costacctg13_sm_ch03

costacctg13_sm_ch03 - CHAPTER 3 COST­VOLUME­PROFIT...

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Unformatted text preview: CHAPTER 3 COST­VOLUME­PROFIT ANALYSIS NOTATION USED IN CHAPTER 3 SOLUTIONS SP: Selling price VCU: Variable cost per unit CMU: Contribut ion margin per unit FC: Fixed costs TOI: Target operating inco me 3­1 Cost­volume­profit (CVP) analysis examines the behavior o f total revenues, total costs, and operating inco me as changes occur in the units sold, selling price, variable cost per unit, or fixed costs of a product. 3­2 1. 2. 3. The assumpt ions underlying the CVP analysis outlined in Chapter 3 are Changes in the level of revenues and costs arise only because o f changes in the number of product (or service) units so ld. Total costs can be separated into a fixed co mponent that does not vary wit h the units sold and a component that is variable wit h respect to the units so ld. When represented graphically, the behavior of total revenues and total costs are linear (represented as a straight line) in relat ion to units sold wit hin a relevant range and t ime period. The selling price, variable cost per unit, and fixed costs are known and constant. 4. 3­3 Operating inco me is total revenues fro m operations for the account ing period minus cost of goods sold and operating costs (excluding income taxes): Costs of goods sold and operating Operating inco me = Total revenues fro m operations – costs (excluding inco me taxes) Net inco me is operating inco me plus nonoperating revenues (such as interest revenue) minus nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperating revenues and nonoperating costs are zero. Thus, Chapter 3 computes net inco me as: Net inco me = Operating inco me – Income taxes 3­4 Contribut ion margin is the difference between total revenues and total variable costs. Contribut ion margin per unit is the difference between selling price and variable cost per unit. Contribut ion­margin percentage is the contribut ion margin per unit divided by selling price. 3­5 Three methods to express CVP relat ionships are the equation method, the contribut ion margin method, and the graph method. The first two methods are most useful for analyzing operating inco me at a few specific levels of sales. The graph method is useful for visualizing the effect of sales on operating inco me over a wide range of quant it ies so ld. 3­1 3­6 Breakeven analysis denotes the study o f the breakeven point, which is often only an incidental part of the relat ionship between cost, volume, and profit. Cost­volume­profit relat ionship is a more comprehensive term than breakeven analysis. 3­7 CVP certainly is simple, with its assumpt ion o f output as the only revenue and cost driver, and linear revenue and cost relat ionships. Whether these assumpt ions make it simplist ic depends on the decisio n context. In some cases, these assumptions may be sufficient ly 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 Pr oblem for Self­Study) illustrate how CVP can provide such ins ights. In more complex cases, the basic ideas of simple CVP analys is can be expanded. 3­8 An increase in the inco me tax rate does not affect the breakeven po int. Operating inco me at the breakeven point is zero, and no inco me taxes are paid at this po int. 3­9 Sensit ivit y analys is is a “what­if” technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumpt ion changes. The advent of the electronic spreadsheet has great ly increased the abilit y to explore the effect of alternat ive assumpt ions at minimal cost. CVP is one o f the most widely used so ftware applicat ions in the management accounting area. 3­10 Examples include: Manufacturing––subst ituting a robotic machine for hourly wage workers. Marketing––changing a sales force compensation plan fro m a percent of sales do llars to a fixed salary. Customer service––hiring a subcontractor to do customer repair visits on an annual retainer basis rather than a per­visit basis. 3­11 Examples include: Manufacturing––subcontracting a co mponent to a supplier on a per­unit basis to avoid purchasing a machine with a high fixed depreciat ion cost. Marketing––changing a sales co mpensat ion plan fro m a fixed salary to percent of sales dollars basis. Customer service––hiring a subcontractor to do customer service on a per­visit basis rather than an annual retainer basis. 3­12 Operating leverage describes the effects that fixed costs have on changes in operating inco me as changes occur in units sold, and hence, in contribution margin. Knowing the degree o f operating leverage at a given level o f sales helps managers calculate the effect of fluctuations in sales on operating incomes. 3­13 CVP analysis is always conducted for a specified time horizon. One extreme is a ver y short­time horizon. For example, so me vacat ion cruises o ffer 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. 3­2 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 beco me variable costs with a longer time horizon. 3­14 A company wit h mult iple products can co mpute a breakeven po int by assuming there is a constant sales mix o f products at different levels o f total revenue. 3­15 Yes, gross margin calculations emphasize the dist inct ion between manufacturing and nonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing costs). Contribution margin calculat ions emphasize the dist inct ion between fixed and variable costs. Hence, contribut ion margin is a more useful concept than gross margin in CVP analysis. 3­16 (10 min.) CVP computations. Variable Revenues Costs $ 500 $2,000 2,000 1,500 1,000 700 1,500 900 Fixed Costs $300 300 300 300 Total Costs $ 800 1,800 1,000 1,200 Operating Contribution Income Margin $1,200 $1,500 200 500 0 300 300 600 Contribution Margin % 75.0% 25.0% 30.0% 40.0% a. b. c. d. 3­17 (10–15 min.) CVP computations. 1a. Sales ($30 per unit × 200,000 units) Variable costs ($25 per unit × 200,000 units) Contribut ion margin Contribut ion margin (fro m above) Fixed costs Operating inco me Sales (fro m above) Variable costs ($16 per unit × 200,000 units) Contribut ion margin Contribut ion margin Fixed costs Operating inco me $6,000,000 5,000,000 $1,000,000 $1,000,000 800,000 $ 200,000 $6,000,000 3,200,000 $2,800,000 $2,800,000 2,400,000 $ 400,000 1b. 2a. 2b. 3. Operating income is expected to increase by $200,000 if Ms. Schoenen’s proposal is accepted. The management would consider other factors before making the final decis io n. It is likely that product qualit y would improve as a result of using state of the art equipment. Due to increased automat ion, probably many workers will have to be laid o ff. Patel’s management will have to consider the impact of such an act ion on emplo yee morale. In addit ion, the proposal increases the co mpany’s fixed costs dramat ically. This will increase the co mpany’s operating leverage and risk. 3­3 3­18 (35–40 min.) CVP analysis, changing revenues and costs. 