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1、CHAPTER 3COST-VOLUME-PROFIT ANALYSIS3-1Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs per unit, or fixed costs.3-2The assumptions underlying the CVP analysis outlined in
2、Chapter 3 are:1.Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold.2.Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.3.When graphed, the behavior
3、 of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range.4.The unit selling price, unit variable costs, and fixed costs are known and constant.5.The analysis either covers a single product or assumes that the sales mix, when multiple products
4、 are sold, will remain constant as the level of total units sold changes.6.All revenues and costs can be added and compared without taking into account the time value of money.3-3Operating income is total revenues from operations for the accounting period minus total costs from operations (excluding
5、 income taxes):Operating income = Total revenues Total costsNet 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
6、 3 computes net income as:Net income = Operating income Income taxes3-4Contribution margin is computed as 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
7、the contribution margin per unit divided by selling price.3-5Three methods to calculate the breakeven point are the equation method, the contribution margin method, and the graph method.3-6Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the rela
8、tionship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis.3-7CVP 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
9、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 provid
10、e such insights. In more complex cases, the basic ideas of simple CVP analysis can be expanded.3-8An increase in the income tax rate does not affect the breakeven point. Operating income at the breakeven point is zero, and thus no income taxes will be paid at this point.3-9Sensitivity analysis is a
11、what-if technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes. The advent of spreadsheet software has greatly increased the ability to explore the effect of alternative assumptions at minimal cost. CVP is one of the mo
12、st widely used software applications in the management accounting area.3-10Examples 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 t
13、o do customer repair visits on an annual retainer basis rather than a per-visit basis.3-11Examples 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 fi
14、xed 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.3-12Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold and he
15、nce 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. 3-13CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time horizon. For example,
16、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.CVP itself is not made any less relevant
17、 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.3-14A company with multiple products can compute a breakeven point by assuming there is a constant mix of products at different levels of total
18、revenue.3-15Yes, 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, contri
19、bution margin is a more useful concept than gross margin in CVP analysis.3-16(10 min.) CVP computations.VariableFixedTotalOperatingContributionContributionRevenuesCostsCostsCostsIncomeMarginMargin %a.$2,000$ 500$300$ 800$1,200$1,50075.0%b.2,0001,5003001,80020050025.0%c.1,0007003001,000030030.0%d.1,5
20、009003001,20030060040.0%3-17(10-20 min.) CVP computations.a.TCM=Q (USP UVC)=70,000 ($30 $20)=$700,000TFC= TCM OI=$700,000 - ( $15,000) = $715,000b.TCM=Q (USP UVC)$900,000=180,000 ($25 UVC)UVC=$20OI=TCM TFC=$900,000 $800,000 = $100,000c.TCM=Q (USP UVC)$300,000=150,000 (USP $10)USP=$12OI=TCM TFC=$300,
21、000 $220,000 = $80,000d.Q=TCM (USP UVC)=$120,000 ($20 $14)=20,000TFC=TCM OI=$120,000 $12,000 = $108,0003-18(1520 min.) CVP analysis, changing revenues and costs.1.USP=8% $1,000 = $80UVC=$35 ($17 + $18)UCM=$45FC=$22,000 a montha.Q=489 tickets (rounded up)b.Q=712 tickets (rounded up)2.USP=$80UVC=$29 (
22、$17 + $12)UCM=$51FC=$22,000 a montha.Q=432 tickets (rounded up)b.Q=628 tickets (rounded up)3-19 (20 min.) CVP, changing revenues and costs. (Continuation of 3-18) 1.Sunshine charges $1,000 per round-trip ticket. Hence, each ticket will yield only a $48 commission.USP=$48UVC=$29 ($17 + $12)UCM=$19FC=
23、$22,000a.Q=1,158 tickets (rounded up)b.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%Old Commission(3-18 Requirement 2)Upper Limit onCommission of $48Breakeven pointAttain OI
24、 of $10,0004326281,1581,6852.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 UCM by $5:USP=$53 ($48 + $5)UVC=$29 ($17 + $12)UCM=$24FC=$22,000a.Q=917 tickets (rounded up)b.Q=1,334 tickets (rounded up)The $5 deliver
25、y fee results in a higher contribution margin which reduces both the breakeven point and the tickets sold to attain operating income of $10,000.3-20(20 min.) CVP exercises.RevenuesVariableCostsContributionMarginFixedCostsBudgetedOperatingIncomeOrig.$10,000,000G$8,200,000G$1,800,000$1,700,000G$100,00
