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1、管理会计（高等教育出版社）CHAPTER 16COST-VOLUME-PROFIT ANALYSIS: A MANAGERIAL PLANNING TOOLQUESTIONS FOR WRITING AND DISCUSSION5251. CVP analysis allows managers to focus on selling prices, volume, costs, profits, and sales mix. Many diffe rent “what if” questions can be asked to assess the effect on profits of
2、changes in key variables.2. The units-sold approach defines sales vo- lume in terms of units of product and gives answers in these same terms. The sales- revenue approach defines sales volume in terms of revenues and provides answers in these same terms.3. Break-even point is the level of sales acti
3、vity where total revenues equal total costs, or where zero profits are earned.4. At the break-even point, all fixed costs are covered. Above the break-even point, only variable costs need to be covered. Thus, contribution margin per unit is profit per unit, provided that the unit selling price is gr
4、eater than the unit variable cost (which it must be for break-even to be achieved).5. Profit = $7.00 5,000 = $35,0006. Variable cost ratio = Variable costs/Sales. Contribution margin ratio = Contribution margin/Sales. Contribution margin ratio = 1 Variable cost ratio.7. Break-even revenues = $20,000
5、/0.40 =$50,0008. No. The increase in contribution is $9,000 (0.30 $30,000), and the increase in adver- tising is $10,000.9. Sales mix is the relative proportion sold of each product. For example, a sales mix of 3:2 means that three units of one product are sold for every two of the second product.10
6、. Packages of products, based on the ex- pected sales mix, are defined as a single product. Selling price and cost information for this package can then be used to carry out CVP analysis.11. Package contribution margin: (2 $10) + (1 $5) = $25. Break-even point = $30,000/$25= 1,200 packages, or 2,400
7、 units of A and 1,200 units of B.12. Profit = 0.60($200,000 $100,000) =$60,00013. A change in sales mix will change the contri- bution margin of the package (defined by the sales mix) and, thus, will change the units needed to break even.14. Margin of safety is the sales activity in excess of that n
8、eeded to break even. The higher the margin of safety, the lower the risk.15. Operating leverage is the use of fixed costs to extract higher percentage changes inprofits as sales activity changes. It is achieved by increasing fixed costs while lo- wering variable costs. Therefore, increased leverage
9、implies increased risk, and vice versa.16. Sensitivity analysis is a “what if” technique that examines the impact of changes in un- derlying assumptions on an answer. A com- pany can input data on selling prices, varia- ble costs, fixed costs, and sales mix and set up formulas to calculate break-eve
10、n points and expected profits. Then, the data can be varied as desired to see what impact changes have on the expected profit.17. By specifically including the costs that vary with nonunit drivers, the impact of changes in the nonunit drivers can be examined. In traditional CVP, all nonunit costs ar
11、e lumped together as “fixed costs.” While the costs are fixed with respect to units, they vary with re- spect to other drivers. ABC analysis reminds us of the importance of these nonunit drivers and costs.18. JIT simplifies the firms cost equation since more costs are classified as fixed (e.g., di-
12、rect labor). Additionally, the batch-level vari- able is gone (in JIT, the batch is one unit). Thus, the cost equation for JIT includes fixed costs, unit variable cost times the number of units sold, and unit product-level cost times the number of products sold (or related costdriver). JIT means tha
13、t CVP analysis ap- proaches the standard analysis with fixed and unit-level costs only.EXERCISES1611. e2. c3. d4. b5. a1621. f2. d3. b4. a5. g6. e7. c1631.Units= Fixed cost/Contribution margin= $10,350/($15 $12)= 3,4502.Sales (3,450 $15)$51,750Variable costs (3,450 $12) 41,400Contribution margin$ 10
14、,350Fixed costs10,350Operating income$03.Units= (Target income + Fixed cost)/Contribution margin= ($9,900 + $10,350)/($15 $12)= $20,250/$3= 6,7501641.Contribution margin per unit = $15 $12 = $3 Contribution margin ratio = $3/$15 = 0.20, or 20%2.Variable cost ratio = $60,000/$75,000 = 0.80, or 80%3.
