3 CHAPTER COST-VOLUME-PROFIT ANALYSIS NOTATION USED IN CHAPTER 3 SOLUTIONS SP: VCU: CMU: FC: TOI: Selling price Variable cost per unit Contribution margin per unit Fixed costs Target operating income
3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the units sold, selling price, variable cost per unit, or fixed costs of a product. 3-2 1. 2. 3. 4. The assumptions underlying the CVP analysis outlined in Chapter 3 are Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units sold. Total costs can be separated into a fixed component that does not vary with the units sold and a component that is variable with respect to the units sold. When represented graphically, the behavior of total revenues and total costs are linear (represented as a straight line) in relation to units sold within a relevant range and time period. The selling price, variable cost per unit, and fixed costs are known and constant.
3.3 Operating income is total revenues from operations for the accounting period minus cost of goods sold and operating costs (excluding income taxes): Operating income = Total revenues from operations Net income is operating income 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 income as: Net income = Operating income Income taxes 3-4 Contribution margin is the difference between total revenues and total variable costs. Contribution margin per unit is the difference between selling price and variable cost per unit. Contribution-margin percentage is the contribution margin per unit divided by selling price. 3-5 Three methods to express CVP relationships are the equation method, the contribution margin method, and the graph method. The first two methods are most useful for analyzing operating income at a few specific levels of sales. The graph method is useful for visualizing the effect of sales on operating income over a wide range of quantities sold.
3-1
3-6 Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the relationship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis. 3-7 CVP certainly is simple, with its assumption of output as the only revenue and cost driver, and linear revenue and cost relationships. Whether these assumptions make it simplistic depends on the decision context. In some cases, these assumptions may be sufficiently accurate for CVP to provide useful insights. The examples in Chapter 3 (the software package context in the text and the travel agency example in the Problem for Self-Study) illustrate how CVP can provide such insights. In more complex cases, the basic ideas of simple CVP analysis can be expanded. 3-8 An increase in the income tax rate does not affect the breakeven point. Operating income at the breakeven point is zero, and no income taxes are paid at this point. 3-9 Sensitivity analysis is a what-if technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes. The advent of the electronic spreadsheet has greatly increased the ability to explore the effect of alternative assumptions at minimal cost. CVP is one of the most widely used software applications in the management accounting area. 3-10 Examples include: Manufacturingsubstituting a robotic machine for hourly wage workers. Marketingchanging a sales force compensation plan from a percent of sales dollars to a fixed salary. Customer servicehiring a subcontractor to do customer repair visits on an annual retainer basis rather than a per-visit basis. Examples include: Manufacturingsubcontracting a component to a supplier on a per-unit basis to avoid purchasing a machine with a high fixed depreciation cost. Marketingchanging a sales compensation plan from a fixed salary to percent of sales dollars basis. Customer servicehiring a subcontractor to do customer service on a per-visit basis rather than an annual retainer basis.
3-11
3-12 Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold, and hence, in contribution margin. Knowing the degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes. 3-13 CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time horizon. For example, some vacation cruises offer deep price discounts for people who offer to take any cruise on a days 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.
3-2
CVP itself is not made any less relevant when the time horizon lengthens. What happens is that many items classified as fixed in the short run may become variable costs with a longer time horizon. 3-14 A company with multiple products can compute a breakeven point by assuming there is a constant sales mix of products at different levels of total revenue. 3-15 Yes, gross margin calculations emphasize the distinction between manufacturing and nonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing costs). Contribution margin calculations emphasize the distinction between fixed and variable costs. Hence, contribution margin is a more useful concept than gross margin in CVP analysis. 3-16 (10 min.) CVP computations. Revenues $2,000 2,000 1,000 1,500 Variable Costs $ 500 1,500 700 900 Fixed Costs $300 300 300 300 Total Costs $ 800 1,800 1,000 1,200 Operating Income $1,200 200 0 300 Contribution Margin $1,500 500 300 600 Contribution Margin % 75.0% 25.0% 30.0% 40.0%
a. b. c. d.
