1 111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111111111 1111111CHAPTER 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 break-even 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: ( = operating profit, P = average unit selling price, V = average unit variable cost, X = quantity of units, F = 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 breakeven 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 breakeven point would be higher since it would require more sales to cover the same amount of fixed costs 13 The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue It can be used in a variety of ways For example, the change in total contribution margin from a given change in total sales revenue can be estimated by multiplying the change in total sales revenue by the CM ratio If fixed costs not change, then a peso increase in contribution margin will result in a peso increase in net operating income The CM ratio can also be used in break-even analysis Therefore, knowledge of a product’s CM ratio is extremely helpful in forecasting contribution margin and net operating income 14 Incremental analysis focuses on the changes in revenues and costs that will result from a particular action 15 All other things equal, Company B, with its higher fixed costs and lower variable costs, will have a higher contribution margin ratio than Company A Therefore, it will tend to realize a larger increase in contribution margin and in profits when sales increase 16 (a) If the selling price decreased, then the total revenue line would rise less steeply, and the break-even point would occur at a higher unit volume (b) If the fixed cost increased, then both the fixed cost line and the total cost line would shift upward and the break-even point would occur at a higher unit volume (c) If the variable cost increased, then the total cost line would rise more steeply and the break-even point would occur at a higher unit volume II Exercises Exercise (Using a Contribution Format Income Statement) Requirement TotalPer UnitSales (30,000 units × 1.15 = 34,500 units) P172,500P5.00Less variable expenses 103,500 3.00Contribution margin 69,000P2.00Less fixed expenses 50,000Net operating income P33333333 1393,30303033333333 3R3e3q3u3i3r3e3m3e3n3t3 323 3S3a3l3e3s3 3(33303,3030303 3u3n3i3t3s3 3×3 313.32303 3=3 33363,3030303 3u3n3i3t3s3)3 33P3136323,30303033P343.3530333L3e3s3s3 3v3a3r3i3a3b3l3e3 3e3x3p3e3n3s3e3s3 33 3130383,30303033 333.3030333C3o3n3t3r3i3b3u3t3i3o3n3 3m3a3r3g3i3n3 335343,30303033P313.3530333L3e3s3s3 3f3i3x3e3d3 3e3x3p3e3n3s3e3s3 33 3 35303,3030303333N3e3t3 3o3p3e3r3a3t3i3n3g3 3i3n3c3o3m3e3 33P3 43,30303033333333R3e3q3u3i3r3e3m3e3n3t3 333 3S3a3l3e3s3 3(33303,3030303 3u3n3i3t3s3 3×3 303.39353 3=3 32383,3530303 3u3n3i3t3s3)3 33P3135363,37353033P353.3530333L3e3s3s3 3v3a3r3i3a3b3l3e3 3e3x3p3e3n3s3e3s3 33 3 38353,35303033 333.3030333C3o3n3t3r3i3b3u3t3i3o3n3 3m3a3r3g3i3n3 337313,32353033P323.3530333L3e3s3s3 3f3i3x3e3d3 3e3x3p3e3n3s3e3s3 3(3P35303,3030303 3+3 3P31303,3030303)3 33 3 36303,3030303333N3e3t3 3o3p3e3r3a3t3i3n3g3 3i3n3c3o3m3e3 33P3 1313,32353033333333R3e3q3u3i3r3e3m3e3n3t3 343 3S3a3l3e3s3 3(33303,3030303 3u3n3i3t3s3 3×3 303.39303 3=3 32373,3030303 3u3n3i3t3s3)3 33P3135313,32303033P353.3630333L3e3s3s3 3v3a3r3i3a3b3l3e3 3e3x3p3e3n3s3e3s3 33 3 38363,34303033 333.3230333C3o3n3t3r3i3b3u3t3i3o3n3 3m3a3r3g3i3n3 336343,38303033P323.3430333L3e3s3s3 3f3i3x3e3d3 3e3x3p3e3n3s3e3s3 33 3 35303,3030303333N3e3t3 3o3p3e3r3a3t3i3n3g3 3i3n3c3o3m3e3 33P3 1343,3830303333 3E3x3e3r3c3i3s3e3 323 3(3B3r3e3a3k3-3e3v3e3n3 3A3n3a3l3y3s3i3s3 3a3n3d3 3C3V3P3 3G3r3a3p3h3i3n3g3)3 3R3e3q3u3i3r3e3m3e3n3t3 313 The contribution margin per person would be: Price per ticket P30Less variable expenses:Dinner P7Favors and