15、Revenue = Fixed cost/Contribution margin ratio= $10,350/0.20= $51,7504. Revenue = (Target income + Fixed cost)/Contribution margin ratio= ($9,900 + $10,350)/0.20= $101,2501655261.0.15($15)(Units)$2.25(Units)$10,350Units= $15(Units) $12(Units) $10,350= $3(Units) $10,350= $0.75(Units)= 13,8002.Sales (
16、13,800 $15)$ 207,000Variable costs (13,800 $12)165,600Contribution margin$41,400Fixed costs 10,350Operating income$31,050$31,050 does equal 15% of $207,000, so the answer of 13,800 units is correct.1661. Before-tax income = (After-tax income)/(1 Tax rate)= $6,000/(1 0.40)= $10,000Units= (Target inco
17、me + Fixed cost)/Contribution margin= ($10,000 + $10,350)/($15 $12)= 6,783*The answer is 6,783.3333, and so it must be rounded to a whole unit. You may prefer that students round up the answer to 6,784, instead, since it is better to be marginally above break-even than marginally below it.2. Before-
18、tax income = (After-tax income)/(1 Tax rate)= $6,000/(1 0.50)= $12,000Units= (Target income + Fixed cost)/Contribution margin= ($12,000 + $10,350)/($15 $12)= 7,4503. Before-tax income = (After-tax income)/(1 Tax rate)= $6,000/(1 0.30)= $8,571Units= (Target income + Fixed cost)/Contribution margin= (
19、$8,571 + $10,350)/($15 $12)= 6,3071671.Break-even units= Fixed costs/(Price Variable cost)= $150,000/($2.45 $1.65)= $150,000/$0.80= 187,5002.Units= ($150,000 + $12,600)/($2.45 $1.65)= $162,600/$0.80= 203,2503.Unit variable cost = $1.65Unit variable manufacturing cost = $1.65 $0.17 = $1.48The unit va
20、riable cost is used in cost-volume-profit analysis, since it includesallof the variable costs of the firm.5271681.Before-tax income = $25,200/(1 0.40) = $42,000Units= ($150,000 + $42,000)/$0.80= $192,000/$0.80= 240,0002.Before-tax income = $25,200/(1 0.30) = $36,000Units= ($150,000 + $36,000)/$0.80=
21、 $186,000/$0.80= 232,5003.Before-tax income = $25,200/(1 0.50) = $50,400 Units= ($150,000 + $50,400)/$0.80= $200,400/$0.80= 250,5004.215,000 187,500 = 27,500 pansor$526,750 $459,375 = $67,375528169 A B C DSales$ 5,000$ 15,600*$ 16,250*$9,000Variable costs4,00011,7009,7505,400*Contribution margin$ 1,
22、000$ 3,900$ 6,500*$3,600*Fixed costs 500* 4,000 6,100* 750Operating income (loss)$500$ (100)*$400$2,850Units sold1,000*1,30012590Price/unit$5$12*$130$100*Variable cost/unit$4*$9$78*$60*Contribution margin/unit$1*$3$52*$40*Contribution margin ratio20%*25%*40%40%*Break-even in units500*1,334*118*19*De
23、signates calculated amount.Note: When the calculated break-even in units includes a fractional amount, it has been rounded up to the next whole unit.16101.Variable cost ratio = Variable costs/Sales= $399,900/$930,000= 0.43, or 43%Contribution margin ratio = (Sales Variable costs)/Sales= ($930,000 $3
24、99,900)/$930,000= 0.57, or 57%2.Break-even sales revenue = $307,800/0.57 = $540,0003. Margin of safety = Sales Break-even sales= $930,000 $540,000 = $390,0004. Contribution margin from increased sales = ($7,500)(0.57) = $4,275 Cost of advertising = $5,000No, the advertising campaign is not a good id
25、ea, because the companys o p- erating income will decrease by $725 ($4,275 $5,000).52916115301. Income 0 0$570,000P= Revenue Variable cost Fixed cost= 1,500P $300(1,500) $120,000= 1,500P $450,000 $120,000= 1,500P= $3802.$160,000/($3.50 Unit variable cost) = 128,000 units Unit variable cost = $2.2516
26、121.Contribution margin per unit = $5.60 $4.20*= $1.40*Variable costs per unit:$0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20Contribution margin ratio = $1.40/$5.60 = 0.25 = 25%2.Break-even in units = ($32,300 + $12,500)/$1.40 = 32,000 boxes Break-even in sales = 32,000 $5.60 = $179,200or= ($
27、32,300 + $12,500)/0.25 = $179,2003.Sales ($5.60 35,000)Variable costs ($4.20 35,000) Contribution marginFixed costs Operating income$ 196,000147,000$49,000 44,800$4,2004.Margin of safety = $196,000 $179,200 = $16,8005.Break-even in units = 44,800/($6.20 $4.20) = 22,400 boxesNew operating income = $6
