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MANAGEMENT ACCOUNTING (VOLUME I) - Solutions Manual CHAPTER 13 COST-VOLUME-PROFIT RELATIONSHIPS I Questions The total “contribution margin” is the excess of total revenue over total variable costs The unit contribution margin is the excess of the unit price over the unit variable costs Total contribution margin: Selling price - manufacturing variable costs expensed nonmanufacturing variable costs expensed = Total contribution margin Gross margin: Selling price - variable manufacturing costs expensed - fixed manufacturing costs expensed = Gross margin A company operating at “break-even” is probably not covering costs which are not recorded in the accounting records An example of such a cost is the opportunity cost of owner-invested capital In some small businesses, owner-managers may not take a salary as large as the opportunity cost of forgone alternative employment Hence, the opportunity cost of owner labor may be excluded In the short-run, without considering asset replacement, net operating cash flows would be expected to exceed net income, because the latter includes depreciation expense, while the former does not Thus, the cash basis break-even would be lower than the accrual break-even if asset replacement is ignored However, if asset replacement costs are taken into account, (i.e., on a “cradle to grave” basis), the long-run net cash flows equal long-run accrual net income, and the long-run breakeven points are the same Both unit price and unit variable costs are expressed on a per product basis, as: = (P1 - V1) X1 + (P2 - V2) X2 + + (Pn - Vn) Xn - F, for all products to n where: P = = operating profit, average unit selling price, 13-1 Chapter 13 Cost-Volume-Profit Relationships V = X = F = average unit variable cost, quantity of units, total fixed costs for the period If the relative proportions of products (i.e., the product “mix”) is not held constant, products may be substituted for each other Thus, there may be almost an infinite number of ways to achieve a target operating profit As shown from the multiple product profit equation, there are several unknowns for one equation: = (P1 - V1) X1 + (P2 - V2) X2 + + (Pn - Vn) Xn - F, for all products to n A constant product mix is assumed to simplify the analysis Otherwise, there may be no unique solution Operating leverage measures the impact on net operating income of a given percentage change in sales The degree of operating leverage at a given level of sales is computed by dividing the contribution margin at that level of sales by the net operating income Three approaches to break-even analysis are (a) the equation method, (b) the contribution margin method, and (c) the graphical method In the equation method, the equation is: Sales = Variable expenses + Fixed expenses + Profits, where profits are zero at the break-even point The equation is solved to determine the break-even point in units or peso sales 10 The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales It states the amount by which sales can drop before losses begin to be incurred 11 The sales mix is the relative proportions in which a company’s products are sold The usual assumption in cost-volume-profit analysis is that the sales mix will not change 12 A higher break-even point and a lower net operating income could result if the sales mix shifted from high contribution margin products to low contribution margin products Such a shift would cause the average contribution margin ratio in the company to decline, resulting in less total contribution margin for a given amount of sales Thus, net operating income would decline With a lower contribution margin ratio, the break-even point would be higher since it would require more sales to cover the same amount of fixed costs II Exercises 13-2 Cost-Volume-Profit Relationships Chapter 13 Exercise (Using a Contribution Format Income Statement) Requirement Total Per Unit Sales (30,000 units × 1.15 = 34,500 units) P172,500 P5.00 Less variable expenses 103,500 3.00 Contribution margin 69,000 P2.00 Less fixed expenses 50,000 P 19,000 Net operating income Requirement Sales (30,000 units × 1.20 = 36,000 units) P162,000 P4.50 