000 4. Incorrect reporting of environmental costs with the goal of continuing operations is unethical. In assessing the situation, the specific ―Standards of Ethical Conduct for Management Accountants‖ (described in Exhibit 1-7) that the management accountant should consider are listed below. 3-62 EA Competence Clear reports using relevant and reliable information should be prepared. Preparing reports on the basis of incorrect environmental costs to make the company’s performance look better than it is violates competence standards. It is unethical for DiNunzo not to report environmental costs to make the plant’s performance look good. Integrity The management accountant has a responsibility to avoid actual or apparent conflicts of interest and advise all appropriate parties of any potential conflict. DiNunzo may be tempted to report lower environmental costs to please Kirby and Gibbs and save the jobs of his colleagues. This action, however, violates the responsibility for integrity. The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information. Credibility The management accountant’s Standards of Ethical Conduct require that information should be fairly and objectively communicated and that all relevant information should be disclosed. From a management accountant’s standpoint, underreporting environmental costs to make performance look good would violate the standard of objectivity. DiNunzo should indicate to Gibbs that estimates of environmental costs and liabilities should be included in the analysis. If Gibbs still insists on modifying the numbers and reporting lower environmental costs, DiNunzo should raise the matter with Kirby or one of Gibbs’s superiors. If after taking all these steps, there is continued pressure to understate environmental costs, DiNunzo should consider resigning from the company and not engage in unethical behavior. ERRATA NOTE: There were revisions made to the question and the solution. Please refer to the figures in the question set here in the ISM. The print version will be corrected at reprinting. 3-54 Deciding where to produce. (CMA, adapted) Central térmica, Inc., produces the same power generator in two Spanish plants, a new plant in Los Barrios and an older plant in Ascó. The following data are available for the two plants. 3-63 EA All fixed costs per unit are calculated based on a normal capacity usage consisting of 240 working days. When the number of working days exceeds 240, overtime charges raise the variable manufacturing costs of additional units by $5.00 per unit in Los Barrios and $10.00 per unit in Ascó. Central térmica, Inc., is expected to produce and sell 240,000 power generators during the coming year. Wanting to take advantage of the higher operating income per unit at Ascó, the company’s production manager has decided to manufacture 120,000 units at each plant, resulting in a plan in which Ascó operates at maximum capacity (400 units per day × 300 days) and Los Barrios operates at its normal volume (500 units per day × 240 days). Required: 1. Calculate the breakeven point in units for the Los Barrios plant and for the Ascó plant. 2. Calculate the operating income that would result from the production manager’s plan to produce 120,000 units at each plant. 3. Determine how the production of 240,000 units should be allocated between the Los Barrios and Ascó plants to maximize operating income for Central térmica, Inc. Show your calculations. SOLUTION (35 min.) Deciding where to produce. Los Barrios Ascó Selling price $200.00 $200.00 Variable cost per unit $80.00 $85.00 Manufacturing 0.00 0.00 Marketing and distribution 20.00 100.00 25.00 110.00 Contribution margin per unit (CMU) $100.00 $90.00 Fixed costs per unit Manufacturing 35.00 27.00 Marketing and distribution 30.00 65.00 24.00 51.00 Operating income per unit $35.00 $39.00 CMU of normal production (as shown above) CMU of overtime production ($100 - $5; $90 - $10) 1. Annual fixed costs = Fixed cost per unit  Daily production rate  Normal annual capacity ($65 500 units  240 days; $51  400 units  240 days) Breakeven volume = FC CMU of normal production ($7,800,000 $100; $100.00 95.00 Los Barrios $7,800,000 78,000 units 3-64 $90.00 80.00 Ascó $4,896,000 54,400 units EA $4,896,000 90) 2. Units produced and sold 120,000 Normal annual volume (units) (500 × 240; 400 × 240) 120,000 Units over normal volume (needing overtime) 0 CM from normal production units (normal annual volume  CMU normal production) (120,000 × $100; 96,000 × $90) $12,000,000 CM from overtime production units (0; 24,000  $80) 0 Total contribution margin $12,000,000 Total fixed costs 7,800,000 Operating income $4,200,000 Total operating income $9,864,000 120,000 96,000 24,000 $8,640,000 1,920,000 10,560,000 4,896,000 $5,664,000 3. The optimal production plan is to produce 150,000 units at the Los Barrios plant and 90,000 units at the Ascó plant. The full capacity of the Los Barrios plant, 150,000 units (500 units × 300 days), should be used because the contribution from these units is higher at all levels of production than is the contribution from units produced at the Ascó plant. Operating income at optimum production level: Los Barrios: 120,000 × $100 Los Barrios: 30,000 × ($100 – $5) Ascó: 90,000 × $90 Total contribution margin Deduct total fixed costs Operating income $ 12,000,000 2,850,000 8,100,000 22,950,000 12,696,000 $ 10,254,000 The contribution margin is higher when 150,000 units are produced at the Los Barrios plant and 90,000 units at the Ascó plant. As a result, operating income will also be higher in this case because total fixed costs for the division remain unchanged regardless of the quantity produced at each plant. Try It 3-1 Solution Equation Method: Selling   price  Quantity  of     units sold  Variable  cost    per unit     of Quantity   units  sold  Fixed  Operating    income   costs Operating income = ($500 × 2,000) – ($400 × 2,000) – $150,000 = $1,000,000 − $800,000 − $150,000 = $50,000 Contribution Method: 3-65 EA Rearranging the equation above, Selling Variable cost  Quantity of      per unit  units sold  price  Fixed Operating    income  costs  Contribution margin Quantity of  Fixed Operating     per unit units sold  costs income  Contribution margin per unit = Selling price – Variable cost per unit = $500 – $400 = $100 Operating income = $100 × 2,000 – $150,000 = $50,000 3-66 EA Try It 3-2 Solution (a) Recall the equation method (equation 1): Selling Quantity of  Variable  cost Quantity of      units sold   per unit units sold  price  Fixed Operating    income  costs  Setting operating income equal to $0 and denoting quantity of output units that must be sold by Q, the breakeven number of units is $500 Q   $400  Q $150,000 $0 $100 Q $150,000 Q $150,000 $100 per unit 1, 500 units Recall the contribution margin method (equation 2):  Contribution Quantity of    Fixed costs Operating income margin per unit units sold  At the breakeven point, operating income is by definition $0, and so, Contribution margin per unit Breakeven quantity of units Fixed costs (Equation 3) Rearranging equation 3 and entering the data, Breakeven number of units Fixed costs   $150,000 1,500 units Contribution margin per unit $100 per unit Breakeven revenues Breakeven number of units Selling price 1,500 units $500 per unit $750,000 (b) Selling   price      Quantity of  units sold   Variable  cost    per unit     of Quantity   units  sold  Fixed  Operating    costs income   (Equation 1) We denote by Q the unknown quantity of units Bernard Windows must sell to earn an operating income of $100,000. Selling price is $500, variable cost per package is $400, fixed costs are $150,000, and target operating income is $100,000. Substituting these values into equation 1, we have $500 Q   $400  Q $150,000 $100, 000 $100 Q  $150, 000 $100, 000 $250, 000 Q $250,000 $100 per unit 2,500 units Alternatively, we could use equation 2, 3-67 EA Contribution margin Quantity of  Fixed Operating     per unit units sold  costs income  (Equation 2) Given a target operating income ($100,000 in this case), we can rearrange terms to get equation 4. Quantity of units required to be sold  Fixed costs Target operating income Contribution margin per unit Quantity of units required to be sold (Equation 4) $150,000 $100,000 2,500 units $100 per unit Revenues to earn an operating income of $100,000 is Revenues = Number of units required to be sold × Selling price 2,500 units × $500 = $1,250,000 Try It 3-3 Solution    Target Target Tax rate Target net income    operating income operating income   Target net income (Target operating income) (1 Tax rate) Target net income $63,000   $90, 000 Target operating income  1 Tax rate 1 0.30 In other words, to earn a target net income of $63,000, Bernard Windows’s target operating income is $90,000. Proof: Target operating income Tax at 30% (0.30  $90,000) $90,000 Target net income $63,000 27,000 The key step is to take the target net income number and convert it into the corresponding target operating income number. We can then use equation 1 to determine the target operating income and substitute numbers from our Bernard Windows example. Selling Quantity of  Variable  cost Quantity of      price units sold per unit units sold     Fixed Operating  (Equation 1)   income  costs  $500 Q   $400  Q $150,000 $90, 000 $100 Q $240,000 Q $240,000 $100 per unit 2, 400 units Alternatively, we can calculate the number of units Bernard