3-18 1a.
(3540 min.) CVP analysis, changing revenues and costs. 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 = $45 per ticket CMU
= 489 tickets (rounded up) 1b. Q = $22,000 + $10,000 FC + TOI = $45 per ticket CMU $32,000 $45 per ticket
=
= 712 tickets (rounded up) 2a. SP VCU CMU FC = $80 per ticket = $29 per ticket = $80 $29 = $51 per ticket = $22,000 a month
3-3
Q
=
$22,000 FC = $51 per ticket CMU
= 432 tickets (rounded up) 2b. Q = $22,000 + $10,000 FC + TOI = $51 per ticket CMU
$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 = $19 per ticket CMU = 1,158 tickets (rounded up) = = $22,000 + $10,000 FC + TOI = $19 per ticket CMU $32,000 $19 per ticket
3b.
Q
=
= 1,685 tickets (rounded up) The reduced commission sizably increases the breakeven point and the number of tickets required to yield a target operating income of $10,000: 8% Commission (Requirement 2) 432 628 Fixed Commission of $48 1,158 1,685
Breakeven point Attain OI of $10,000
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 = $53 ($48 + $5) per ticket VCU = $29 per ticket CMU = $53 $29 = $24 per ticket
3-4
FC Q
= $22,000 a month = $22,000 FC = $24 per ticket CMU
= 917 tickets (rounded up) 4b. Q = $22,000 + $10,000 FC + TOI = $24 per ticket CMU $32,000 $24 per ticket
=
= 1,334 tickets (rounded up) The $5 delivery fee results in a higher contribution margin which reduces both the breakeven point and the tickets sold to attain operating income of $10,000.
3-5
3-20 1a. 1b.
(20 min.) CVP exercises. [Units sold (Selling price Variable costs)] Fixed costs = Operating income [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 Contribution margin ratio = Selling price $0.50 - $0.30 = = 0.40 $0.50 Fixed costs Contribution margin ratio = 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
2. 3. 4. 5. 6.
3-6
3-22 1.
(2025 min.) CVP analysis, income taxes.
Variable cost percentage is $3.20 $8.00 = 40% Let R = Revenues needed to obtain target net income $105,000 R 0.40R $450,000 = 1 0.30 0.60R = $450,000 + $150,000 R = $600,000 0.60 R = $1,000,000 or, $105,000 Target net income $450,000 + 1 0.30 = $1,000,000 1 Tax rate = Breakeven revenues = 0.60 Contribution margin percentage Proof: Revenues Variable costs (at 40%) Contribution margin Fixed costs Operating income Income taxes (at 30%) Net income $1,000,000 400,000 600,000 450,000 150,000 45,000 $ 105,000
2.a.
Customers needed to earn net income of $105,000: Total revenues Sales check per customer $1,000,000 $8 = 125,000 customers Customers needed to break even: Contribution margin per customer = $8.00 $3.20 = $4.80 Breakeven number of customers = Fixed costs Contribution margin per customer = $450,000 $4.80 per customer = 93,750 customers Using the shortcut approach: Change in net income = (1 Tax rate) = (150,000 125,000) $4.80 (1 0.30) = $120,000 0.7 = $84,000 New net income = $84,000 + $105,000 = $189,000 $1,200,000 480,000 720,000 450,000 270,000 81,000 $ 189,000
b.
3.
The alternative approach is: Revenues, 150,000 $8.00 Variable costs at 40% Contribution margin Fixed costs Operating income Income tax at 30% Net income
3-7
3-24
(10 min.) CVP analysis, margin of safety. Fixed costs 1. Breakeven point revenues = Contribution margin percentage $600,000 Contribution margin percentage = = 0.40 or 40% $1,500,000 Selling price Variable cost per unit 2. Contribution margin percentage = Selling price SP $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 safety 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 safety $2,000,000 1,500,000 $ 500,000
3-8
3-9
3.26
(15 min.) CVP analysis, international cost structure differences.