Less variable expenses 108,000 3.00 Contribution margin 54,000 P1.50 Less fixed expenses 50,000 P 4,000 Net operating income Requirement Sales (30,000 units × 0.95 = 28,500 units) P156,750 P5.50 Less variable expenses 85,500 3.00 Contribution margin 71,250 P2.50 Less fixed expenses (P50,000 + P10,000) 60,000 P 11,250 Net operating income Requirement Sales (30,000 units × 0.90 = 27,000 units) P151,200 P5.60 Less variable expenses 86,400 3.20 Contribution margin 64,800 P2.40 Less fixed expenses 50,000 P 14,800 Net operating income Exercise (Break-even Analysis and CVP Graphing) Requirement The contribution margin per person would be: Price per ticket P30 13-3 Chapter 13 Cost-Volume-Profit Relationships Less variable expenses: Dinner P7 Favors and program 10 Contribution margin per person P20 The fixed expenses of the Extravaganza total P8,000; therefore, the breakeven point would be computed as follows: Sales = Variable expenses + Fixed expense + Profits P30Q P20Q Q Q = = = = P10Q + P8,000 + P0 P8,000 P8,000 ÷ P20 per person 400 persons; or, at P30 per person, P12,000 Alternative solution: Break-even point in unit sales = Fixed expenses Unit contribution margin = P8,000 P20 per person = 400 persons or, at P30 per person, P12,000 Requirement Variable cost per person (P7 + P3) P10 Fixed cost per person (P8,000 ÷ 250 persons) 32 Ticket price per person to break even P42 Requirement Cost-volume-profit graph: 13-4 Cost-Volume-Profit Relationships Chapter 13 P22,000 P20,000 P18,000 Total Sales P16,000 Break-even point: 400 persons, or P12,000 in sales Pesos P14,000 P12,000 P10,000 Total Expenses Fixed Expenses P8,000 P6,000 P4,000 P2,000 P0 100 200 300 400 500 600 Number of Persons Exercise (Break-even and Target Profit Analysis) Requirement Sales P900Q P270Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P630Q + P1,350,000 + P0 P1,350,000 P1,350,000 ÷ P270 per lantern 5,000 lanterns, or at P900 per lantern, P4,500,000 in sales Alternative solution: Break-even point in unit sales = Fixed expenses Unit contribution margin =13-5 = P1,350,000 P270 per lantern 5,000 lanterns Chapter 13 Cost-Volume-Profit Relationships or at P900 per lantern, P4,500,000 in sales Requirement An increase in the variable expenses as a percentage of the selling price would result in a higher break-even point The reason is that if variable expenses increase as a percentage of sales, then the contribution margin will decrease as a percentage of sales A lower CM ratio would mean that more lanterns would have to be sold to generate enough contribution margin to cover the fixed costs Requirement Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Present: Proposed: 8,000 Lanterns 10,000 Lanterns* Total Per Unit Total Per Unit P7,200,000 P900 P8,100,000 P810 ** 5,040,000 630 6,300,000 630 2,160,000 P270 1,800,000 P180 1,350,000 1,350,000 P 810,000 P 450,000 * 8,000 lanterns × 1.25 = 10,000 lanterns ** P900 per lantern × 0.9 = P810 per lantern As shown above, a 25% increase in volume is not enough to offset a 10% reduction in the selling price; thus, net operating income decreases Requirement Sales P810Q P180Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P630Q + P1,350,000 + P720,000 P2,070,000 P2,070,000 ÷ P180 per lantern 11,500 lanterns 13-6 Cost-Volume-Profit Relationships Chapter 13 Alternative solution: Unit sales to attain target profit = Fixed expenses + Target profit Unit contribution margin = P1,350,000 + P720,000 P180 per lantern = 11,500 lanterns Exercise (Operating Leverage) Requirement Sales (30,000 doors) P18,000,000 P600 Less variable expenses 12,600,000 420 Contribution margin 5,400,000 P180 Less fixed expenses 4,500,000 Net operating income P 900,000 Degree of operating leverage = Contribution margin Net operating income = P5,400,000 P900,000 = Requirement a Sales of 37,500 doors represents an increase of 7,500 doors, or 25%, over present sales of 30,000 doors Since the degree of operating leverage is 6, net operating income should increase by times as much, or by 150% (6 × 25%) b Expected total peso net operating income for the next year is: Present net operating income P 900,000 Expected increase in net operating income next year (150% × P900,000) 