1a. SP VCU CMU FC Q = 8% × $1,000 = $80 per ticket = $35 per ticket = $80 – $35 = $45 per ticket = $22,000 a month = $22,000 FC = CMU $45 per ticket = 489 tickets (rounded up) 1b. Q = FC + TOI $22,000 + $10,000 = CMU $45 per ticket = $32,000 $45 per ticket = 712 tickets (rounded up) 2a. SP VCU CMU FC Q = $80 per ticket = $29 per ticket = $80 – $29 = $51 per ticket = $22,000 a month = $22,000 FC = CMU $51 per ticket = 432 tickets (rounded up) 2b. Q = FC + TOI $22,000 + $10,000 = CMU $51 per ticket $32,000 $51 per ticket = 628 tickets (rounded up) = 3a. SP VCU CMU FC Q = $48 per ticket = $29 per ticket = $48 – $29 = $19 per ticket = $22,000 a month $22,000 FC = CMU $19 per ticket = 1,158 tickets (rounded up) = 3­4 3b. Q = FC + TOI $22,000 + $10,000 = CMU $19 per ticket = $32,000 $19 per ticket = 1,685 tickets (rounded up) The reduced commissio n sizably increases the breakeven po int and the number of t ickets required to yield a target operating inco me of $10,000: 8% Commission (Requirement 2) 432 628 Breakeven point Attain OI of $10,000 Fixed Commission of $48 1,158 1,685 4a. The $5 delivery fee can be treated as either an extra source of revenue (as done below) or as a cost offset. Either approach increases CMU $5: SP VCU CMU FC Q = $53 ($48 + $5) per ticket = $29 per ticket = $53 – $29 = $24 per ticket = $22,000 a month = $22,000 FC = CMU $24 per ticket = 917 tickets (rounded up) 4b. Q = FC + TOI $22,000 + $10,000 = CMU $24 per ticket = $32,000 $24 per ticket = 1,334 tickets (rounded up) The $5 delivery fee results in a higher contribut ion margin which reduces both the breakeven point and the tickets sold to attain operating inco me of $10,000. 3­5 3­19 (20 min.) CVP exercises. Budgeted Operating Income $200,000 400,000 0 110,000 290,000 360,000 40,000 220,000 510,000 Revenues Orig. 1. 2. 3. 4. 5. 6. 7. 8. Variable Costs Contribution Margin $2,000,000 a 2,200,000 b 1,800,000 2,000,000 2,000,000 2,160,000 1,840,000 2,200,000 2,400,000 Fixed Costs G $1,800,000 1,800,000 1,800,000 c 1,890,000 d 1,710,000 1,800,000 1,800,000 k 1,980,000 m 1,890,000 G G $10,000,000 $8,000,000 10,000,000 7,800,000 10,000,000 8,200,000 10,000,000 8,000,000 10,000,000 8,000,000 e f 10,800,000 8,640,000 g h 9,200,000 7,360,000 i j 11,000,000 8,800,000 l 10,000,000 7,600,000 G tan ds for given . s a 000,000 × 1.10 b 000,000 × 0.90; c$1,800,000 × 1.05; d ,800,000 × 0.95; e$10,000,000 × 1.08; ; $2, $2, $1 f 000,000 × 1.08; g ,000,000 × 0.92; h 000,000 × 0.92; i 0,000,000 × 1.10; j$8,000,000 × 1.10; $8, $10 $8, $1 k 800,000 × 1.10; l ,000,000 × 0.95; m ,800,000 × 1.05 $1, $8 $1 3­20 (20 min.) CVP exercises. 1a. [Units so ld (Selling price – Variable costs)] – Fixed costs = Operating inco me [5,000,000 ($0.50 – $0.30)] – $900,000 = $100,000 Fixed costs ÷ Contribution margin per unit = Breakeven units $900,000 ÷ [($0.50 – $0.30)] = 4,500,000 units Breakeven units × Selling price = Breakeven revenues 4,500,000 units × $0.50 per unit = $2,250,000 or, Selling price ­Variable costs Contribut ion margin rat io = Selling price $0.50 ­ $0.30 = = 0.40 $0. 50 Fixed costs ÷ Contribution margin rat io = Breakeven revenues $900,000 ÷ 0.40 = $2,250,000 5,000,000 ($0.50 – $0.34) – $900,000 [5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)] [5,000,000 (1.4) ($0.40 – $0.27)] – [$900,000 (0.8)] $900,000 (1.1) ÷ ($0.50 – $0.30) ($900,000 + $20,000) ÷ ($0.55 – $0.30) = $ (100,000) = $ 110,000 = $ 190,000 = = 4,950,000 units 3,680,000 units 1b. 2. 3. 4. 5. 6. 3­6 3­21 (10 min.) CVP analysis, income taxes. 1. Monthly fixed costs = $60,000 + $70,000 + $10,000 = Contribut ion margin per unit = $26,000 – $22,000 – $500 = Monthly fixed costs $140,000 Breakeven units per month = = = Contribution margin per unit $3,500 per car 2. Tax rate Target net income $140,000 $ 3,500 40 cars 40% $63,000 Target net income $63, 000 $63, 000 = = = Target operating inco me = $105,000 1 ­ tax rate (1 - 0.40) 0.60 Quantity of output units = Fixed costs + Target operating income = $140, 000 + $105, 000 = 70 cars required to be sold Contribution margin per unit $3, 500 3­7 3­22 (20–25 min.) CVP analysis, income taxes. 1. Variable cost percentage is $3.20 ¸ $8.00 = 40% Let R = Revenues needed to obtain target net inco me $105, 00 0 R – 0.40R – $450,000 = 1 - 0. 0 3 0.60R = $450,000 + $150,000 R = $600,000 ¸ 0.60 R = $1,000,000 or, $105, 00 0 Target net income $450,000 + 1 - 0. 0 = $1,000,000 3 1 - Tax rate = Breakeven revenues = Contribut ion margin percentage 0.60 Proof: Revenues Variable costs (at 40%) Contribut ion margin Fixed costs Operating inco me Inco me taxes (at 30%) Net inco me $1,000,000 400,000 600,000 450,000 150,000 45,000 $ 105,000 2.a. Customers needed to earn net inco me of $105,000: Total revenues ¸ Sales check per customer $1,000,000 ¸ $8 = 125,000 customers Customers needed to break even: Contribut ion margin per customer = $8.00 – $3.20 = $4.80 Breakeven number of customers = Fixed costs ¸ Contribut ion margin per customer = $450,000 ¸ $4.80 per customer = 93,750 customers Using the shortcut approach: Unit ö æ Change in æ ö çcontribution ÷ ´ (1 – Tax rate) Change in net inco me = çnumber of customers÷ ´ ç ÷ è ø è margin ø = (150,000 – 125,000) ´ $4.80 ´ (1 – 0.30) = $120,000 ´ 0.7 = $84,000 New net income = $84,000 + $105,000 = $189,000 b. 3. The alternat ive approach is: Revenues, 150,000 ´ $8.00 Variable costs at 40% Contribut ion margin Fixed costs Operating inco me Inco me tax at 30% Net inco me $1,200,000 480,000 720,000 450,000 270,000 81,000 $ 189,000 3­8 3­23 1. (30 min.) CVP analysis, sensitivity analysis. SP = $30.00 ´ (1 – 0.30 margin to bookstore) = $30.00 ´ 0.70 = $21.00 VCU = $ 4.00 variable production and market ing cost 3.15 variable author royalt y cost (0.15 ´ $21.00) $ 7.15 CMU = $21.00 – $7.15 = $13.85 per copy FC = $ 500,000 fixed production and market ing cost 3,000,000 up­front payment to Washington $3,500,000 Solution Exhibit 3­23A shows the PV graph. SOLUTION EXHIBIT 3­23A PV Graph for Media Publishers $4,000 FC = $3,500,000 CMU = $13.85 per book sold 3,000 2,000 Operating income (000’s) 1,000 0 10 0,0 00 20 0,0 00 30 0,0 00 40 0,0 00 50 0,0 00 U n its so l d ­1,000 252,708 units ­2,000 ­3,000 $3.5 million ­4,000 3­9 2a. Breakeven FC = number of unit s CMU $3, 500, 000 = $13. 85 = 252,708 copies so ld (rounded up) 2b. Target OI = FC + OI CMU $3,500,000 + $2,000,000 $13. 85 $5, 500, 000 = $13. 85 = 397,112 copies so ld (rounded up) = 3a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the fo llo wing effects: SP = $30.00 ´ (1 – 0.20) = $30.00 ´ 0.80 = $24.00 VCU = $ 4.00 variable production and marketing cost + 3.60 variable author royalt y cost (0.15 ´ $24.00) $ 7.60 CMU = $24.00 – $7.60 = $16.40 per copy Breakeven FC number of unit s = CMU $3, 500, 000 = $16. 40 = 213,415 copies so ld (rounded up) The breakeven point decreases fro m 252,708 copies in requirement 2 to 213,415 copies. 3b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30% has the fo llowing effects: SP = $40.00 ´ (1 – 0.30) = $40.00 ´ 0.70 = $28.00 VCU = $ 4.00 variable production and market ing cost + 4.20 variable author royalt y cost (0.15 ´ $28.00) $ 8.20 CMU= $28.00 – $8.20 = $19.80 per copy 3­10 Breakeven $3, 500, 000 = number of unit s $19. 80 = 176,768 copies so ld (rounded up) The breakeven point decreases fro m 252,708 copies in requirement 2 to 176,768 copies. 3c. The answers to requirements 3a and 3b decrease the breakeven po int relat ive to that in requirement 2 because in each case fixed costs remain the same at $3,500,000 while the contribution margin per unit increases. 3­24 (10 min.) CVP analysis, margin of safety. Fixed costs 1. Breakeven point revenues = Contributi n margin percentage o $600,000 Contribut ion margin percentage = = 0.40 or 40% $1,500,000 Selling price - Variable cost per unit 2. Contribut ion margin percentage = Selling price S P - $15 0.40 = SP 0.40 SP = SP – $15 0.60 SP = $15 SP = $25 3. Breakeven sales in units = Revenues ÷ Selling price = $1,500,000 ÷ $25 = 60,000 units Margin of safet y in units = sales in units – Breakeven sales in units = 80,000 – 60,000 = 20,000 units Revenues, 80,000 units ´ $25 Breakeven revenues Margin of safet y $2,000,000 1,500,000 $ 500,000 3­11 3­25 (25 min.) Operating leverage. 