Windows must sell by using the contribution margin method and equation 4: 3-68 EA Quantity of units required to be sold  Fixed costs Target operating income Contribution margin per unit  $150, 000 $90, 000 2, 400 units $100 per unit (Equation 4) Revenues to earn net income of $63,000 or equivalently operating income of $90,000 is Revenues = Number of units required to be sold × Selling price 2,400 units × $500 = $1,200,000 Try It 3-4 Solution Budgeted Breakeven     Margin of safety  $1, 200, 000 $750,000 $450,000 revenues revenues Margin of Budgeted Breakeven    500  2, 400 1, 900 units safety (in units) sales (units) sales (units) The margin of safety indicates that sales would have to decrease by 900 units and revenues by $450,000 before the breakeven point is reached. Sometimes margin of safety is expressed as a percentage: Margin of safety percentage  Margin of safety in dollars Budgeted or actual revenues $450, 000 37.5% In our example, margin of safety percentage  $1, 200, 000 This result means that revenues would have to decrease substantially, by 60%, to reach the breakeven revenues. The high margin of safety gives management of Bernard Windows confidence that the company is unlikely to suffer a loss. Try It 3-5 Solution At any given level of sales, Degree of operating leverage Contribution margin  Operating income The following table shows the degree of operating leverage at sales of 2,500 units for the two options. 3-69 EA Option 1 Option 2 No Commission 5% Commission 1. Selling price $ 500 $ 500 2. Variable cost ($400; $400 + 0.05 × $500) $ 400 $ 425 3. Contribution margin per unit $ 100 $ 75 4. Contribution margin (row 3 2,500 units) $250,000 $187,500 5. Fixed costs $150,000 $ 87,500 $100,000 $100,000 3. Operating income (from Exhibit 3-5) 4. Degree of operating leverage (row 2  row 3) $250, 000 2.50 $100, 000 $187,500 1.875 $100, 000 These results indicate that, when sales are 2,500 units, a 1% change in sales and contribution margin will result in 2.5% change in operating income for Option 1. For Option 2, a 1% change in sales and contribution margin will result in only a 1.875% change in operating income. The degree of operating leverage at a given level of sales helps managers calculate the effect of sales fluctuations on operating income. Try It 3-6 Solution We assume that the budgeted sales mix (2,500 units of Chad Windows sold for every 1,000 units of Musk Windows sold, that is, a ratio of 5:2) will not change at different levels of total unit sales. That is, we think of Bernard Windows selling a bundle of 5 units of Chad Windows and 2 units of Musk Windows. (Note that this does not mean that Bernard Windows physically bundles the two products together into one big package.) Each bundle yields a contribution margin of $650, calculated as follows: Number of Units of Chad Windows and Musk Windows in Each Bundle Contribution Margin per Unit for Chad Windows and Musk Windows Chad Windows 5 $100 Musk Windows 2 75 Contribution Margin of the Bundle Total $500 150 $650 To compute the breakeven point, we calculate the number of bundles Bernard needs to sell. Breakeven Fixed costs  $195, 000 300 bundles point in  Contribution margin per bundle $650 per bundle bundles The breakeven point in units of Chad Windows and Musk Windows is as follows: 3-70 EA Chad Windows: 300 bundles  5 units per bundle 1,500 units Musk Windows: 300 bundles  2 units per bundle 600 units Total number of units to break even 2,100 units The breakeven point in dollars for Chad Windows and Musk Windows is as follows: Chad Windows: 1,500 units  $500 per unit $750,000 Musk Windows: 600 units  $350 per unit 210,000 Breakeven revenues $960,000 When there are multiple products, it is often convenient to use the contribution margin percentage. Under this approach, Bernard also calculates the revenues from selling a bundle of 5 units of Chad Windows and 2 units of Musk Windows: Number of Units of Chad Windows and Musk Windows in Each Bundle Selling Price for Chad Windows and Musk Windows Chad Windows 5 $500 Musk Windows 2 350 Total Revenue of the Bundle $2,500 700 $3,200 Contribution margin percentage for Contribution margin of the bundle  $650 0.203125, or 20.3125% Revenue of the bundle $3, 200 the bundle Breakeven Fixed costs  $195,000 $960,000 revenues Contribution margin % for the bundle 0.203125 Number of bundles Breakeven revenues $960,000  300 bundles required to be sold  Revenue per bundle $3, 200 per bundle to break even The breakeven point in units and dollars for Chad Windows and Musk Windows are as follows: Chad Windows: 300 bundles × 5 units per bundle = 1,500 units × $500 = $750,000 Musk Windows: 300 bundles × 2 units per bundle = 600 units × $350 = $210,000 3-71