program 10Contribution margin per person P20 The fixed expenses of the Extravaganza total P8,000; therefore, the break-even point would be computed as follows: Sales =Variable expenses + Fixed expense + ProfitsP30Q=P10Q + P8,000 + P0P20Q=P8,000Q=P8,000 ÷ P20 per personQ=400 persons; or, at P30 per person, P12,000 Alternative solution: or, at P30 per person, P12,000 Requirement Variable cost per person (P7 + P3) P10Fixed cost per person (P8,000 ÷ 250 persons) 32Ticket price per person to break even P42 Requirement Cost-volume-profit graph: EMBED MSGraph.Chart.8 \s ﾵ ﾵ Exercise (Break-even and Target Profit Analysis) Requirement Sales=Variable expenses + Fixed expenses + ProfitsP900Q=P630Q + P1,350,000 + P0P270Q=P1,350,000Q=P1,350,000 ÷ P270 per lanternQ=5,000 lanterns, or at P900 per lantern, P4,500,000 in sales Alternative solution: 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 Present: 8,000 Lanterns Proposed: 10,000 Lanterns*TotalPer UnitTotalPer UnitSales P7,200,000P900P8,100,000P810**Less variable expenses 5,040,000 630 6,300,000 630Contribution margin 2,160,000P2701,800,000P180 Less fixed expenses 1,350,000 1,350,000Net operating income P 555555555555555555555555555555555555555555555555555555555555555555555555 555555555555555555555555555555555555555555555555555555555555555555555555 5555555555555 851505,505050555P5 455505,50505055555 5 5*5 585,5050505 5l5a5n5t5e5r5n5s5 5×5 515.52555 5=5 51505,5050505 5l5a5n5t5e5r5n5s5 5*5*5 5P5950505 5p5e5r5 5l5a5n5t5e5r5n5 5×5 505.595 5=5 5P5851505 5p5e5r5 5l5a5n5t5e5r5n5 5 5A5s5 5s5h5o5w5n5 5a5b5o5v5e5,5 5a5 52555%5 5i5n5c5r5e5a5s5e5 5i5n5 5v5o5l5u5m5e5 5i5s5 5n5o5t5 5e5n5o5u5g5h5 5t5o5 5o5f5f5s5e5t5 5a5 51505%5 5r5e5d5u5c5t5i5o5n5 5i5n5 5t5h5e5 5s5e5l5l5i5n5g5 5p5r5i5c5e5;5 5t5h5u5s5,5 5n5e5t5 5o5p5e5r5a5t5i5n5g5 5i5n5c5o5m5e5 5d5e5c5r5e5a5s5e5s5.5 Requirement Sales=Variable expenses + Fixed expenses + ProfitsP810Q=P630Q + P1,350,000 + P720,000P180Q=P2,070,000Q=P2,070,000 ÷ P180 per lanternQ=11,500 lanterns Alternative solution: Exercise (Operating Leverage) Requirement Sales (30,000 doors) P18,000,000P600Less variable expenses 12,600,000 420Contribution margin 5,400,000P180Less fixed expenses 4,500,000Net operating income P 900,000 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 900,000Expected increase in net operating income next year (150% × P900,000) 1,350,000Total expected net operating income P2,250,000 Exercise (Multiproduct Break-even Analysis) Requirement Model E700Model J1500Total CompanyAmount%Amount%Amount%Sales P700,000100P300,000100P1,000,000100Less variable expenses 280,000 40 90,000 30 370,000 37Contribution margin P420,000 60P210,000 70630,000 63*Less fixed expenses 598,500Net operating income P 31,500 * 630,000 ÷ P1,000,000 = 63% Requirement The break-even point for the company as a whole would be: 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=Variable expenses + Fixed expenses + ProfitsP40Q=P28Q + P150,000 + P0P12Q=P150,000Q=P150,000 ÷ P12 per unitQ=12,500 units, or at P40 per unit, P500,000 Alternatively: 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 TotalUnitSales (14,000 units × P40 per unit) P560,000P40Less variable expenses (14,000 units × P28 per unit) 392,000 28Contribution margin (14,000 units × P12 per unit) 168,000P12Less fixed expenses7 77 7175707,7070707777N7e7t7 7o7p7e7r7a7t7i7n7g7 7i7n7c7o7m7e7 77P7 1787,7070707777 8R8e8q8u8i8r8e8m8e8n8t8 848 8M8a8r8g8i8n8 8o8f8 8s8a8f8e8t8y8 8i8n8 8p8e8s8o8 8t8e8r8m8s8:8 8M8a8r8g8i8n8 8o8f8 8s8a8f8e8t8y8 8i8n8 8p8e8s8o8s8 8=8 8T8o8t8a8l8 8s8a8l8e8s8 8 8B8r8e8a8k8-8e8v8e8n8 8s8a8l8e8s8 8 8 8 8 8=8 8P8680808,8080808 8P8580808,8080808 8=8 8P8180808,8080808 8 8M8a8r8g8i8n8 8o8f8 8s8a8f8e8t8y8 8i8n8 8p8e8r8c8e8n8t8a8g8e8 8t8e8r8m8s8:8 88 8 8 8 8R8e8q8u8i8r8e8m8e8n8t8 