1,350,000 Total expected net operating income P2,250,000 Exercise (Multiproduct Break-even Analysis) Requirement 13-7 Chapter 13 Cost-Volume-Profit Relationships Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Model E700 Model J1500 Total Company Amount % Amount % Amount % P700,000 100 P300,000 100 P1,000,000 100 280,000 P420,000 40 90,000 60 P210,000 30 70 370,000 630,000 598,500 P 31,500 37 63 * * 630,000 ÷ P1,000,000 = 63% Requirement The break-even point for the company as a whole would be: Break-even point Fixed expenses = in total peso sales Overall CM ratio P598,500 = 0.63 = P950,000 in sales Requirement The additional contribution margin from the additional sales can be computed as follows: P50,000 × 63% CM ratio = P31,500 Assuming no change in fixed expenses, all of this additional contribution margin should drop to the bottom line as increased net operating income This answer assumes no change in selling prices, variable costs per unit, fixed expenses, or sales mix Exercise (Break-even Analysis; Target Profit; Margin of Safety) Requirement Sales P40Q P12Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P28Q + P150,000 + P0 P150,000 P150,000 ÷ P12 per unit 12,500 units, or at P40 per unit, P500,000 13-8 Cost-Volume-Profit Relationships Chapter 13 Alternatively: Break-even point in unit sales = Fixed expenses Unit contribution margin = P150,000 P12 per unit = 12,500 units or, at P40 per unit, P500,000 Requirement The contribution margin at the break-even point is P150,000 since at that point it must equal the fixed expenses Requirement Unit sales to attain target profit = Fixed expenses + Target profit Unit contribution margin = P150,000 + P18,000 P12 per unit = 14,000 units Total Unit Sales (14,000 units × P40 per unit) P560,000 P40 Less variable expenses (14,000 units × P28 per unit) 392,000 28 Contribution margin (14,000 units × P12 per unit) 168,000 P12 Less fixed expenses 150,000 P 18,000 Net operating income Requirement Margin of safety in peso terms: Margin of safety in pesos = Total sales – 13-9 Break-even sales Chapter 13 Cost-Volume-Profit Relationships = P600,000 – P500,000 = P100,000 Margin of safety in percentage terms: Margin of safety Margin of safety in pesos = percentage Total sales P100,000 P600,000 = = 16.7% (rounded) Requirement The CM ratio is 30% Expected total contribution margin: P680,000 × 30% P204,000 Present total contribution margin: P600,000 × 30% 180,000 P 24,000 Increased contribution margin Alternative solution: P80,000 incremental sales × 30% CM ratio = P24,000 Since in this case the company’s fixed expenses will not change, monthly net operating income will increase by the amount of the increased contribution margin, P24,000 III Problems Problem (CVP Relationships) Requirement CM ratio = Variable expense ratio = Contribution margin Selling price = P15 P60 Variable expense Selling price = P45 P60 Requirement 13-10 = 25% = 75% Cost-Volume-Profit Relationships Chapter 13 Sales P60Q P15Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P45Q + P240,000 + P0 P240,000 P240,000 ÷ P15 per unit 16,000 units, or at P60 per unit, P960,000 Alternative solution: X 0.25X X X = = = = 0.75X + P240,000 + P0 P240,000 P240,000 ÷ 0.25 P960,000; or at P60 per unit, 16,000 units Requirement Increase in sales Multiply by the CM ratio Expected increase in contribution margin P400,000 x 25% P100,000 Since the fixed expenses are not expected to change, net operating income will increase by the entire P100,000 increase in contribution margin computed above Requirement Sales P60Q P15Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P45Q + P240,000 + P90,000 P330,000 P330,000 ÷ P15 per unit 22,000 units Contribution margin method: Fixed expenses + Target profit Contribution margin per unit = P240,000 + P90,000 P15 per unit = 22,000 units Requirement Margin of safety in pesos = Total sales – Break-even sales = P1,200,000 – P960,000 13-11 = P240,000 Chapter 13 Cost-Volume-Profit Relationships P240,000 Margin of safety Margin of safety in pesos = = P1,200,000 = 20% percentage Total sales Requirement a.Degree of operating leverage b = Contribution margin = P300,000 P60,000 Net operating income Expected increase