1a. Let Q denote the quant it y of carpets sold Breakeven point under Option 1 $500Q - $350Q = $5,000 $150Q = $5,000 Q = $5,000 ¸ $150 = 34 carpets (rounded up) 1b. Breakeven point under Option 2 $500Q - $350Q - (0.10 ´ $500Q) = 100Q = Q = 0 0 0 2. Operating inco me underOption 1 = $150Q - $5,000 Operating inco me under Option 2 = $100Q Find Q such that $150Q - $5,000 = $100Q $50Q = $5,000 Q = $5,000 ¸ $50 = 100 carpets Revenues = $500 × 100 carpets = $50,000 For Q = 100 carpets, operating inco me under both Option 1 and Option 2 = $10,000 For Q > 100, say, 101 carpets, Option 1 gives operating inco me = ($150 ´ 101) - $5,000 = $10,150 Option 2 gives operating inco me = $100 ´ 101 = $10,100 So Color Rugs will prefer Option 1. For Q < 100, say, 99 carpets, Option 1 gives operating inco me = ($150 ´ 99) - $5,000 = $9,850 Option 2 gives operating inco me = $100 ´ 99 = $9,900 So Color Rugs will prefer Option 2. 3. Contributi n margin o Operating income $150 ´ 100 Under Option 1, degree of operating leverage = = 1.5 $10,000 $100 ´ 100 Under Option 2, degree of operating leverage = = 1.0 $10,000 Degree of operating leverage = 4. The calculations in requirement 3 indicate that when sales are 100 units, a percentage change in sales and contribut ion margin will result in 1.5 t imes that percentage change in operating inco me for Option 1, but the same percentage change in operating inco me for Option 2. The degree o f operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes. 3­12 3­26 (15 min.) CVP analysis, international cost structure differences. Variable Variable Operating Income for Sales price Annual Manufacturing Marketing & Contribution Budgeted Sales of Country to retail Fixed Cost Distribution Cost Margin Breakeven Breakeven 800,000 outlets Costs per Sweater per Sweater Per Unit Units Revenues Sweaters (1) (2) (3) (4) (5)=(1)­(3)­(4) (6)=(2) ¸ (5) (6) ´ (1) (7)=[800,000 ´ (5)] – (2) Singapor e $32.00 $ 6,500,000 $ 8.00 $11.00 $13.00 500,000 $16,000,000 $3,900,000 Thailand 32.00 4,500,000 5.50 11.50 15.00 300,000 9,600,000 7,500,000 United States 32.00 12,000,000 13.00 9.00 10.00 1,200,000 38,400,000 (4,000,000) Requirement 1 Requirement 2 Thailand has the lowest breakeven po int since it has both the lowest fixed costs ($4,500,000) and the lowest variable cost per unit ($17.00). Hence, for a given selling price, Thailand will always have a higher operating income (or a lower operating loss) than Singapore or the U.S. The U.S. breakeven po int is 1,200,000 units. Hence, with sales o f only 800,000 units, it has an operating loss of $4,000,000. 3­13 3­27 (30 min.) Sales mix, new and upgrade customers. 1. New Upgrade Customers Customers $210 $120 90 40 120 80 SP VCU CMU The 60%/40% sales mix implies that, in each bundle, 3 unit s are so ld to new customers and 2 units are so ld to upgrade customers. Contribut ion margin o f the bundle = 3 × $120 + 2 × $80 = $360 + $160 = $520 $14, 000, 000 Breakeven point in bundles = = 26,923 bundles $520 Breakeven point in units is: Sales to new customers: 26,923 bundles × 3 units per bundle 80,769 units Sales to upgrade customers: 26,923 bundles × 2 units per bundle 53,846 units Total number of unit s to breakeven (rounded) 134,615 units Alternat ively, Let S = Number of units so ld to upgrade customers 1.5S = Number of units so ld to new customers Revenues – Variable costs – Fixed costs = Operating income [$210 (1.5S) + $120S] – [$90 (1.5S) + $40S] – $14,000,000 = OI $435S – $175S – $14,000,000 = OI Breakeven point is 134,616 units when OI = 0 because $260S S 1.5S BEP = $14,000,000 = 53,846 units sold to upgrade customers (rounded) = 80,770 units sold to new customers (rounded) = 134,616 units Check Revenues ($210 ´ 80,770) + ($120 ´ 53,846) Variable costs ($90 ´ 80,770) + ($40 ´ 53,846) Contribut ion margin Fixed costs Operating inco me (caused by rounding) $23,423,220 9,423,140 14,000,080 14,000,000 $ 80 3­14 2. When 200,000 units are sold, mix is: Units so ld to new customers (60% ´ 200,000) 120,000 Units so ld to upgrade customers (40% ´ 200,000) 80,000 Revenues ($210 ´ 120,000) + ($120 ´ 80,000) Variable costs ($90 ´ 120,000) + ($40 ´ 80,000) Contribut ion margin Fixed costs Operating inco me $34,800,000 14,000,000 20,800,000 14,000,000 $ 6,800,000 3a. At New 50%/Upgrade 50% mix, each bundle contains 1 unit sold to new customer and 1 unit so ld to upgrade customer. Contribut ion margin o f the bundle = 1 ´ $120 + 1 ´ $80 = $120 + $80 = $200 $14, 000, 000 Breakeven point in bundles = = 70,000 bundles $200 Breakeven po int in unit s is: Sales to new customers: 70,000 bundles × 1 unit per bundle 70,000 units Sales to upgrade customers: 70,000 bundles × 1 unit per bundle 70,000 units Total number of unit s to breakeven 140,000 units Alternat ively, Let S = Number of unit s so ld to upgrade customers then S = Number of unit s so ld to new customers [$210S + $120S] – [$90S + $40S] – $14,000,000 = OI 330S – 130S = $14,000,000 200S = $14,000,000 S = 70,000 units sold to upgrade customers S = 70,000 units sold to new customers BEP = 140,000 units Check Revenues ($210 ´ 70,000) + ($120 ´ 70,000) $23,100,000 Variable costs ($90 ´ 70,000) + ($40 ´ 70,000) 9,100,000 Contribut ion margin 14,000,000 Fixed costs 14,000,000 Operating inco me $ 0 3b. At New 90%/ Upgrade 10% mix, each bundle contains 9 units so ld to new customers and 1 unit so ld to upgrade customers. Contribut ion margin o f the bundle = 9 ´ $120 + 1 ´ $80 = $1,080 + $80 = $1,160 $14, 000, 000 Breakeven point in bundles = = 12,069 bundles (rounded) $1,160 Breakeven po int in unit s is: Sales to new customers: 12,069 bundles × 9 units per bundle 108,621 units Sales to upgrade customers: 12,069 bundles × 1 unit per bundle 12,069 units Total number of unit s to breakeven 120,690 units 3­15 Alternat ively, Let S = Number of unit s so ld to upgrade customers then 9S = Number of unit s so ld to new customers [$210 (9S) + $120S] – [$90 (9S) + $40S] – $14,000,000 = OI 2,010S – 850S = $14,000,000 1,160S = $14,000,000 S = 12,069 units sold to upgrade customers (rounded up) 9S = 108,621 units sold to new customers (rounded up) 120,690 units Check Revenues ($210 ´ 108,621) + ($120 ´ 12,069) Variable costs ($90 ´ 108,621) + ($40 ´ 12,069) Contribut ion margin Fixed costs Operating inco me (caused by rounding) $24,258,690 10,258,650 14,000,040 14,000,000 $ 40 3c. As Zapo increases its percentage o f new customers, which have a higher contribut ion margin per unit than upgrade customers, the number of unit s required to break even decreases: New Upgrade Breakeven Customers Customers Point 50% 50% 140,000 60 40 134,616 90 10 120,690 Requirement 3(a) Requirement 1 Requirement 3(b) 3­28 (20 min.) CVP analysis, multiple cost drivers. 1a. Operating income Cost of pictur e Quan tity of ö æ Cost of Number of ö Fixed = Revenues - æ ´ ´ ÷ - ç ÷-ç fr ames pictur e fr ames ø è sh ipmen t sh ipmen ts ø costs è = ($45 ´ 40,000) - ($30 ´ 40,000) - ($60 ´ 1,000) - $240,000 = $1,800,000 - $1,200,000 - $60,000 - $240,000 = $300,000 1b. 2. Operating income = ($45 ´ 40,000) - ($30 ´ 40,000) - ($60 ´ 800) - $240,000 = $312,000 Denote the number of picture frames so ld by Q, then $45Q - $30Q – (500 ´ $60) - $240,000 = 0 $15Q = $30,000 + $240,000 = $270,000 Q = $270,000 ¸ $15 = 18,000 picture frames Suppose Susan had 1,000 shipments. $45Q - $30Q - (1,000 ´ $60) - $240,000 = 0 15Q = $300,000 Q = 20,000 picture frames 3. The breakeven point is not unique because there are two cost drivers—quantity of picture frames and number of shipments. Various combinations of the two cost drivers can yield zero operating income. 3­16 3­29 (25 mins) CVP, Not for profit. 1. Contribut ions Fixed costs Cash available to purchase land Divided by cost per acre to purchase land Acres of land SG can purchase Contribut ions ($19,000,000 – $5,000,000) Fixed costs Cash available to purchase land Divided by cost per acre to purchase land ($3,000 – $1,000) Acres of land SG can purchase $19,000,000 1,000,000 $18,000,000 ÷3,000 6,000 acres $14,000,000 1,000,000 $13,000,000 ÷2,000 6,500 acres 2. On financial considerations alone, SG should take the subsidy because it can purchase 500 more acres (6,500 acres – 6,000 acres). 