26、01.10,000,0008,020,0001,980,0001,700,000280,0002.10,000,0008,380,0001,620,0001,700,000(80,000)3.10,000,0008,200,0001,800,0001,785,00015,0004.10,000,0008,200,0001,800,0001,615,000185,0005.10,800,0008,856,0001,944,0001,700,000244,0006.9,200,0007,544,0001,656,0001,700,000(44,000)7.11,000,0009,020,0001,
27、980,0001,870,000110,0008.10,000,0007,790,0002,210,0001,785,000425,000Gstands for given.3-21(20 min.) CVP exercises.1.a.5,000,000 ($0.50 $0.30) $900,000=$ 100,000b.=$2,250,0002.5,000,000 ($0.50 $0.34) $900,000=$ (100,000)3.5,000,000 (1.1) ($0.50 $0.30) $900,000 (1.1)=$ 110,0004.5,000,000 (1.4) ($0.40
28、 $0.27) $900,000 (0.8)=$ 190,0005.$900,000( 1.1) ($0.50 $0.30)=4,950,000 units6.($900,000 + $20,000) ($0.55 $0.30)=3,680,000 units3-22(1015 min.) CVP analysis, income taxes.1.Operating income= Net income (1 tax rate) = $84,000 (1 0.40)= $140,0002.Contribution margin Fixed costs = Operating incomeCon
29、tribution margin $300,000 = $140,000Contribution margin = $440,0003.Revenues 0.80 Revenues = Contribution margin0.20 Revenues = $440,000Revenues = $2,200,0004.Breakeven point = Fixed costs Contribution margin percentageBreakeven point = $300,000 0.20 = $1,500,0003-23(2025 min.) CVP analysis, income
30、taxes. 1.Variable cost percentage is $3.20 $8.00 = 40%Let R = Revenues needed to obtain target net incomeRR $450,000= R=$450,000 + $150,000R=$600,000 R=$1,000,000Proof:Revenues$1,000,000Variable costs (at 40%) 400,000Contribution margin600,000Fixed costs 450,000Operating income 150,000Income taxes (
31、at 30%) 45,000Net income$ 105,0002.a. Sales checks to earn net income of $105,000:$1,000,000 $8 = 125,000 sales checksb. Sales checks to break even:$450,000 $4.80 = 93,750 sales checks3.Using the shortcut approach:Change in net income = (1 Tax rate)=(150,000 125,000) $4.80 (1 .30)=$120,000 0.7 = $84
32、,000New net income=$84,000 + $105,000 = $189,000Proof:Revenues, 150,000 $8.00$1,200,000Variable costs at 40% 480,000Contribution margin 720,000Fixed costs 450,000Operating income 270,000Income tax at 30% 81,000Net income$ 189,0003-24(10 min.) CVP analysis, margin of safety.1.Breakeven point revenues
33、=Contribution margin percentage=2.Contribution margin percentage=0.40=0.40 USP=USP $120.60 USP=$12USP=$203.Revenues, 80,000 units $20$1,600,000Breakeven revenues 1,000,000Margin of safety$ 600,0003-25 (25 min.) Operating leverage.1.Let Q denote the quantity of carpets solda.Breakeven point under Opt
34、ion 1$500Q - $350Q =$5,000$150Q=$5,000Q=$5,000 $150 = 34 carpets (rounded)b.Breakeven point under option 2$500Q - $350Q - (0.10 $500Q) = 0100Q=0Q=02.Operating income under Option 1 = $150Q - $5,000Operating income under Option 2 = $100QFind Q such that $150Q - $5,000 = $100Q$50Q= $5,000Q= $5,000 $50
35、 = 100 carpetsFor Q = 100 carpets, operating income under both Option 1 and Option 2 = $10,0003a.For Q 100, say, 101 carpets,Option 1 gives operating income =$150 101 - $5,000=$10,150Option 2 gives operating income=$100 101=$10,100So Color Rugs will prefer Option 1.3b.For Q 100, say, 99 carpets,Opti
36、on 1 gives operating income =$150 99 - $5,000=$9,850Option 2 gives operating income=$100 99=$9,900So Color Rugs will prefer Option 2.3-25 (Contd.)4.Degree of operating leverage=5.The calculations in requirement 4 indicate that when sales are 100 units, a percentage change in sales and contribution m
37、argin will result in 1.5 times that percentage change in operating income for option 1, but the same percentage change in operating income for option 2. The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes.3-26(3
38、0 min.) CVP analysis, sensitivity analysis.1.USP=$30.00 (1 0.30 margin to bookstore)=$30.00 UVC=$ 4.00variable production and marketing costvariable author royalty cost (0.15 $30.00 0.70)FC=$ 500,000fixed production and marketing cost 3,000,000up-front payment to Washington$3,500,0003-26 (Contd.)Exh
39、ibit 3-26A shows the PV graph.EXHIBIT 3-26APV Graph for Media Publishers2.a.=252,708 copies sold (rounded up)b.Target OI=397,112 copies sold (rounded up)3-26 (Contd.)3.a.Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the following effects:USP=$30.00 (1 0.20)=$
40、30.00 UVC=$ 4.00variable production and marketing costvariable author royalty cost (0.15 $30.00 0.80)=213,415 copies sold (rounded)The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies.b.Increasing the listed bookstore price to $40 while keeping the bookstore margin at
41、 30% has the following effects:USP=$40.00 (1 0.30)=$40.00 UVC=$ 4.00variable production and marketing costvariable author royalty cost (0.15 $40.00 0.70)=176,768 copies sold (rounded)The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies.c.The answer to requirements 3a
42、and 3b decreases the breakeven point relative to requirement 2 because in each case fixed costs remain the same at $3,500,000 while contribution margin per unit increases.3-27(10 min.) CVP analysis, international cost structure differences.1.Annual Fixed Costs(1)Selling Price(2)Variable Manuf. Costs per Sweater(3)Variable Mark/Dist Costs per Sweater(4)Unit Contrib. Margin(5)=(2) (3) (4)Breakeven Point in Units(6) = (1) (5)Singapore$ 6,500,000$32$13500,000Thailand4,500,0003215300,000U.S.12,000,00032101,200,000(a)Breakeven point in units sold(b)Breakeven point in rev