Operating Income for Budgeted Sales of 800,000 Sweaters (7)=[800,000 (5)] (2) $3,900,000 7,500,000 (4,000,000)
Variable Variable Sales price Annual Manufacturing Marketing & Contribution Country to retail Fixed Cost Distribution Cost Margin Breakeven Breakeven outlets Costs per Sweater per Sweater Per Unit Units Revenues (1) (2) (3) (4) (5)=(1)-(3)-(4) (6)=(2) (5) (6) (1) Singapore $32.00 $ 6,500,000 $ 8.00 $11.00 $13.00 500,000 $16,000,000 Thailand 32.00 4,500,000 5.50 11.50 15.00 300,000 9,600,000 United States 32.00 12,000,000 13.00 9.00 10.00 1,200,000 38,400,000
Thailand has the lowest breakeven point since it has both the lowest fixed costs ($4,500,000) and the Requirement 1 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 point is 1,200,000 units. Hence, with sales of only 800,000 units, it has an operating loss of $4,000,000.
Requirement 2
3-10
3-28 1a.
(20 min.) CVP analysis, multiple cost drivers. Operating income Cost of picture Quantity of Cost of Number of Fixed = Revenues frames picture frames shipment shipments costs = ($45 40,000) ($30 40,000) ($60 1,000) $240,000 = $1,800,000 $1,200,000 $60,000 $240,000 = $300,000 = ($45 40,000) ($30 40,000) ($60 800) $240,000 = $312,000
1b. 2.
Operating income
Denote the number of picture frames sold 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 3. Suppose Susan had 1,000 shipments. $45Q $30Q (1,000 $60) $240,000 = 0 15Q = $300,000 Q = 20,000 picture frames
3
Thebreakevenpointisnotuniquebecausetherearetwocostdriversquantityofpicture framesandnumberofshipments.Variouscombinationsofthetwocostdriverscanyieldzero operatingincome.
3-11
3-12
3-30 1.
(15 min.) Contribution margin, decision making. Revenues Deduct variable costs: Cost of goods sold Sales commissions Other operating costs Contribution margin $500,000 $200,000 50,000 40,000 $210,000 = 42% $500,000
290,000 $210,000
2.
Contribution margin percentage =
3.
Incremental revenue (20% $500,000) = $100,000 Incremental contribution 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 income will increase by $32,000, converting an operating loss of $10,000 to an operating income of $22,000. Proof (Optional): Revenues (120% $500,000) Cost of goods sold (40% of sales) Gross margin 360,000 Operating costs: Salaries and wages Sales commissions (10% of sales) Depreciation of equipment and fixtures Store rent Advertising Other operating costs: $40,000 Variable ( $600,000) $500,000 Fixed Operating income $150,000 60,000 12,000 48,000 10,000 48,000 10,000 338,000 $ 22,000 $600,000 240,000
3-13
3-14
3-32 (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
3-15
3. Dawmart should consider the impact of the different systems on its relationship with suppliers. The interface with Dawmarts 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 Dawmarts supply chain because the cost of the system change would be prohibitive. Dawmart may also want to consider other factors such as the reliability of different systems and the effect on employee morale if employees have to be laid off as it automates its systems.
3-16
3.34 (30 min.) 1.
CVP, target income, service firm. $600 200 $400
Revenue per child Variable costs per child Contribution margin per child Breakeven quantity =
Fixed costs Contribution margin per child $5,600 = 14 children $400
=
2.
Target quantity =
Fixed costs + Target operating income Contribution margin per child $5,600 + $10,400 = 40 children $400 $1,000 1,000 $2,000 40 $ 50
= 3.