3. Let the decrease in contribut ions be $ x . Cash available to purchase land = $19,000,000 – $ x – $1,000,000 Cost to purchase land = $3,000 – $1,000 = $2,000 To purchase 6,000 acres, we solve the fo llowing equation for x . 19, 000, 000 - x - 1, 000, 000 = 6, 000 2, 000 18, 000, 000 - x = 6, 000 ´ 2, 000 18, 000, 000 - x = 12, 000, 000 x = $6, 000, 000 SG will be indifferent between taking the government subsidy or not if contribut ions decrease by $6,000,000. 3­17 3­30 (15 min.) Contribution margin, decision making. 1. Revenues Deduct variable costs: Cost of goods sold Sales commissio ns Other operating costs Contribut ion margin Contribut ion margin percentage = $500,000 $200,000 50,000 40,000 290,000 $210,000 2. 3. $210,000 = 42% $500,000 Incremental revenue (20% × $500,000) = $100,000 Incremental contribut ion margin (42% × $100,000) Incremental fixed costs (advertising) Incremental operating income $42,000 10,000 $32,000 If Mr. Schmidt spends $10,000 more on advertising, the operating inco me will increase by $32,000, convert ing an operating loss of $10,000 to an operating inco me of $22,000. Proof (Optional): Revenues (120% × $500,000) Cost of goods sold (40% of sales) Gross margin Operating costs: Salaries and wages Sales commissio ns (10% of sales) Depreciat ion of equipment and fixtures Store rent Advert ising Other operating costs: $40,000 Variable ( × $600,000) $500,000 Fixed Operating inco me $600,000 240,000 360,000 $150,000 60,000 12,000 48,000 10,000 48,000 10,000 338,000 $ 22,000 3­18 3­31 (20 min.) Contribution margin, gross margin and margin of safety. 1. Mirabella Cosmetics Operating Income Statement, June 2008 Units so ld Revenues Variable costs Variable manufacturing costs Variable marketing costs Total variable costs Contribut ion margin Fixed costs Fixed manufacturing costs Fixed market ing & administration costs Total fixed costs Operating inco me 10,000 $100,000 $ 55,000 5,000 60,000 40,000 $ 20,000 10,000 30,000 $ 10,000 2. $40,000 = $4 per unit 10,000 units Fixed costs $30, 000 = = 7, 500 units Breakeven quant it y = Contribution margin per unit $4 per unit Revenues $100, 000 = = $10 per unit Selling price = Units sold 10,000 units Breakeven revenues = 7,500 units ´ $10 per unit = $75,000 Contribut ion margin per unit = Alternat ively, Contribut ion margin percentage = Contribution margin $40, 000 = = 40% Revenues $100, 000 Breakeven revenues = Fixed costs $30, 000 = = $75, 000 Contribution margin percentage 0.40 3. Margin of safet y (in units) = Units so ld – Breakeven quant it y = 10,000 units – 7,500 units = 2,500 units 4. Units so ld Revenues (Units so ld ´ Selling price = 8,000 ´ $10) Contribut ion margin (Revenues ´ CM percentage = $80,000 ´ 40%) Fixed costs Operating inco me Taxes (30% ´ $2,000) Net inco me 8,000 $80,000 $32,000 30,000 2,000 600 $ 1,400 3­19 3­32 (30 min.) Uncertainty and expected costs. 1. Monthly Number of Orders 300,000 400,000 500,000 600,000 700,000 Monthly Number of Orders 300,000 400,000 500,000 600,000 700,000 Monthly Number of Orders 300,000 400,000 500,000 600,000 700,000 2. Current System Expected Cost: $13,000,000 × 0.1 = $ 1,300,000 17,000,000 × 0.25 = 4,250,000 21,000,000 × 0.40 = 8,400,000 25,000,000 × 0.15 = 3,750,000 29,000,000 × 0.10 = 2,900,000 $ 20,600,000 Partially Automated System Expected Cost: $14,000,000 × 0.1 = $ 1 ,400,000 17,000,000 × 0.25 = 4,250,000 20,000,000 × 0.40 = 8,000,000 23,000,000 × 0.15 = 3,450,000 26,000,000 × 0.1 = 2,600,000 $19,700,000 Fully Automated System Expected Cost: $16,000,000 × 0.1 = $ 1,600,000 18,000,000 × 0.25 = 4,500,000 20,000,000 × 0.40 = 8,000,000 22,000,000 × 0.15 = 3,300,000 24,000,000 × 0.10 = 2,400,000 $19,800,000 Cost of Current System $1,000,000 + $40(300,000) = $13,000,000 $1,000,000 + $40(400,000) = $17,000,000 $1,000,000 + $40(500,000) = $21,000,000 $1,000,000 + $40(600,000) = $25,000,000 $1,000,000 + $40(700,000) = $29,000,000 Cost of Partially Automated System $5,000,000 + $30(300,000) = $14,000,000 $5,000,000 + $30(400,000) = $17,000,000 $5,000,000 + $30(500,000) = $20,000,000 $5,000,000 + $30(600,000) = $23,000,000 $5,000,000 + $30(700,000) = $26,000,000 Cost of Fully Automated System $10,000,000 + $20(300,000) = $16,000,000 $10,000,000 + $20(400,000) = $18,000,000 $10,000,000 + $20(500,000) = $20,000,000 $10,000,000 + $20(600,000) = $22,000,000 $10,000,000 + $20(700,000) = $24,000,000 3­20 3. Dawmart should consider the impact of the different systems on its relat ionship wit h 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 prohibit ive. Dawmart may also want to consider other factors such as the reliabilit y o f different systems and the effect on emplo yee morale if emplo yees have to be laid off as it automates its systems. 3­33 (15–20 min.) CVP analysis, service firm. 1. Revenue per package Variable cost per package Contribut ion margin per package $4,000 3,600 $ 400 Breakeven (unit s) = Fixed costs ÷ Contribut ion margin per package $480,000 = = 1,200 tour packages $400 per package 2. Contribut ion margin rat io = Contributi n margin per package o $ 400 = = 10% Selling price $4,000 Revenue to achieve target inco me = (Fixed costs + target OI) ÷ Contribut ion margin ratio $480,000 + $100,000 = = $5,800,000, or 0. 10 $480, 000 + $100, 000 Number of tour packages to earn $100,000 operating income: = = 1,450 tour packages $400 Revenues to earn $100,000 OI = 1,450 tour packages × $4,000 = $5,800,000. 3. Fixed costs = $480,000 + $24,000 = $504,000 Breakeven (units) = Fixed costs Contributi n margin per unit o Fixed costs Breakeven (units) $504,000 = = $420 per tour package 1,200 tour packages Contribut ion margin per unit = Desired variable cost per tour package = $4,000 – $420 = $3,580 Because the current variable cost per unit is $3,600, the unit variable cost will need to be reduced by $20 to achieve the breakeven po int calculated in requirement 1. Alternate Method: If fixed cost increases by $24,000, then total variable costs must be reduced by $24,000 to keep the breakeven point of 1,200 tour packages. Therefore, the variable cost per unit reduction = $24,000 ÷ 1,200 = $20 per tour package 3­21 3­34 1. (30 min.) CVP, target income, service firm. Revenue per child Variable costs per child Contribut ion margin per child Breakeven quant it y = $600 200 $400 Fixed costs Contributi n margin per child o $5, 600 = 14 children $400 = 2. Target quantit y = Fixed costs + Target operating income Contributi n margin per child o $5,600 + $10,400 = 40 children $400 = 3. Increase in rent ($3,000 – $2,000) Field trips Total increase in fixed costs Divide by the number of children enro lled Increase in fee per child $1,000 1,000 $2,000 ÷ 40 $ 50 Therefore, the fee per child will increase fro m $600 to $650. Alternat ively, New contribut ion margin per child = $5,600 + $2, 00 + $10,400 0 = $450 40 New fee per child = Variable costs per child + New contribut ion margin per child = $200 + $450 = $650 3­22 3­35 1. (20–25 min.) CVP analysis. Selling price Variable costs per unit: Purchase price $10.00 Shipping and handling 2.00 Contribut ion margin per unit (CMU) Breakeven point in units = $16.00 12.00 $ 4.00 Fixed costs $600, 000 = = 150,000 units Contr. margin per unit $4. 00 Margin of safet y (unit s) = 200,000 – 150,000 = 50,000 units 2. Since Galaxy is operating above the breakeven po int, any incremental contribut ion margin will increase operating inco me dollar for dollar. Increase in unit s sales = 10% × 200,000 = 20,000 Incremental contribut ion margin = $4 × 20,000 = $80,000 Therefore, the increase in operating income will be equal to $80,000. Galaxy’s operating inco me in 2008 would be $200,000 + $80,000 = $280,000. 