858 8T8h8e8 8C8M8 8r8a8t8i8o8 8i8s8 83808%8.8 8E8x8p8e8c8t8e8d8 8t8o8t8a8l8 8c8o8n8t8r8i8b8u8t8i8o8n8 8m8a8r8g8i8n8:8 8P8688808,8080808 8×8 83808%8 88P8280848,808080888P8r8e8s8e8n8t8 8t8o8t8a8l8 8c8o8n8t8r8i8b8u8t8i8o8n8 8m8a8r8g8i8n8:8 8P8680808,8080808 8×8 83808%8 88 8188808,808080888I8n8c8r8e8a8s8e8d8 8c8o8n8t8r8i8b8u8t8i8o8n8 8m8a8r8g8i8n8 88P8 2848,808080888 8 8A8l8t8e8r8n8a8t8i8v8e8 8s8o8l8u8t8i8o8n8:8 8P88808,8080808 8i8n8c8r8e8m8e8n8t8a8l8 8s8a8l8e8s8 8×8 83808%8 8C8M8 8r8atio = 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 Exercise (Changes in Variable Costs, Fixed Costs, Selling Price, and Volume) Requirement (1) The following table shows the effect of the proposed change in monthly advertising budget: Sales WithAdditionalCurrentAdvertisingSalesBudgetDifferenceSales P225,000P240,000P15,000Variable expenses 135,000 144,000 9,000Contribution margin 90,00096,0006,000Fixed expenses 75,000 83,000 8,000Net operating income P 15,000P 13,000P(2,000) Assuming that there are no other important factors to be considered, the increase in the advertising budget should not be approved since it would lead to a decrease in net operating income of P2,000 Alternative Solution Expected total contribution margin: P240,000 × 40% CM ratioP96,000Present total contribution margin: P225,000 × 40% CM ratio 90,000Incremental contribution margin 6,000Change in fixed expenses: Less incremental advertising expense 8,000Change in net operating income P(2,000) Alternative Solution Incremental contribution margin: P15,000 × 40% CM ratio P 6,000Less incremental advertising expense 8,000Change in net operating income P(2,000) Requirement (2) The P3 increase in variable costs will cause the unit contribution margin to decrease from P30 to P27 with the following impact on net operating income: Expected total contribution margin with the higher-quality components: 3,450 units × P27 per unit P93,150Present total contribution margin: 3,000 units × P30 per unit 90,000Change in total contribution margin P 3,150 Assuming no change in fixed costs and all other factors remain the same, the higher-quality components should be used Exercise (Compute the Margin of Safety) Requirement (1) To compute the margin of safety, we must first compute the break-even unit sales Sales= Variable expenses + Fixed expenses + ProfitsP25Q= P15Q + P8,500 + P0P10Q= P8,500Q= P8,500 ÷ P10 per unitQ= 850 units Sales (at the budgeted volume of 1,000 units) P25,000Break-even sales (at 850 units) 21,250Margin of safety (in pesos) P 3,750 Requirement (2) The margin of safety as a percentage of sales is as follows: Margin of safety (in pesos) P3,750÷ Sales P25,000Margin of safety as a percentage of sales 15.0% Exercise (Compute and Use the Degree of Operating Leverage) Requirement (1) The company’s degree of operating leverage would be computed as follows: Contribution margin operating leverage Requirement (2) P36,000÷ Net operating income 3.0 P12,000Degree of A 10% increase in sales should result in a 30% increase in net operating income, computed as follows: Degree of operating leverage 3.0× Percent increase in sales percent increase in net operating income 30% Requirement (3) 10%Estimated The new income statement reflecting the change in sales would be: AmountPercent of SalesSales P132,000100%Variable expenses 92,400 70%Contribution margin 39,600 30%Fixed expenses 24,000Net operating income P 15,600 Net operating income reflecting change in sales P15,600Original net operating income P12,000Percent change in net operating income 30% Exercise 10 (Compute the Break-Even Point for a Multiproduct Company) Requirement (1) The overall contribution margin ratio can be computed as follows: P0P15Q=P240,000Q=P240,000 ÷ P15 per unitQ=16,000 