Increase in rent ($3,000 $2,000) Field trips Total increase in fixed costs Divide by the number of children enrolled Increase in fee per child
Therefore, the fee per child will increase from $600 to $650. Alternatively, New contribution margin per child = $5,600 + $2,000 + $10,400 = $450 40
New fee per child = Variable per costs child + New contribution margin per child = $200 + $450 = $650
3-17
3-18
3-36 1.
(3040 min.) CVP analysis, income taxes. Revenues Variable costs Fixed costs = Let X = Net income for 2008 Target net income 1 Tax rate
X 1 0.40 X
20,000($25.00) 20,000($13.75) $135,000 = $500,000 $275,000 $135,000 =
0.60 $300,000 $165,000 $81,000 = X X = $54,000
Alternatively, Operating income = Revenues Variable costs Fixed costs
= $500,000 $275,000 $135,000 = $90,000
Income taxes = 0.40 $90,000 = $36,000 Net income = Operating income Income 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 income 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 Q = $146,250 $11.25 Breakeven revenues = 13,000 $25.00 = 0 = 13,000 units = $325,000
5.
Let S = Required sales units to equal 2008 net income
$25.00S $13.75S $146,250 = $54,000 0.60 $11.25S = $236,250 S = 21,000 units Revenues = 21,000 units $25 = $525,000
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
3-19
3-38
(2030 min.) CVP analysis, shoe stores. $ 9.00 40,000
1. CMU (SP VCU = $30 $21) a. Breakeven units (FC CMU = $360,000 $9 per unit) b. Breakeven revenues (Breakeven units SP = 40,000 units $30 per unit) 2. Pairs sold Revenues, 35,000 $30 Total cost of shoes, 35,000 $19.50 Total sales commissions, 35,000 $1.50 Total variable costs Contribution margin Fixed costs Operating income (loss) 3. Unit variable data (per pair of shoes) Selling price Cost of shoes Sales commissions Variable cost per unit Annual fixed costs Rent Salaries, $200,000 + $81,000 Advertising Other fixed costs Total fixed costs CMU, $30 $19.50 a. Breakeven units, $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 commissions 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 sold 3-20
$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
Revenues (50,000 pairs $30 per pair) Total cost of shoes (50,000 pairs $19.50 per pair) Sales commissions on first 40,000 pairs (40,000 pairs $1.50 per pair) Sales commissions on additional 10,000 pairs [10,000 pairs ($1.50 + $0.30 per pair)] Total variable costs Contribution margin Fixed costs Operating income Alternative approach:
$1,500,000 $ 975,000 60,000 18,000 $1,053,000 $ 447,000 360,000 $ 87,000
Breakeven point in units = 40,000 pairs Store manager receives commission of $0.30 on 10,000 (50,000 40,000) pairs. Contribution margin per pair beyond breakeven point of 10,000 pairs = $8.70 ($30 $21 $0.30) per pair. Operating income = 10,000 pairs $8.70 contribution margin per pair = $87,000.
3-21
3-40 (30 min.)
CVP analysis, shoe stores (continuation of 3-38).