3. Selling price Variable costs: Purchase price $10 × 130% Shipping and handling Contribut ion margin per unit Target sales in units = $16.00 $13.00 2.00 15.00 $ 1.00 FC + TOI $600,000 + $200,000 = = 800,000 units CMU $1 Target sales in do llars = $16 × 800,000 = $12,800,000 3­23 3­36 (30–40 min.) CVP analysis, income taxes. 1. Revenues – Variable costs – Fixed costs = Let X = Net inco me for 2008 20,000($25.00) – 20,000($13.75) – $135,000 = X 1 - 0.40 X $500,000 – $275,000 – $135,000 = 0.60 $300,000 $165,000 – $81,000 = X X = $54,000 Target net inco me 1 - Tax rat e Alternat ively, Operating inco me = Revenues – Variable costs – Fixed costs = $500,000 – $275,000 – $135,000 = $90,000 Income taxes = 0.40 × $90,000 = $36,000 Net inco me = Operating inco me – Inco me taxes = $90,000 – $36,000 = $54,000 2. Let Q = Number of units to break even $25.00Q – $13.75Q – $135,000 = 0 Q = $135,000 ¸ $11.25 = 12,000 units 3. Let X = Net inco me for 2009 22,000($25.00) – 22,000($13.75) – ($135,000 + $11,250) = $550,000 – $302,500 – $146,250 = $101,250 = X 1 - 0.40 X 0.60 X 0.60 X = $60,750 4. Let Q = Number of units to break even with new fixed costs of $146,250 $25.00Q – $13.75Q – $146,250 = 0 Q = $146,250 ¸ $11.25 = 13,000 units Breakeven r evenues = 13,000 ´ $25.00 = $325,000 5. Let S = Required sales units to equal 2008 net income 0. 60 $11.25S = $236,250 S = 21,000 units Revenues = 21,000 units ´ $25 = $525,000 $25.00S – $13.75S – $146,250 = $54, 000 6. Let A = Amount spent for advertising in 2009 $550,000 – $302,500 – ($135,000 + A) = $60, 000 0. 60 $550,000 – $302,500 – $135,000 – A = $100,000 $550,000 – $537,500 = A A = $12,500 3­24 3­37 (25 min.) CVP, sensitivity analysis. Contribut ion margin per corkscrew = $4 – 3 = $1 Fixed costs = $6,000 Units so ld = Total sales ÷ Selling price = $40,000 ÷ $4 per corkscrew = 10,000 corkscrews 1. Sales increase 10% Sales revenues 10,000 ´ 1.10 ´ $4.00 Variable costs 10,000 ´ 1.10 ´ $3.00 Contribut ion margin Fixed costs Operating inco me $44,000 33,000 11,000 6,000 $ 5,000 2. Increase fixed costs $2,000; Increase sales 50% Sales revenues 10,000 ´ 1.50 ´ $4.00 $60,000 Variable costs 10,000 ´ 1.50 ´ $3.00 45,000 Contribut ion margin 15,000 Fixed costs ($6,000 + $2,000) 8,000 Operating inco me $ 7,000 3. Increase selling price to $5.00; Sales decrease 20% Sales revenues 10,000 ´ 0.80 ´ $5.00 $40,000 Variable costs 10,000 ´ 0.80 ´ $3.00 24,000 Contribut ion margin 16,000 Fixed costs 6,000 Operating inco me $10,000 4. Increase selling price to $6.00; Variable costs increase $1 per corkscrew Sales revenues 10,000 ´ $6.00 $60,000 Variable costs 10,000 ´ $4.00 40,000 Contribut ion margin 20,000 Fixed costs 6,000 Operating inco me $14,000 Alternat ive 4 yields the highest operating income. If TOP is confident that unit sales will not decrease despite increasing the selling price, it should choose alternative 4. 3­25 3­38 (20–30 min.) CVP analysis, shoe stores. 1. CMU (SP – VCU = $30 – $21) a. Breakeven unit s (FC ¸ CMU = $360,000 ¸ $9 per unit) b. Breakeven revenues (Breakeven units ´ SP = 40,000 units ´ $30 per unit) 2. Pairs so ld Revenues, 35,000 ´ $30 Total cost of shoes, 35,000 ´ $19.50 Total sales co mmissio ns, 35,000 ´ $1.50 Total variable costs Contribut ion margin Fixed costs Operating inco me ( loss) 3. Unit variable data (per pair of shoes) Selling price Cost of shoes Sales commissio ns Variable cost per unit Annual fixed costs Rent Salaries, $200,000 + $81,000 Advert ising Other fixed costs Total fixed costs CMU, $30 – $19.50 a. Breakeven unit s, $441,000 ¸ $10.50 per unit b. Breakeven revenues, 42,000 units ´ $30 per unit 4. Unit variable data (per pair of shoes) Selling price Cost of shoes Sales commissio ns Variable cost per unit Total fixed costs CMU, $30 – $21.30 a. Break even units= $360,000 ¸ $8.70 per unit b. Break even revenues = 41,380 units ´ $30 per unit 5. Pairs so ld Revenues (50,000 pairs ´ $30 per pair) Total cost of shoes (50,000 pairs ´ $19.50 per pair) Sales commissio ns on first 40,000 pairs (40,000 pairs ´ $1.50 per pair) Sales commissio ns on addit ional 10,000 pairs 3­26 $ 9.00 40,000 $1,200,000 35,000 $1,050,000 682,500 52,500 735,000 315,000 360,000 $ (45,000) $ 30.00 19.50 0 $ 19.50 $ 60,000 281,000 80,000 20,000 $ 441,000 $ 10.50 42,000 $1,260,000 $ 30.00 19.50 1.80 $ 21.30 $ 360,000 $ 8.70 41,380 (rounded up) $1,241,400 50,000 $1,500,000 $ 975,000 60,000 [10,000 pairs ´ ($1.50 + $0.30 per pair)] Total variable costs Contribut ion margin Fixed costs Operating inco me Alternat ive approach: 18,000 $1,053,000 $ 447,000 360,000 $ 87,000 Breakeven point in units = 40,000 pairs Store manager receives co mmission o f $0.30 on 10,000 (50,000 – 40,000) pairs. Contribut ion margin per pair beyo nd breakeven point of 10,000 pairs = $8.70 ($30 – $21 – $0.30) per pair. Operating inco me = 10,000 pairs ´ $8.70 contribut ion margin per pair = $87,000. 3­27 3­39 (30 min.) CVP analysis, shoe stores (continuation of 3­38). Salaries + Commission Plan No. of CM units sold per Unit CM (1) (2) (3)=(1) ´ (2) 40,000 $9.00 $360,000 42,000 9.00 378,000 44,000 9.00 396,000 46,000 9.00 414,000 48,000 9.00 432,000 50,000 9.00 450,000 52,000 9.00 468,000 54,000 9.00 486,000 56,000 9.00 504,000 58,000 9.00 522,000 60,000 9.00 540,000 62,000 9.00 558,000 64,000 9.00 576,000 66,000 9.00 594,000 Fixed Operating Costs Income (4) (5)=(3)–(4) $360,000 0 360,000 18,000 360,000 36,000 360,000 54,000 360,000 72,000 360,000 90,000 360,000 108,000 360,000 126,000 360,000 144,000 360,000 162,000 360,000 180,000 360,000 198,000 360,000 216,000 360,000 234,000 CM per Unit (6) $10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 Higher Fixed Salaries Only Operating CM Fixed Costs Income (7)=(1) ´ (6) (8) (9)=(7)–(8) $420,000 $441,000 $ (21,000) 441,000 441,000 0 462,000 441,000 21,000 483,000 441,000 42,000 504,000 441,000 63,000 525,000 441,000 84,000 546,000 441,000 105,000 567,000 441,000 126,000 588,000 441,000 147,000 609,000 441,000 168,000 630,000 441,000 189,000 651,000 441,000 210,000 672,000 441,000 231,000 693,000 441,000 252,000 Difference in favor of higher­fixed­ salary­only (10)=(9)–(5) $(21,000) (18,000) (15,000) (12,000) (9,000) (6,000) (3,000) 0 3,000 6,000 9,000 12,000 15,000 18,000 3­28 1. See preceding table. The new store will have the same operating inco me under eit her compensat ion plan when the volume o f sales is 54, 000 pairs o f shoes. This can also be calculated as the unit sales level at which both compensat ion plans result in the same total costs: Let Q = unit sales level at which total costs are same forboth plans $19.50Q + $360,000 + $ $81,000 = $21Q + $360,000 $1.50 Q = $81,000 Q = 54,000 pairs 2. When sales vo lume is above 54,000 pairs, the higher­ fixed­salaries plan results in lower costs and higher operating inco mes than the salary­plus­commissio n plan. So, for an expected vo lume o f 55,000 pairs, the owner would be inclined to choose the higher­fixed­salaries­only plan. But it is likely that sales vo lume itself is determined by the nature of the co mpensatio n plan. The salary­plus­co mmissio n plan provides a greater motivat ion to the salespeople, and it may well be that for the same amount of mo ney paid to salespeople, the salary­plus­co mmissio n plan generates a higher vo lume of sales than the fixed­salary plan. 3. Let TQ = Target number of units For the salary­only plan, $30.00TQ – $19.50TQ – $441,000 $10.50TQ TQ TQ For the salary­plus­co mmissio n plan, $30.00TQ – $21.00TQ – $360,000 $9.00TQ TQ TQ = $168,000 = $609,000 = $609,000 ÷ $10.50 = 58,000 units = $168,000 = $528,000 = $528,000 ÷ $9.00 = 58,667 units (rounded up) The decisio n regarding the salary plan depends heavily o n predict ions of demand. For instance, the salary plan o ffers the same operating inco me at 58,000 units as the commissio n plan offers at 58,667 units. 