in sales Degree of operating leverage Expected increase in net operating income = 8% x 40% c If sales increase by 8%, then 21,600 units (20,000 x 1.08 = 21,600) will be sold next year The new income statement will be as follows: Sales (21,600 units) Less variable expenses Contribution margin Less fixed expenses Net operating income Total P1,296,000 972,000 324,000 240,000 P 84,000 Per Unit P60 45 P15 Percent of Sales 100% 75% 25% Thus, the P84,000 expected net operating income for next year represents a 40% increase over the P60,000 net operating income earned during the current year: P84,000 – P60,000 = P60,000 P24,000 P60,000 = 40% increase Note from the income statement above that the increase in sales from 20,000 to 21,600 units has resulted in increases in both total sales and total variable expenses It is a common error to overlook the increase in variable expense when preparing a projected income statement Requirement a A 20% increase in sales would result in 24,000 units being sold next year: 20,000 units x 1.20 = 24,000 units Sales (24,000 units) Less variable expenses Total P1,440,000 1,152,000 13-12 Per Unit P60 48* Percent of Sales 100% 80% Cost-Volume-Profit Relationships Chapter 13 Contribution margin Less fixed expenses Net operating income 288,000 210,000† P 78,000 P12 20% * P45 + P3 = P48; P48 P60 = 80% † P240,000 – P30,000 = P210,000 Note that the change in per unit variable expenses results in a change in both the per unit contribution margin and the CM ratio b Break-even point = in unit sales Fixed expenses Contribution margin per unit = P210,000 P12 per unit = 17,500 units Break-even point = in peso sales Fixed expenses CM ratio P210,000 0.20 c Yes, based on these data the should be made The changes will = changes P1,050,000 increase the company’s net operating income from the present P60,000 to P78,000 per year Although the changes will also result in a higher break-even point (17,500 units as compared to the present 16,000 units), the company’s margin of safety will actually be wider than before: = Margin of safety in pesos = Total sales – Break-even sales = P1,440,000 – P1,050,000 = P390,000 As shown in requirement (5) above, the company’s present margin of safety is only P240,000 Thus, several benefits will result from the proposed changes Problem (Basics of CVP Analysis; Cost Structure) Requirement The CM ratio is 30% 13-13 Chapter 13 Cost-Volume-Profit Relationships Total P270,000 189,000 P 81,000 Sales (13,500 units) Less variable expenses Contribution margin Per Unit P20 14 P 6 Percentage 100 % 70 30 % The break-even point is: Sales P20Q P 6Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P14Q + P90,000 + P0 P90,000 P90,000 ÷ P6 per unit 15,000 units 15,000 units × P20 per unit = P300,000 in sales Alternative solution: Break-even point = in unit sales = P90,000 P6 per unit = 15,000 units Break-even point in sales pesos = = Requirement Fixed expenses Contribution margin per unit = Fixed expenses CM ratio P90,000 0.30 P300,000 in sales Incremental contribution margin: P70,000 increased sales × 30% CM ratio P21,000 Less increased fixed costs: Increased advertising cost 8,000 13-14 Cost-Volume-Profit Relationships Chapter 13 Increase in monthly net operating income P13,000 Since the company presently has a loss of P9,000 per month, if the changes are adopted, the loss will turn into a profit of P4,000 per month Requirement Sales (27,000 units × P18 per unit*) P486,000 Less variable expenses (27,000 units × P14 per unit) 378,000 Contribution margin 108,000 Less fixed expenses (P90,000 + P35,000) 125,000 Net operating loss P(17,000) *P20 – (P20 × 0.10) = P18 Requirement Sales P 20Q P5.40Q Q Q = = = = = Variable expenses + Fixed expenses + Profits P14.60Q* + P90,000 + P4,500 P94,500 P94,500 ÷ P5.40 per unit 17,500 units * P14.00 + P0.60 = P14.60 Alternative solution: Unit sales to attain target profit = = = Fixed expenses + Target profit CM per unit P90,000 + P4,500 P5.40 per unit** 17,500 units ** P6.00 – P0.60 = P5.40 Requirement 13-15 Chapter 13 Cost-Volume-Profit Relationships a The new CM ratio would be: Per Unit P20 P13 Sales Less variable expenses Contribution margin Percentage 100 % 35 65 % The new