Salaries + Commission Plan Higher Fixed Salaries Only 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 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 higher-fixedsalary-only (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
No. of units CM sold per Unit (1) (2) 40,000 $9.00 42,000 9.00 44,000 9.00 46,000 9.00 48,000 9.00 50,000 9.00 52,000 9.00 54,000 9.00 56,000 9.00 58,000 9.00 60,000 9.00 62,000 9.00 64,000 9.00 66,000 9.00
CM (3)=(1) (2) $360,000 378,000 396,000 414,000 432,000 450,000 468,000 486,000 504,000 522,000 540,000 558,000 576,000 594,000
Fixed Costs (4) $360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000
Operating Income (5)=(3)(4) 0 18,000 36,000 54,000 72,000 90,000 108,000 126,000 144,000 162,000 180,000 198,000 216,000 234,000
3-22
1. See preceding table. The new store will have the same operating income under either compensation plan when the volume of sales is 54,000 pairs of shoes. This can also be calculated as the unit sales level at which both compensation plans result in the same total costs: Let Q = unit sales level at which total costs are same forboth plans $19.50Q + $360,000 + $ $81,000 = $21Q + $360,000 $1.50 Q = $81,000 Q = 54,000 pairs 2. When sales volume is above 54,000 pairs, the higher-fixed-salaries plan results in lower costs and higher operating incomes than the salary-plus-commission plan. So, for an expected volume of 55,000 pairs, the owner would be inclined to choose the higher-fixed-salaries-only plan. But it is likely that sales volume itself is determined by the nature of the compensation plan. The salary-plus-commission plan provides a greater motivation to the salespeople, and it may well be that for the same amount of money paid to salespeople, the salary-plus-commission plan generates a higher volume of sales than the fixed-salary plan. 3. Let TQ = Target number of units For the salary-only plan, $30.00TQ $19.50TQ $441,000 $10.50TQ TQ TQ For the salary-plus-commission 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 decision regarding the salary plan depends heavily on predictions of demand. For instance, the salary plan offers the same operating income at 58,000 units as the commission 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 Commissions = Revenues 5% = $1,476,000 0.05 Contribution margin Fixed costs Operating income $1,476,000 975,000 73,800 427,200 360,000 $ 67,200
3-23
3-24
3-42
(30 min.) CVP analysis, income taxes, sensitivity.
1a. To break even, Almo Company must sell 500 units. This amount represents the point where revenues equal total costs. Let Q denote the quantity of canopies sold. Revenue = Variable costs + Fixed costs $400Q = $200Q + $100,000 $200Q = $100,000 Q = 500 units Breakeven can also be calculated using contribution margin per unit. Contribution margin per unit = Selling price Variable cost per unit = $400 $200 = $200 Breakeven = Fixed Costs Contribution margin per unit = $100,000 $200 = 500 units 1b. To achieve its net income objective, Almo Company must sell 2,500 units. This amount represents the point where revenues equal total costs plus the corresponding operating income objective to achieve net income 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 income objective, Almo Company should select the first alternative 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 alternative that equals or exceeds the companys net income objective. Calculations for the three alternatives are shown below. Alternative 1 Revenues Variable costs Operating income Net income Alternative 2 Revenues Variable costs Operating income Net income 3-25 = = = = ($400 350) + ($370c 2,200) = $954,000 ($200 350) + ($190d 2,200) = $488,000 $954,000 $488,000 $100,000 = $366,000 $366,000 (1 0.40) = $219,600 = = = = ($400 350) + ($360a 2,700) = $1,112,000 $200 3,050b = $610,000 $1,112,000 $610,000 $100,000 = $402,000 $402,000 (1 0.40) = $241,200
a$400 $40; b350 units + 2,700 units.
c$400 $30; d$200 $10.
3-26
Alternative 3 Revenues Variable costs Operating income Net income = = = = ($400 350) + ($380e 2,000) = $900,000 $200 2,350f = $470,000 $900,000 $470,000 $90,000g = $340,000 $340,000 (1 0.40) = $204,000
e$400 (0.05 $400) = $400 $20; f350 units + 2,000 units; g$100,000 $10,000
3-44
(1525 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. Contribution margin of the bundle = 1 $3 + 5 $2 + 4 $1 = $3 + $10 + $4 = $17 $255,000 Breakeven point in bundles = = 15,000 bundles $17 Breakeven point in units 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 units to breakeven 150,000 units Alternatively, Let Q = Number of units of A to break even 5Q = Number of units of B to break even 4Q = Number of units of C to break even Contribution 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
3-27
2.
Contribution margin: A: 20,000 $3 B: 100,000 $2 C: 80,000 $1 Contribution margin Fixed costs Operating income Contribution margin A: 20,000 $3 B: 80,000 $2 C: 100,000 $1 Contribution margin Fixed costs Operating income
$ 60,000 200,000 80,000 $340,000 255,000 $ 85,000 $ 60,000 160,000 100,000 $320,000 255,000 $ 65,000
3.