4. WalkRite Shoe Company Operating Income Statement, 2008 Revenues (48,000 pairs ´ $30) + (2,000 pairs ´ $18) Cost of shoes, 50,000 pairs ´ $19.50 Commissio ns = Revenues ´ 5% = $1,476,000 ´ 0.05 Contribut ion margin Fixed costs Operating inco me $1,476,000 975,000 73,800 427,200 360,000 $ 67,200 3­29 3­40 (40 min.) Alternative cost structures, uncertainty, and sensitivity analysis. 1. Contribut ion margin assuming fixed rental arrangement = $50 – $30 = $20 per bouquet Fixed costs = $5,000 Breakeven point = $5,000 ÷ $20 per bouquet = 250 bouquets Contribut ion margin assuming $10 per arrangement rental agreement = $50 – $30 – $10 = $10 per bouquet Fixed costs = $0 Breakeven point = $0 ÷ $10 per bouquet = 0 (i.e. EB makes a profit no matter how few bouquets it sells) 2. Let x denote the number of bouquets EB must sell for it to be indifferent between the fixed rent and royalt y agreement. To calculate x we solve the fo llowing equat ion. $50 x – $30 x – $5,000 = $50 x – $40 x $20 x – $5,000 = $10 x $10 x = $5,000 x = $5,000 ÷ $10 = 500 bouquets For sales between 0 to 500 bouquets, EB prefers the royalt y agreement because in this range, $10 x > $20 x – $5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this range, $20 x – $5,000 > $10 x . 3. If we assume the $5 savings in variable costs applies to both options, we solve the fo llo wing equat ion for x . $50 x – $25 x – $5,000 = $50 x – $35 x $25 x – $5,000 = $15 x $10 x = $5,000 x = $5,000 ÷ $10 per bouquet = 500 bouquets The answer is the same as in Requirement 2, that is, for sales between 0 to 500 bouquets, EB prefers the royalt y agreement because in this range, $15 x > $25 x – $5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this range, $25 x – $5,000 > $15 x . 4. Fixed rent agreement: Bouquets Sold Revenue (1) (2) 200 200 ´ $50=$10,000 400 400 ´ $50=$20,000 600 600 ´ $50=$30,000 800 800 ´ $50=$40,000 1,000 1,000 ´ $50=$50,000 Expected value of rent agreement Fixed Costs (3) $5,000 $5,000 $5,000 $5,000 $5,000 Variable Costs (4) 200 ´ $30=$ 6,000 400 ´ $30=$12,000 600 ´ $30=$18,000 800 ´ $30=$24,000 1,000 ´ $30=$30,000 Operating Income (Loss) (5)=(2)–(3)–(4) $ (1,000) $ 3,000 $ 7,000 $11,000 $15,000 Probability (6) 0.20 0.20 0.20 0.20 0.20 Expected Operating Income (7)=(5) ´ (6) $ ( 200) 600 1,400 2,200 3,000 $7,000 3­30 Royalt y agreement: Bouquets Variable Operating Sold Revenue Costs Income (1) (2) (3) (4)=(2)–(3) 200 200 ´ $50=$10,000 200 ´ $40=$ 8,000 $2,000 400 400 ´ $50=$20,000 400 ´ $40=$16,000 $4,000 600 600 ´ $50=$30,000 600 ´ $40=$24,000 $6,000 800 800 ´ $50=$40,000 800 ´ $40=$32,000 $8,000 1,000 1,000 ´ $50=$50,000 1,000 ´ $40=$40,000 $10,000 Expected value of royalty agreement Probability (5) 0.20 0.20 0.20 0.20 0.20 Expected Operating Income (6)=(4) ´ (5) $ 400 800 1,200 1,600 2,000 $6,000 EB should choose the fixed rent agreement because the expected value is higher than the royalt y agreement. EB will lo se money under the fixed rent agreement if EB sells only 200 bouquets but this loss is more than made up for by high operating incomes when sales are high. 3­41 (20­30 min.) CVP, alternative cost structures. 1. Variable cost per glass of lemo nade = $0.15 + ($0.10 ÷ 2) = $0.20 Contribut ion margin per glass = Selling price –Variable cost per glass = $0.50 – $0.20 = $0.30 Breakeven point = Fixed costs ÷ Contribut ion margin per glass = $6.00 ÷ $0.30 = 20 glasses (per day) Fixed costs + Target operating income Contribution margin per glass $6 + $3 = = 30 glasses $0.30 3. Contribut ion margin per glass = Selling price – Variable cost per glass = $0.50 – $0.15 = $0.35 Fixed costs = $6 + $1.70 = $7.70 Fixed costs $7.70 Breakeven point = = = 22 glasses Contribution margin per glass $0.35 2. Target number of glasses = 4. Let x be the number of glasses for which Sarah is indifferent between hiring Jessica or hiring David. Sarah will be indifferent when the profits under the two alternat ives are equal. $0.30 x – $6 = $0.35 x – $7.70 1.70 = 0.05 x x = $1.70 ÷ $0.05 = 34 glasses For sales between 0 and 34 glasses, Sarah prefers Jessica to squeeze the lemons because in this range, $0.30 x – $6 > $0.35 x – $7.70. For sales greater than 34 glasses, Sarah prefers David to squeeze the lemo ns because in this range, $0.35 x – $7.70 > $0.30 x – $6. 3­31 3­42 (30 min.) CVP analysis, income taxes, sensitivity. 1a. To break even, Almo Co mpany must sell 500 units. This amount represents the point where revenues equal total costs. Let Q denote the quant it y of canopies so ld. Revenue = Variable costs + Fixed costs $400Q = $200Q + $100,000 $200Q = $100,000 Q = 500 units Breakeven can also be calculated using contribut ion margin per unit. Contribut ion margin per unit = Selling price – Variable cost per unit = $400 – $200 = $200 Breakeven = Fixed Costs ¸ Contribut ion margin per unit = $100,000 ¸ $200 = 500 units 1b. To achieve its net inco me objective, Almo Co mpany must sell 2,500 unit s. This amount represents the po int where revenues equal total costs plus the corresponding operating inco me object ive to achieve net inco me of $240,000. Revenue = Variable costs + Fixed costs + [Net income ÷ (1 – Tax rate)] $400Q = $200Q + $100,000 + [$240,000 ¸ (1 - 0.4)] $400 Q = $200Q + $100,000 + $400,000 Q = 2,500 units 2. To achieve its net inco me object ive, Almo Co mpany should select the first alternat ive where the sales price is reduced by $40, and 2,700 units are sold during the remainder of the year. This alternative results in the highest net income and is the only alternat ive that equals or exceeds the company’s net inco me object ive. Calculat ions for the three alternat ives are shown below. Alternative 1 Revenues Variable costs Operating inco me Net inco me = = = = a ($400 ´ 350) + ($360 ´ 2,700) = $1,112,000 b $200 ´ 3,050 = $610,000 $1,112,000 - $610,000 - $100,000 = $402,000 $402,000 ´ (1 - 0.40) = $241,200 a$400 – $40; b units + 2,700 units. 350 Alternative 2 Revenues Variable costs Operating inco me Net inco me c$400 – $30; d 00 – $10. $2 = = = = c ($400 ´ 350) + ($370 ´ 2,200) = $954,000 d ($200 ´ 350) + ($190 ´ 2,200) = $488,000 $954,000 - $488,000 - $100,000 = $366,000 $366,000 ´ (1 - 0.40) = $219,600 3­32 Alternative 3 Revenues Variable costs Operating inco me Net inco me = = = = e ($400 ´ 350) + ($380 ´ 2,000) = $900,000 f $200 ´ 2,350 = $470,000 g $900,000 - $470,000 - $90,000 = $340,000 $340,000 ´ (1 - 0.40) = $204,000 e$400 – (0.05 ´ $400) = $400 – $20; f units + 2,000 units; g 0,000 – $10,000 350 $10 3­43 (30 min.) Choosing between compensation plans, operating leverage. 1. We can recast Marston’s inco me statement to emphasize contribut ion margin, and then use it to compute the required CVP parameters. Marston Corporation Income Statement For the Year Ended December 31, 2008 Using Sales Agents $26,000,000 $11,700,000 4,680,000 Using Own Sales Force $26,000,000 $11,700,000 2,600,000 Revenues Variable Costs Cost of goods sold—variable Marketing commissions Contribution margin Fixed Costs Cost of goods sold—fixed Marketing—fixed Operating income Contribution margin percentage ($9,620,000 ¸ 26,000,000; $11,700,000 ¸ $26,000,000) Breakeven r evenues ($6,290,000 ¸ 0.37; $8,370,000 ¸ 0.45) Degr ee of operating leverage ($9,620,000 ¸ $3,330,000; $11,700,000 ¸ $3,330,000) 2. 