break-even point would be: Break-even point = in unit sales Fixed expenses Contribution margin per unit = P208,000 P13 per unit = 16,000 units Break-even point in sales pesos = = = Fixed expenses CM ratio P208,000 0.65 P320,000 in sales b Comparative income statements follow: Sales (20,000 units) Less variable expenses Contribution margin Less fixed expenses Net operating income Not Automated Automated Total Per Unit % Total Per Unit P400,000 P20 100 P400,000 P20 280,000 14 70 140,000 120,000 P 30 260,000 P13 90,000 208,000 P 30,000 P 52,000 % 100 35 65 c Whether or not one would recommend that the company automate its operations depends on how much risk he or she is willing to take, and depends heavily on prospects for future sales The proposed changes would increase the company’s fixed costs and its break-even point However, the changes would also increase the company’s CM ratio (from 30% to 65%) The higher CM ratio means that once the breakeven point is reached, profits will increase more rapidly than at present If 20,000 units are sold next month, for example, the higher CM ratio will generate P22,000 more in profits than if no changes are made 13-16 Cost-Volume-Profit Relationships Chapter 13 The greatest risk of automating is that future sales may drop back down to present levels (only 13,500 units per month), and as a result, losses will be even larger than at present due to the company’s greater fixed costs (Note the problem states that sales are erratic from month to month.) In sum, the proposed changes will help the company if sales continue to trend upward in future months; the changes will hurt the company if sales drop back down to or near present levels Note to the Instructor: Although it is not asked for in the problem, if time permits you may want to compute the point of indifference between the two alternatives in terms of units sold; i.e., the point where profits will be the same under either alternative At this point, total revenue will be the same; hence, we include only costs in our equation: Let Q = Point of indifference in units sold P14Q + P90,000 = P7Q + P208,000 P7Q = P118,000 Q = P118,000 ÷ P7 per unit Q = 16,857 units (rounded) If more than 16,857 units are sold, the proposed plan will yield the greatest profit; if less than 16,857 units are sold, the present plan will yield the greatest profit (or the least loss) Problem (Sales Mix; Multiproduct Break-even Analysis) Requirement Percentage of total sales Sales Less variable expenses Contribution margin Less fixed expenses Net operating income (loss) Products Sinks Mirrors Vanities Total 32% 40% 28% 100% P160,000 100 % P200,000 100 % P140,000 100 % P500,000 100% 48,000 30 160,000 80 77,000 55 285,000 57 P112,000 70 % P 40,000 20 % P 63,000 45 % 215,000 43%* 223,600 P ( 8,600) * P215,000 ÷ P500,000 = 43% Requirement Break-even sales: Break-even point in total peso sales = = = Fixed expenses CM ratio 13-17 P223,600 0.43 P520,000 in sales Chapter 13 Cost-Volume-Profit Relationships Requirement Memo to the president: Although the company met its sales budget of P500,000 for the month, the mix of products sold changed substantially from that budgeted This is the reason the budgeted net operating income was not met, and the reason the break-even sales were greater than budgeted The company’s sales mix was planned at 48% Sinks, 20% Mirrors, and 32% Vanities The actual sales mix was 32% Sinks, 40% Mirrors, and 28% Vanities As shown by these data, sales shifted away from Sinks, which provides our greatest contribution per peso of sales, and shifted strongly toward Mirrors, which provides our least contribution per peso of sales Consequently, although the company met its budgeted level of sales, these sales provided considerably less contribution margin than we had planned, with a resulting decrease in net operating income Notice from the attached statements that the company’s overall CM ratio was only 43%, as compared to a planned CM ratio of 52% This also explains why the break-even point was higher than planned With less average contribution margin per peso of sales, a greater level of sales had to be achieved to provide sufficient contribution margin to cover fixed costs