units, or at P60 per unit, P960,000 Alternative solution: X=0.75X + P240,000 + P00.25X =P240,000 X=P240,000 ÷ 0.25X=P960,000; or at P60 per unit, 16,000 units Requirement Increase in sales P400,000 Multiply by the CM ratio x 25% Expected increase in contribution margin 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=Variable expenses + Fixed expenses + ProfitsP60Q=P45Q + P240,000 + P90,000P15Q=P330,000Q=P330,000 ÷ P15 per unitQ=22,000 units Contribution margin method: Requirement Margin of safety in pesos = Total sales – P240,000 – Break-even sales = P960,000 = P1,200,000 Requirement a b Expected increase in sales 8% Degree of operating leverage x Expected increase in net operating income 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: Total Per UnitPercent of SalesSales (21,600 units) P1,296,000P60100%Less variable expenses 972,000 45 75%Contribution margin 324,000P15 25%Less fixed expenses 240,000Net operating income P 84,000 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: 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 Total Per UnitPercent of SalesSales (24,000 units) P1,440,000P60100%Less variable expenses 1,152,000 48* 80%Contribution margin 288,000P12 20%Less fixed expenses 210,000†Net operating income P 78,000 * 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 c Yes, based on these data the changes should be made The changes will 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 = = P1,440,000 Total sales – – P1,050,000 Break-even sales = 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% TotalPer UnitPercentageSales (13,500 units) P270,000P20100%Less variable expenses 189,000 14 70Contribution margin P1 717171717171717171717171717171717171717171717171717171717171717171717171 717171717171717171717171717171717171717171717171717171717171717171717171 717171717171717171717171717171717171717171717171717171717171717171717171 717171717171717171717171717171717171717171717171717171717171717171717171 717171717171717171717171717171717171717171717171717171717171717171717171 717171717171717171717171717171717171717171717171717171717171717171717171 7171717171717171717171717171717171717171717171717171717171717 817117,1701701701717P17 61717 1731701717%171717 17 17 17 17 17 17T17h17e17 17b17r17e17a17k17-17e17v17e17n17 17p17o17i17n17t17 17i17s17:17 17 17S17a17l17e17s1717=1717V17a17r17i17a17b17l17e17 17e17x17p17e17n17s17e17s17 17+17 17F17i17x17e17d17 17e17x17p17e17n17s17e17s17 17+17 17P17r17o17f17i17t17s171717P17217017Q1717=1717P17117417Q17 17+17 17P17917017,17017017017 17+17 17P170171717P17 17 17617Q1717=1717P17917017,170170170171717Q1717=1717P17917017,17017017017 18÷18 18P18618 18p18e18r18 18u18n18i18t181818Q1818=1818118518,18018018018 18u18n18i18t18s181818 18 18 18 18118518,18018018018 18u18n18i18t18s18 18×18 18P18218018 18p18e18r18 18u18n18i18t18 18=18 18P18318018018,18018018018 18i18n18 18s18a18l18e18s18 18 18 18 18 18 18 18 18 18A18lternative solution: Requirement Incremental contribution margin:P70,000 increased sales × 30% CM ratio P21,000Less increased fixed costs:Increased advertising cost 8,000Increase 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*) P486,000Less variable expenses (27,000 units × P14 per unit) 378,000Contribution margin 108,000Less fixed expenses (P90,000 + P35,000) 125,000Net operating loss P(17,000) *P20 – (P20 × 0.10) = P18 Requirement Sales=Variable expenses + Fixed expenses + ProfitsP 20Q=P14.60Q* + P90,000 + P4,500P5.40Q=P94,500Q=P94,500 ÷ P5.40 per unitQ=17,500 units * P14.00 + P0.60 = P14.60 Alternative solution: ** P6.00 – P0.60 = P5.40 Requirement a The new CM ratio would be: Per UnitPercentageSales P20100%Less variable expenses 35 Contribution margin P13 65% The new break-even point would be: b Comparative income statements