16,380,000 $9,620,000 14,300,000 $11,700,000 2,870,000 3,420,000 6,290,000 $3,330,000 2,870,000 5,500,000 8,370,000 $ 3,330,000 37% 45% $17,000,000 $18,600,000 2.89 3.51 The calculat ions indicate that at sales o f $26,000,000, a percentage change in sales and contribution margin will result in 2.89 times that percentage change in operating inco me if Marston continues to use sales agents and 3.51 t imes that percentage change in operating inco me if Marston emplo ys its own sales staff. The higher contribut ion margin per dollar of sales and higher fixed costs gives Marston more operating leverage, that is, greater benefits (increases in operating inco me) if revenues increase but greater risks (decreases in operating inco me) if revenues decrease. Marston also needs to consider the skill levels and incent ives under the two alternat ives. Sales agents have more incent ive compensation and hence may be more motivated to increase sales. On the other hand, Marston’s own sales force may be more knowledgeable and skilled in selling the co mpany’s products. That is, the sales vo lume itself will be affected by who sells and by the nature of the compensat ion plan. 3­33 3. Variable costs of market ing Fixed market ing costs = 15% of Revenues = $5,500,000 Variable Fixed Operating inco me = Revenues - Variable - Fixed - market ing - market ing manuf. costs manuf. costs co sts co sts Denote the revenues required to earn $3,330,000 of operating income byR, then R - 0.45R - $2,870,000 - 0.15R - $5,500,000 = $3,330,000 R - 0.45R - 0.15R = $3,330,000 + $2,870,000 + $5,500,000 0.40R = $11,700,000 R = $11,700,000 ¸ 0.40 = $29,250,000 3­44 (15–25 min.) Sales mix, three products. 1. Sales of A, B, and C are in ratio 20,000 : 100,000 : 80,000. So for every 1 unit of A, 5 (100,000 ÷ 20,000) units of B are sold, and 4 (80,000 ÷ 20,000) units of C are sold. Contribut ion margin o f the bundle = 1 ´ $3 + 5 ´ $2 + 4 ´ $1 = $3 + $10 + $4 = $17 $255, 000 Breakeven point in bundles = = 15,000 bundles $17 Breakeven po int in unit s is: Product A: 15,000 bundles × 1 unit per bundle 15,000 units Product B: 15,000 bundles × 5 units per bundle 75,000 units Product C: 15,000 bundles × 4 units per bundle 60,000 units Total number of unit s to breakeven 150,000 units Alternat ively, Let Q = Number of units o f A to break even 5Q = Number of units o f B to break even 4Q = Number of units o f C to break even Contribut ion margin – Fixed costs = Zero operating income $3Q + $2(5Q) + $1(4Q) – $255,000 $17Q Q 5Q 4Q Total = 0 = $255,000 = 15,000 ($255,000 ÷ $17) units of A = 75,000 units of B = 60,000 units of C = 150,000 units 3­34 2. Contribut ion margin: A: 20,000 ´ $3 B: 100,000 ´ $2 C: 80,000 ´ $1 Contribut ion margin Fixed costs Operating inco me Contribut ion margin A: 20,000 ´ $3 B: 80,000 ´ $2 C: 100,000 ´ $1 Contribut ion margin Fixed costs Operating inco me $ 60,000 200,000 80,000 $340,000 255,000 $ 85,000 3. $ 60,000 160,000 100,000 $320,000 255,000 $ 65,000 Sales o f A, B, and C are in ratio 20,000 : 80,000 : 100,000. So for every 1 unit of A, 4 (80,000 ÷ 20,000) units of B and 5 (100,000 ÷ 20,000) units of C are sold. Contribut ion margin o f the bundle = 1 ´ $3 + 4 ´ $2 + 5 ´ $1 = $3 + $8 + $5 = $16 $255, 000 Breakeven point in bundles = = 15,938 bundles (rounded up) $16 Breakeven po int in unit s is: Product A: 15,938 bundles × 1 unit per bundle 15,938 units Product B: 15,938 bundles × 4 units per bundle 63,752 units Product C: 15,938 bundles × 5 units per bundle 79,690 units Total number of unit s to breakeven 159,380 units Alternat ively, Let Q = Number of unit s of A to break even 4Q = Number of unit s of B to break even 5Q = Number of unit s of C to break even Contribut ion margin – Fixed costs = Breakeven point $3Q + $2(4Q) + $1(5Q) – $255,000 $16Q Q 4Q 5Q Total = 0 = $255,000 = 15,938 ($255,000 ÷ $16) units of A (rounded up) = 63,752 units of B = 79,690 units of C = 159,380 units Breakeven po int 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. 3­35 3­45 (40 min.) Multi­product CVP and decision making. 1. Faucet filter: Selling price Variable cost per unit Contribut ion margin per unit Pitcher­cum­filter: Selling price Variable cost per unit Contribut ion margin per unit $80 20 $60 $90 25 $65 Each bundle contains 2 faucet models and 3 pitcher models. So contribut ion margin o f a bundle = 2 ´ $60 + 3 ´ $65 = $315 Breakeven Fixed costs $945, 000 point in = = = 3, 000 bundles Contribution margin per bundle $315 bundles Breakeven point in units of faucet models and pitcher models is: Faucet models: 3,000 bundles ´ 2 units per bundle = 6,000 units Pitcher models: 3,000 bundles ´ 3 units per bundle = 9,000 units Total number of unit s to breakeven 15,000 units Breakeven point in do llars for faucet models and pitcher models is: Faucet models: 6,000 units ´ $80 per unit = $ 480,000 Pitcher models: 9,000 units ´ $90 per unit = 810,000 Breakeven revenues $ 1,290,000 Alternatively, weighted average contribution margin per unit = Breakeven point = $945,000 = 15, 000 units $63 (2 ´ $60) + (3 ´ $65) = $63 5 2 Faucet filter: ´ 15,000 units = 6,000 units 5 3 Pitcher­cum­filter: ´ 5, 000 units = 9, 000 units 1 5 Breakeven point in do llars Faucet filter: 6,000 units ´ $80 per unit = $480,000 Pitcher­cum­filter: 9,000 units ´ $90 per unit = $810,000 2. Faucet filter: Selling price Variable cost per unit Contribut ion margin per unit $80 15 $65 3­36 Pitcher­cum­filter: Selling price Variable cost per unit Contribut ion margin per unit $90 16 $74 Each bundle contains 2 faucet models and 3 pitcher models. So contribut ion margin o f a bundle = 2 ´ $65 + 3 ´ $74 = $352 Breakeven Fixed costs $945, 000 + $181, 400 point in = = = 3, 200 bundles Contribution margin per bundle $352 bundles Breakeven point in units of faucet models and pitcher models is: Faucet models: 3,200 bundles ´ 2 units per bundle = 6,400 units Pitcher models: 3,200 bundles ´ 3 units per bundle = 9,600 units Total number of unit s to breakeven 16,000 units Breakeven point in do llars for faucet models and pitcher models is: Faucet models: 6,400 bundles ´ $80 per unit = $ 512,000 Pitcher models: 9,600 bundles ´ $90 per unit = 864,000 Breakeven revenues $1,376,000 Alternatively, weighted average contribution margin per unit = Breakeven point = Faucet filter: $945,000+181,400 = 16, 000 units $70.40 (2 ´ $65) + (3 ´ $74) = $70.40 5 2 ´ 16,000 units = 6,400 units 5 3 Pitcher­cum­filter: ´ 16, 000 units = 9, 600 units 5 Breakeven point in do llars: Faucet filter: 6,400 units ´ $80 per unit = $512,000 Pitcher­cum­filter: 9,600 units ´ $90 per unit = $864,000 3. Let x be the number of bundles for Pure Water Products to be indifferent between the old and new production equipment. Operating inco me using o ld equipment = $315 x – $945,000 Operating inco me using new equipment = $352 x – $945,000 – $181,400 At point of indifference: $315 x – $945,000 = $352 x – $1,126,400 $352 x – $315 x = $1,126,400 – $945,000 $37 x = $181,400 x = $181,400 ÷ $37 = 4,902.7 bundles = 4,903 bundles (rounded) 3­37 Faucet models = 4,903 bundles ´ 2 units per bundle = 9,806 units Pitcher models = 4,903 bundles ´ 3 units per bundle = 14,709 units Total number of unit s 24,515 units Let x be the number of bundles, When total sales are less than 24,515 units (4,903 bundles), $315x - $945,000 > $352x - $1,126,400, so Pure Water Products is better off wit h the old equipment. When total sales are greater than 24,515 units (4,903 bundles), $352x - $1,126,400 > $315x - $945,000, so Pure Water Products is better off buying the new equipment. At total sales of 30,000 units (6,000 bundles), Pure Water Products should buy the new production equipment. Check $352 ´ 6,000 – $1,126,400 = $985,600 is greater than $315 ´ 6,000 –$945,000 = $945,000. 3­46 (20–25 min.) Sales mix, two products. 