Sales of 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. Contribution margin of 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 point in units 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 units to breakeven 159,380 units Alternatively, Let Q = Number of units of A to break even 4Q = Number of units of B to break even 5Q = Number of units of C to break even Contribution 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 point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C.
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(2025 min.) Sales mix, two products.
1. Sales of standard and deluxe carriers are in the ratio of 150,000 : 50,000. So for every 1 unit of deluxe, 3 (150,000 50,000) units of standard are sold. Contribution margin of the bundle = 3 $6 + 1 $12 = $18 + $12 = $30 $1, 200,000 Breakeven point in bundles = = 40,000 bundles $30 Breakeven point in units 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 units to breakeven 160,000 units Alternatively, Let Q = Number of units of Deluxe carrier to break even 3Q = Number of units of Standard carrier to break even Revenues Variable costs Fixed costs = Zero operating income $20(3Q) + $30Q $14(3Q) $18Q $1,200,000 = $60Q + $30Q $42Q $18Q = $30Q = Q = 3Q = units. 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
2a. 2b.
Unit contribution margins are: Standard: $20 $14 = $6; Deluxe: $30 $18 = $12 If only Standard carriers were sold, the breakeven point would be: $1,200,000 $6 = 200,000 units. If only Deluxe carriers were sold, the breakeven point 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
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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. Contribution margin of the bundle = 9 $6 + 1 $12 = $54 + $12 = $66 $1, 200,000 Breakeven point in bundles = = 18,182 bundles (rounded up) $66 Breakeven point in units 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 units to breakeven 181,820 units Alternatively, Let Q = Number of units of Deluxe product to break even 9Q = Number of units 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 of 181,820 units. The major lesson of this problem is that changes in the sales mix change breakeven points and operating incomes. In this example, the budgeted and actual total sales in number of units were identical, but the proportion of the product having the higher contribution margin declined. Operating income suffered, falling from $300,000 to $120,000. Moreover, the breakeven point rose from 160,000 to 181,820 units.
3-48 1.
(30 min.)
Ethics, CVP analysis. Revenues Variable costs Revenues $5,000,000 $3,000,000 $5,000,000 $2,000,000 = 40% $5,000,000 Fixed costs Contribution margin percentage
Contribution margin percentage = = = Breakeven revenues =
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= 2.
$2,160,000 = $5,400,000 0.40
If variable costs are 52% of revenues, contribution margin percentage equals 48% (100% 52%) Breakeven revenues = = Fixed costs Contribution margin percentage $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 income
4. Incorrect reporting of environmental costs with the goal of continuing operations is unethical. In assessing the situation, the specific Standards of Ethical Conduct for Management Accountants (described in Exhibit 1-7) that the management accountant should consider are listed below. Competence Clear reports using relevant and reliable information should be prepared. Preparing reports on the basis of incorrect environmental costs to make the companys performance look better than it is violates competence standards. It is unethical for Bush not to report environmental costs to make the plants performance look good. Integrity The management accountant has a responsibility to avoid actual or apparent conflicts of interest and advise all appropriate parties of any potential conflict. Bush may be tempted to report lower environmental costs to please Lemond and Woodall and save the jobs of his colleagues. This action, however, violates the responsibility for integrity. The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information. Credibility The management accountants Standards of Ethical Conduct require that information should be fairly and objectively communicated and that all relevant information should be disclosed. From a management accountants standpoint, underreporting environmental costs to make performance look good would violate the standard of objectivity. Bush should indicate to Lemond that estimates of environmental costs and liabilities should be included in the analysis. If Lemond still insists on modifying the numbers and reporting lower environmental costs, Bush should raise the matter with one of Lemonds superiors. If after taking all these steps, there is continued pressure to understate environmental costs, Bush should consider resigning from the company and not engage in unethical behavior.
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