follow: Not AutomatedAutomatedTotalPer Unit%TotalPer Unit%Sales (20,000 units) P400,000P20100P400,000P20100Less variable expenses 280,000 14 70 140,000 35Contribution margin 120,000P 30260,000P13 65Less fixed expenses 90,000 208,000Net operating income P1919191919191919191919191919191919191919191919191919191919 319019,19019019019191919P19 519219,1901901901919191919 20c20.20 20W20h20e20t20h20e20r20 20o20r20 20n20o20t20 20o20n20e20 20w20o20u20l20d20 20r20e20c20o20m20m20e20n20d20 20t20h20a20t20 20t20h20e20 20c20o20m20p20a20n20y20 20a20u20t20o20m20a20t20e20 20i20t20s20 20o20p20e20r20a20t20i20o20n20s20 20d20e20p20e20n20d20s20 20o20n20 20h20o20w20 20m20u20c20h20 20r20i20s20k20 20h20e20 20o20r20 20s20h20e20 20i20s20 20w20i20l20l20i20n20g20 20t20o20 20t20a20k20e20,20 20a20n20d20 20d20e20p20e20n20d20s20 20h20e20a20v20i20l20y20 20o20n20 20p20r20o20s20p20e20c20t20s20 20f20o20r20 20f20u20t20u20r20e20 20s20a20l20e20s20.20 20 20T20h20e20 20p20r20o20p20o20s20e20d20 20c20h20a20n20g20e20s20 20w20o20u20l20d20 20i20n20c20r20e20a20s20e20 20t20h20e20 20c20o20m20p20a20n20y20’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 break-even 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 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 soldP14Q + P90,000=P7Q + P208,000P7Q=P118,000Q=P118,000 ÷ P7 per unitQ=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 ProductsSinksMirrorsVanitiesTotalPercentage of total sales 32%40%28%100%Sales P160,000100%P200,000100%P140,000100%P500,000100%Less variable expenses 48,000 30 160,000 80 77,000 55 285,000 57Contribution margin P112,000 70%P 40,000 20%P 63,000 45%215,000 43%*Less fixed expenses 223,600Net operating income (loss) P ( 8,600) * P215,000 ÷ P500,000 = 43% Requirement Break-even sales: 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 P150100%Less variable expenses P 90 60%Requirement 60 40Contribution margin Requirement 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 b × 15% = 90% increase in net operating income Requirement Last Year: 28,000 unitsProposed: 42,000 units*TotalPer UnitTotalPer UnitSales P4,200,000P150.00P5,670,000P135.00**Less variable expenses 1,680,000 60.00 2,520,000 60.00Contribution margin 2,520,000P222222 922022.2202202222322,22122522022,2202202202222P22 22722522.22022022222222L 22e22s22s22 22f22i22x22e22d22 22e22x22p22e22n22s22e22s22 2222 22 22122,22822022022,220220220222222 22 22222,22522022022,2202202202222222222N22e22t22 22o22p22e22r22a22t22i22n22g22 22i22n22c22o22m22e22 2222P22 722222022,220220220222222P22 622522022,2202202202222222222 22*22 22222822,22022022022 22u22n22i22t22s22 22×22 22122.22522 22=22 22422222,22022022022 22u22n22i22t22s22 22*22*22 22 22P22122522022 22p22e22r22 22u22n22i22t22 22×22 22022.22922022 22=22 22P22122322522.22022022 22p22e22r22 22u22n22i22t22 22 22N22o22,22 22t22h22e22 22c22h22a22n22g22e22s22 22s22h22o22u22l22d22 22n22o22t22 22b22e22 22m22a22d22e22.22 22 22R22e22q22u22i22r22e22m22e22n22t22 22622 22 23Expected total contribution margin: 28,000 units × 200% × P70 per unit* P3,920,000Present total contribution margin: 28,000 units × P90 per unit 2,520,000Incremental 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 n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added Note from the income statements above that this ratio drops from 55% to 49% with the addition of the third product This product, called HY143, has a CM ratio of only 25%, which causes the average contribution margin ratio to fall This problem shows the somewhat tenuous nature of break-even analysis when more than one product is involved The manager must be very careful of his or her assumptions regarding sales mix when making decisions such as adding or deleting products It should be pointed out to the president that