28、.20(31,500) $4.20(31,500) $44,800= $195,300 $132,300 $44,800 = $18,200Yes, operating income will increase by $14,000 ($18,200 $4,200).16131.Variable cost ratio = $126,000/$315,000 = 0.40 Contribution margin ratio = $189,000/$315,000 = 0.602.$46,000 0.60 = $27,6003.Break-even revenue = $63,000/0.60 =
29、 $105,000 Margin of safety = $315,000 $105,000 = $210,0004.Revenue = ($63,000 + $90,000)/0.60= $255,0005.Before-tax income = $56,000/(1 0.30) = $80,000 Note: Tax rate = $37,800/$126,000 = 0.30 Revenue = ($63,000 + $80,000)/0.60 = $238,333Sales .$ 238,333Less: Variable expenses ($238,333 0.40) . 95,3
30、33Contribution margin .$ 143,000Less: Fixed expenses .63,000Income before income taxes .$80,000Income taxes ($80,000 0.30) .24,000Net income.$56,00053116145321. Operating income(0.20)Revenue (0.20)Revenue (0.40)RevenueRevenue= Revenue(1 Variable cost ratio) Fixed cost= Revenue(1 0.40) $24,000= (0.60
31、)Revenue $24,000= $24,000= $60,000Sales .$ 60,000Variable expenses ($60,000 0.40). 24,000Contribution margin .$ 36,000Fixed expenses.24,000Operating income.$ 12,000$12,000 = $60,000 20%2. If revenue of $60,000 produces a profit equal to 20 percent of sales and if the price per unit is $10, then 6,00
32、0 units must be sold. Let X equal number of units, then:Operating income0.20($10)X$2X$4XX0.25($10)X$2.50X$3.50XX= (Price Variable cost) Fixed cost= ($10 $4)X $24,000= $6X $24,000= $24,000= 6,000 buckets= $6X $24,000= $6X $24,000= $24,000= 6,857 bucketsSales (6,857 $10).$68,570Variable expenses (6,85
33、7 $4). 27,428Contribution margin .$41,142Fixed expenses.24,000Operating income.$17,142$17,142* = 0.25 $68,570 as claimed*Rounded down.Note: Some may prefer to round up to 6,858 units. If this is done, the operat- ing income will be slightly different due to rounding.1614 Concluded3. Net income = 0.2
34、0Revenue/(1 0.40)= 0.3333Revenue5330.3333Revenue 0.3333Revenue 0.2667RevenueRevenue= Revenue(1 0.40) $24,000= 0.60Revenue $24,000= $24,000= $89,98916151.Company A:$100,000/$50,000 = 2 Company B:$300,000/$50,000 = 62.Company AX = $50,000/(1 0.80) X = $50,000/0.20X = $250,000Company BX = $250,000/(1 0
35、.40) X = $250,000/0.60X = $416,667Company B must sell more than Company Ato break even because it must cover $200,000 more in fixed costs (it is more highly leveraged).3.Company A:2 50% = 100%Company B:6 50% = 300%The percentage increase in profits for Company B is much higher than Com- pany As incr
36、ease because Company B has a higher degree of oper ating leve- rage (i.e., it has a larger amount of fixed costs in proportion to variable costs as compared to Company A). Once fixed costs are covered, additional reve- nue must cover only variable costs, and 60 percent of Company Bs revenue above br
37、eak-even is profit, whereas only 20 perce nt of Company As revenue above break-even is profit.16161.VariableUnits inPackageProduct Price*Cost=CM Mix= CMScientific$25$12$131$13Business20911555Total$68*$500,000/20,000 = $25$2,000,000/100,000 = $20X = ($1,080,000 + $145,000)/$68 X = $1,225,000/$68X = 1
38、8,015 packages18,015 scientific calculators (1 18,015)90,075 business calculators (5 18,015)2.Revenue = $1,225,000/0.544* = $2,251,838*($1,360,000/$2,500,000) = 0.54453416171.Sales mix is 2:1 (Twice as many videos are sold as equipment sets.)2.VariableSalesProductPriceCost=CMMix=Total CMVideos$12$4$
39、82$16Equipment sets15691 9Total$25Break-even packages = $70,000/$25 = 2,800Break-even videos= 2 2,800 = 5,600Break-even equipment sets = 1 2,800 = 2,8003.Switzer Company Income StatementFor Last YearSales .$ 195,000Less: Variable costs.70,000Contribution margin .$ 125,000Less: Fixed costs . 70,000Op
40、erating income.$55,000Contribution margin ratio = $125,000/$195,000 = 0.641, or 64.1% Break-even sales revenue = $70,000/0.641 = $109,2044.Margin of safety = $195,000 $109,204 = $85,79653516181. Sales mix is 2:1:4 (Twice as many videos will be sold as equipment sets, and four times as many yoga mats will be sold as equipment sets.)2.VariableSalesProductPrice Cost=CM Mix =Total CMVideos$12$ 4$82$16Equipment sets156919Yoga mats18