1. Sales o f standard and deluxe carriers are in t he ratio of 150,000 : 50,000. So for every 1 unit of deluxe, 3 (150,000 ÷ 50,000) units of standard are sold. Contribut ion margin o f the bundle = 3 ´ $6 + 1 ´ $12 = $18 + $12 = $30 $1, 200, 000 Breakeven point in bundles = = 40,000 bundles $30 Breakeven po int in unit s is: Standard carrier: 40,000 bundles × 3 units per bundle 120,000 units Deluxe carrier: 40,000 bundles × 1 unit per bundle 40,000 units Total number of unit s to breakeven 160,000 units Alternat ively, Let Q = Number of unit s of Deluxe carr ier to break even 3Q = Number of unit s of Standard carrier to break even Revenues – Variable costs – Fixed costs = Zero operating inco me $20(3Q) + $30Q – $14(3Q) – $18Q – $1,200,000 $60Q + $30Q – $42Q – $18Q $30Q Q 3Q = = = = = 0 $1,200,000 $1,200,000 40,000 units of Deluxe 120,000 units of Standard The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of 160,000 units. 3­38 2a. Unit contribut ion margins are: Standard: $20 – $14 = $6; Deluxe: $30 – $18 = $12 If only Standard carriers were so ld, the breakeven point would be: $1,200,000 ¸ $6 = 200,000 units. 2b. If only Deluxe carr iers were sold, the breakeven po int would be: $1,200,000 ¸ $12 = 100,000 units 3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe ­ Fixed costs = 180,000($6) + 20,000($12) – $1,200,000 = $1,080,000 + $240,000 – $1,200,000 = $120,000 Sales of standard and deluxe carriers are in the ratio of 180,000 : 20,000. So for every 1 unit of deluxe, 9 (180,000 ÷ 20,000) units of standard are sold. Contribut ion margin o f the bundle = 9 ´ $6 + 1 ´ $12 = $54 + $12 = $66 $1, 200, 000 Breakeven point in bundles = = 18,182 bundles (rounded up) $66 Breakeven po int in unit s is: Standard carrier: 18,182 bundles × 9 units per bundle 163,638 units Deluxe carrier: 18,182 bundles × 1 unit per bundle 18,182 units Total number of unit s to breakeven 181,820 units Alternat ively, Let Q = Number of unit s of Deluxe product to break even 9Q = Number of unit s of Standard product to break even $20(9Q) + $30Q – $14(9Q) – $18Q – $1,200,000 $180Q + $30Q – $126Q – $18Q $66Q Q 9Q = = = = = 0 $1,200,000 $1,200,000 18,182 units of Deluxe (rounded up) 163,638 units of Standard The breakeven point is 163,638 Standard + 18,182 Deluxe, a total o f 181,820 units. The major lesson o f this problem is that changes in the sales mix change breakeven po ints and operating inco mes. In this example, the budgeted and actual total sales in number o f units were ident ical, but the proportion o f the product having the higher contribution margin declined. Operating inco me suffered, falling fro m $300,000 to $120,000. Moreover, the breakeven point rose from 160,000 to 181,820 units. 3­39 3­47 (20 min.) Gross margin and contribution margin. 1. Ticket sales ($20 ´ 500 attendees) a Variable cost of dinner ($10 ´ 500 attendees) b Variable invitat ions and paperwork ($1 ´ 500) Contribut ion margin Fixed cost of dinner Fixed cost of invitat ions and paperwork Operating profit (loss) a b $10,000 $5,000 500 6,000 2,500 5,500 4,500 8,500 $ (4,000) $5,000/500 attendees = $10/attendee $500/500 attendees = $1/attendee $20,000 $10,000 1,000 6,000 2,500 11,000 9,000 8,500 $ 500 2. Ticket sales ($20 ´ 1,000 attendees) Variable cost of dinner ($10 ´ 1,000 attendees) Variable invitat ions and paperwork ($1 ´ 1,000) Contribut ion margin Fixed cost of dinner Fixed cost of invitat ions and paperwork Operating profit (loss) Ethics, CVP analysis. 3­48 (30 min.) 1. Contribut ion margin percentage = = = Breakeven revenues = = Revenues - Variable c sts o Revenues $5,000,000 - $3,000,000 $5,000,000 $2,000,000 = 40% $5,000,000 Fixed costs Contributi n margin percentage o $2, 160, 000 = $5,400,000 0. 40 2. If variable costs are 52% of revenues, contribution margin percentage equals 48% (100% - 52%) Breakeven revenues Fixed costs Contributi n margin percentage o $2, 160, 000 = = $4,500,000 0. 48 = $5,000,000 2,600,000 2,160,000 $ 240,000 3. Revenues Variable costs (0.52 ´ $5,000,000) Fixed costs Operating inco me 3­40 4. Incorrect reporting o f environmental costs with the goal of cont inuing operations is unethical. In assessing the situat ion, the specific “Standards of Ethical Conduct for Management Accountants” (described in Exhibit 1­7) that the management accountant should consider are listed below. Competence Clear reports using relevant and reliable informatio n should be prepared. Preparing reports on the basis o f incorrect environmental costs to make the company’s performance look better than it is vio lates competence standards. It is unethical for Bush not to report environmental costs to make the plant’s performance look good. Integrity The management accountant has a responsibilit y to avoid actual or apparent conflicts o f interest and advise all appropriate parties o f any potential conflict. Bush may be tempted to report lower environmental costs to please Lemo nd and Woodall and save the jobs o f his co lleagues. This action, however, vio lates the responsibilit y for integrit y. The Standards o f Ethical Conduct require the management accountant to communicate favorable as well as unfavorable informat ion. Credibility The management accountant’s Standards o f Ethical Conduct require that informat ion should be fairly and object ively co mmunicated and that all relevant informat ion should be disclo sed. Fro m a management accountant’s standpoint, underreporting environmental costs to make performance look good would vio late the standard of object ivit y. Bush should indicate to Lemond that estimates of environmental costs and liabilit ies should be included in the analysis. If Lemo nd st ill insists on modifying the numbers and reporting lower environmental costs, Bush should raise the matter with one of Lemo nd’s superiors. If after taking all these steps, there is continued pressure to understate environmental costs, Bush should consider resigning fro m the company and not engage in unethical behavior. 3­49 (35 min.) Deciding where to produce. Peoria Selling price Variable cost per unit Manufacturing Marketing and distribution Contribution margin per unit (CMU) Fixed costs per unit Manufacturing Marketing and distribution Operating income per unit CMU of nor mal production (as shown above) CMU of overtime production ($64 – $3; $48 – $8) $150.00 $72.00 14.00 $88.00 14.00 Moline $150.00 86.00 64.00 102.00 48.00 30.00 19.00 49.00 $ 15.00 $64 61 15.00 14.50 29.50 $ 18.50 $48 40 3­41 1. Annual fixed costs = Fixed cost per unit ´ Daily production rate ´ Norma l annual capacity ($49 ´ 400 units ´ 240 days; $29.50 ´ 320 units ´ 240 days) Breakeven volume = FC ¸ CMU of nor mal production ($4,704,000 ¸ $64; $2,265,600 ¸ 48) 2. Units produced and sold Nor mal annual volume (units) (400 × 240; 320 × 240) Units over nor mal volume (needing overtime) CM from nor mal production units (nor mal annual volume ´ CMU nor mal production) (96,000 × $64; 76,800 × 48) CM from overtime production units (0; 19,200 ´ $40) Total contribution margin Total fixed costs Operating income Total operating income $4,704,000 73,500 units $2,265,600 47,200 Units 96,000 96,000 0 96,000 76,800 19,200 $6,144,000 0 6,144,000 4,704,000 $1,440,000 $3,628,800 $3,686,400 768,000 4,454,400 2,265,600 $2,188,800 3. The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 units at the Mo line plant. The full capacit y o f the Peoria plant, 120,000 units (400 units × 300 days), should be used because the contribut ion from these units is higher at all levels o f production than is the contribution fro m units produced at the Moline plant. Contribut ion margin per plant: Peoria, 96,000 × $64 Peoria 24,000 × ($64 – $3) Moline, 72,000 × $48 Total contribution margin Deduct total fixed costs Operating inco me $ 6,144,000 1,464,000 3,456,000 11,064,000 6,969,600 $ 4,094,400 The contribution margin is higher when 120,000 unit s are produced at the Peoria plant and 72,000 units at the Mo line plant. As a result, operating inco me will also be higher in this case since total fixed costs for the divisio n remain unchanged regardless of the quant it y produced at each plant. 3­42 ...
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