even though the break-even point is higher with the addition of the third product, the company’s margin of safety is also greater Notice that the margin of safety increases from P8,000 to P25,300 or from 6.25% to 15.81% Thus, the addition of the new product shifts the company much further from its break-even point, even though the break-even point is higher Problem (Break-Even Analysis with Step Fixed Costs) Requirement (1) The total annual fixed cost of the Pediatric Ward can be computed as follows: Annual Patient-DaysAidesNursesSupervising NursesTotal PersonnelOther Fixed CostTotal Fixed Cost@ P360,000@ P580,000@ P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00113,750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00013,75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000 Requirement (2) The “break-even” can be computed for each range of activity by dividing the total fixed cost for that range of activity by the contribution margin per patient-day, which is P3,000 (=P4,800 revenue 232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323" n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added N The contribution margin per patch would be: Selling price P30Less variable expenses:Purchase cost of24 24t24h24e24 24p24a24t24c24h24e24s24 2424P24124524242424C24o24m24m24i24s24s24i24o24n24s24 24t24o24 24t24h24e24 24s24t24u24d24e24n24t24 24s24a24l24e24s24p24e24r24s24o24n24s24 2424 24 24 2462424 24 242241242424C24o24n24t24r24i24b24u24t24i24o24n24 24m24a24r24g24i24n24 242424P24 9242424 24 24S24i24n24c24e24 24t24h24e24r24e24 24a24r24e24 24n24o24 24f24i24x24e24d24 24c24o24s24t24s24,24 24t24h24e24 24n24u24m24b24e24r24 24o24f24 24u24n24i24t24 24s24a24l24e24s24 24n24e24e24d24e24d24 24t24o24 24y24i24e24l24d24 24t24h24e24 24d24e24s24i24r24e24d24 24P24724,24224024024 24i24n24 24p24r24o24f24i24t24s24 24c24a24n24 24b24e24 24o24b24t24a24i24n24e24d24 24b24y24 24d24i24v24i24d24i24n24g24 24t24h24e24 24t24a24r24g24e24t24 24p24r24o24f24i24t24 24b24y24 24t24h24e unit contribution margin: 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 P30Less variable expenses (commissions only) 6Contribution margin P24 Since the “fixed” cost of P3,000 must be recovered before Ms Morales shows any profit, the break-even computation would be: 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 n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added Note from the income statements above that this ratio drops from 55% to 49% with the addition of the third product This product, called HY143, has a CM ratio of only 25%, which causes the average contribution margin ratio to fall This problem shows the somewhat tenuous nature of break-even analysis when more than one product is involved The manager must be very careful of his or her assumptions regarding sales mix when making decisions such as adding or deleting products It should be pointed out to the president that even though the break-even point is higher with the addition of the third product, the company’s margin of safety is also greater Notice that the margin of safety increases from P8,000 to P25,300 or from 6.25% to 15.81% Thus, the addition of the new product shifts the company much further from its break-even point, even though the break-even point is higher Problem (Break-Even Analysis with Step Fixed Costs) Requirement (1) The total annual fixed cost of the Pediatric Ward can be computed as follows: Annual Patient-DaysAidesNursesSupervising NursesTotal PersonnelOther Fixed CostTotal Fixed Cost@ P360,000@ P580,000@ P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00113,750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00013,75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000 Requirement (2) The “break-even” can be computed