Problem (Basic CVP Analysis) Requirement The CM ratio is 60%: Selling price Less variable expenses P150 60 13-18 100% 40 Cost-Volume-Profit Relationships Chapter 13 Contribution margin P 90 60% Requirement Break-even point in total sales pesos Requirement = Fixed expenses CM ratio = P1,800,000 0.60 = P3,000,000 in sales P450,000 increased sales × 60% CM ratio = P270,000 increased contribution margin Since fixed costs will not change, net operating income should also increase by P270,000 Requirement a.Degree of operating leverage = Contribution margin = P2,160,000 = P360,000 Net operating income b × 15% = 90% increase in net operating income Requirement Sales Less variable expenses Contribution margin Less fixed expenses Net operating income Last Year: 28,000 units Total Per Unit P4,200,000 P150.00 Proposed: 42,000 units* Total Per Unit P5,670,000 P135.00** 1,680,000 2,520,000 1,800,000 P 720,000 2,520,000 3,150,000 2,500,000 P 650,000 60.00 P 90.00 60.00 P 75.00 * 28,000 units × 1.5 = 42,000 units ** P150 per unit × 0.90 = P135.00 per unit No, the changes should not be made Requirement Expected total contribution margin: 28,000 units × 200% × P70 per unit* P3,920,000 Present total contribution margin: 2,520,000 13-19 Chapter 13 Cost-Volume-Profit Relationships 28,000 units × P90 per unit Incremental contribution margin, and the amount by which advertising can be increased with net operating income remaining unchanged P1,400,000 * P150 – (P60 + P20) = P70 Problem (Break-Even and Target Profit Analysis) Requirement The contribution margin per patch would be: Selling price P30 Less variable expenses: Purchase cost of the patches P15 Commissions to the student salespersons 21 P 9 Contribution margin Since there are no fixed costs, the number of unit sales needed to yield the desired P7,200 in profits can be obtained by dividing the target profit by the unit contribution margin: P7,200 Target profit = P9 per patch = 800 patches Unit contribution margin 800 patches x P30 per patch = P24,000 in total sales Requirement Since an order has been placed, there is now a “fixed” cost associated with the purchase price of the patches (i.e., the patches can’t be returned) For example, an order of 200 patches requires a “fixed” cost (investment) of P3,000 (200 patches × P15 per patch = P3,000) The variable costs drop to only P6 per patch, and the new contribution margin per patch becomes: Selling price P30 Less variable expenses (commissions only) Contribution margin P24 Since the “fixed” cost of P3,000 must be recovered before Ms Morales shows any profit, the break-even computation would be: 13-20 Cost-Volume-Profit Relationships Chapter 13 Break-even point in unit sales Fixed expenses = Unit contribution margin P3,000 = P24 per patch = 125 patches 125 patches x P30 per patch = P3,750 in total sales If a quantity other than 200 patches were ordered, the answer would change accordingly Problem Requirement 1: Break-even chart TR 600,000 500,000 TC 400,000 (P) 300,000 Break-even point 200,000 FC 100,000 5,000 10,000 15,000 20,000 25,000 30,000 13-21 (units) Chapter 13 Cost-Volume-Profit Relationships Requirement 2: Profit-volume graph 250,000 P R O F I T 200,000 150,000 100,000 50,000 Break-even point 5,000 10,000 15,000 20,000 25,000 30,000 50,000 100,000 L O S S 150,000 200,000 250,000 13-22 Cost-Volume-Profit Relationships Chapter 13 IV Multiple Choice Questions B B B C C 10 B D B A D 11 12 13 14 15 B A A C D 16 17 18 19 20 13-23 D D D C D 21 22 23 24 25 A D C B C 26 27 28 29 30 A B C B A ... Analysis; Cost Structure) Requirement The CM ratio is 30% 13- 13 Chapter 13 Cost-Volume-Profit Relationships Total P270,000 189,000 P 81,000 Sales (13, 500 units) Less variable expenses Contribution margin... 150,000 200,000 250,000 13- 22 Cost-Volume-Profit Relationships Chapter 13 IV Multiple Choice Questions B B B C C 10 B D B A D 11 12 13 14 15 B A A C D 16 17 18 19 20 13- 23 D D D C D 21 22 23... P4,500,000 in sales Alternative solution: Break-even point in unit sales = Fixed expenses Unit contribution margin =13- 5 = P1,350,000 P270 per lantern 5,000 lanterns Chapter 13 Cost-Volume-Profit Relationships
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