for each range of activity by dividing the total fixed cost for that range of activity by the contribution margin per patient-day, which is P3,000 (=P4,800 revenue 252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525252525" n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added N Requirement 2: Profit-volume graph n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added Note from the income statements above that this ratio drops from 55% to 49% with the addition of the third product This product, called HY143, has a CM ratio of only 25%, which causes the average contribution margin ratio to fall This problem shows the somewhat tenuous nature of break-even analysis when more than one product is involved The manager must be very careful of his or her assumptions regarding sales mix when making decisions such as adding or deleting products It should be pointed out to the president that even though the break-even point is higher with the addition of the third product, the company’s margin of safety is also greater Notice that the margin of safety increases from P8,000 to P25,300 or from 6.25% to 15.81% Thus, the addition of the new product shifts the company much further from its break-even point, even though the break-even point is higher Problem (Break-Even Analysis with Step Fixed Costs) Requirement (1) The total annual fixed cost of the Pediatric Ward can be computed as follows: Annual Patient-DaysAidesNursesSupervising NursesTotal PersonnelOther Fixed CostTotal Fixed Cost@ P360,000@ P580,000@ P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00113,750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00013,75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000 Requirement (2) The “break-even” can be computed for each range of activity by dividing the total fixed cost for that range of activity by the contribution margin per patient-day, which is P3,000 (=P4,800 revenue 272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727" n the break-even point can be traced to the decrease in the company’s average contribution margin ratio when the third product is added N Problem (Sales Mix; Break-Even Analysis; Margin of Safety) Requirement (1) a.HunYunTotalPesos%P %Euros%Sales P80,000100P48,000100P128,000100Variable expenses 48,000 60 9,600 20 57,600 45Contribution margin P32,000 40P38,400 8070,400 55Fixed expenses 66,000Net operating income b Break-even sales = Fixed expenses ÷ CM ratio = P66,000 ÷ 0.55 = P120,000 P 4,400 Requirement (2) a.HunYun HY143TotalPesos%Pesos%Pesos%Pesos%Sales P80,000100P48,000100P32,000100P160,000100Variable expenses 48,000 60 9,600 20 2,4000 75 81,600 51Contribution margin P32,000 40P38,400 80P 8,000 2578,400 49Fixed expenses 66,000Net operating income P 12,400 b Break-even sales = Fixed expenses ÷ CM ratio = P66,000 ÷ 0.49 = P134,700 (rounded) Requirement (3) The reason for the increase i ... Alternative solution: In units: P1,125,000 ÷ P60 per unit = 18,750 units c In sales pesos: 13, 333 units × P60 per unit = P800,000 (rounded) Alternative solution: In units: P800,000 ÷ P60 per unit = 13, 333... P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00 113, 750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00 013, 75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000... P760,00010,00012,000P2,520,000P8,700,000P2,280,000P13,500,000P27,400,000P40,900,00012,00 113, 750P2,880,000P8,700,000P2,280,000P13,860,000P27,400,000P41,260,00 013, 75116,500P3,240,000P9,280,000P3,040,000P15,560,000P27,400,000P42,960,00016,50118,250P3,600,000P9,280,000P3,040,000P15,920,000P27,400,000P43,320,00018,25120,750P3,600,000P9,860,000P3,800,000P17,260,000P27,400,000P44,660,00020,75123,000P3,960,000P10,440,000P3,800,000P18,200,000P27,400,000P45,600,000