管理会计(英文版)课后习题答案(高等教育出版社)chapter16.doc

523523523 管理会计 高等教育出版社 管理会计 高等教育出版社 于增彪 清华大学 于增彪 清华大学 改编改编 余绪缨 厦门大学 余绪缨 厦门大学 审校审校 CHAPTER 16 COST VOLUME PROFIT ANALYSIS A MANAGERIAL PLANNING TOOL QUESTIONS FOR WRITING AND DISCUSSION 1 CVP analysis allows managers to focus on selling prices volume costs profits and sales mix Many different what if questions can be asked to assess the effect on profits of changes in key variables 2 The units sold approach defines sales volume 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 activity 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 greater than the unit variable cost which it must be for break even to be achieved 5 Profit 7 00 5 000 35 000 6 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 0 40 50 000 8 No The increase in contribution is 9 000 0 30 30 000 and the increase in advertising 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 Packages of products based on the expected 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 units of A and 1 200 units of B 12 Profit 0 60 200 000 100 000 60 000 13 A change in sales mix will change the contribution 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 needed 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 in 524524524 profits as sales activity changes It is achieved by increasing fixed costs while lowering variable costs Therefore increased leverage implies increased risk and vice versa 16 Sensitivity analysis is a what if technique that examines the impact of changes in underlying assumptions on an answer A company can input data on selling prices variable costs fixed costs and sales mix and set up formulas to calculate break even 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 are lumped together as fixed costs While the costs are fixed with respect to units they vary with respect to other drivers ABC analysis reminds us of the importance of these nonunit drivers and costs 18 JIT simplifies the firm s cost equation since more costs are classified as fixed e g direct labor Additionally the batch level variable 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 cost driver JIT means that CVP analysis approaches the standard analysis with fixed and unit level costs only 525525525 EXERCISES 16 1 1 e 2 c 3 d 4 b 5 a 16 2 1 f 2 d 3 b 4 a 5 g 6 e 7 c 16 3 1 Units Fixed cost Contribution margin 10 350 15 12 3 450 2 Sales 3 450 15 51 750 Variable costs 3 450 12 41 400 Contribution margin 10 350 Fixed costs10 350 Operating income 0 3 Units Target income Fixed cost Contribution margin 9 900 10 350 15 12 20 250 3 6 750 526526526 16 4 1 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 Revenue Fixed cost Contribution margin ratio 10 350 0 20 51 750 4 Revenue Target income Fixed cost Contribution margin ratio 9 900 10 350 0 20 101 250 16 5 1 0 15 15 Units 15 Units 12 Units 10 350 2 25 Units 3 Units 10 350 10 350 0 75 Units Units 13 800 2 Sales 13 800 15 207 000 Variable costs 13 800 12 165 600 Contribution margin 41 400 Fixed costs10 350 Operating income 31 050 31 050 does equal 15 of 207 000 so the answer of 13 800 units is correct 527527527 16 6 1 Before tax income After tax income 1 Tax rate 6 000 1 0 40 10 000 Units Target income 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 tax income After tax income 1 Tax rate 6 000 1 0 50 12 000 Units Target income Fixed cost Contribution margin 12 000 10 350 15 12 7 450 3 Before tax income After tax income 1 Tax rate 6 000 1 0 30 8 571 Units Target income Fixed cost Contribution margin 8 571 10 350 15 12 6 307 16 7 1 Break even units Fixed costs Price Variable cost 150 000 2 45 1 65 150 000 0 80 187 500 2 Units 150 000 12 600 2 45 1 65 162 600 0 80 203 250 3 Unit variable cost 1 65 Unit variable manufacturing cost 1 65 0 17 1 48 The unit variable cost is used in cost volume profit analysis since it includes all of the variable costs of the firm 528528528 16 8 1 Before tax income 25 200 1 0 40 42 000 Units 150 000 42 000 0 80 192 000 0 80 240 000 2 Before tax income 25 200 1 0 30 36 000 Units 150 000 36 000 0 80 186 000 0 80 232 500 3 Before tax income 25 200 1 0 50 50 400 Units 150 000 50 400 0 80 200 400 0 80 250 500 4 215 000 187 500 27 500 pans or 526 750 459 375 67 375 529529529 16 9 ABCD Sales 5 000 15 600 16 250 9 000 Variable costs4 00011 7009 7505 400 Contribution margin 1 000 3 900 6 500 3 600 Fixed costs500 4 0006 100 750 Operating income loss 500 100 400 2 850 Units sold1 000 1 30012590 Price 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 Designates calculated amount Note When the calculated break even in units includes a fractional amount it has been rounded up to the next whole unit 16 10 1 Variable cost ratio Variable costs Sales 399 900 930 000 0 43 or 43 Contribution margin ratio Sales Variable costs Sales 930 000 399 900 930 000 0 57 or 57 2 Break even sales revenue 307 800 0 57 540 000 3 Margin of safety Sales Break even sales 930 000 540 000 390 000 4 Contribution margin from increased sales 7 500 0 57 4 275 Cost of advertising 5 000 No the advertising campaign is not a good idea because the company s operating income will decrease by 725 4 275 5 000 530530530 16 11 1 Income Revenue Variable cost Fixed cost 0 1 500P 300 1 500 120 000 0 1 500P 450 000 120 000 570 000 1 500P P 380 2 160 000 3 50 Unit variable cost 128 000 units Unit variable cost 2 25 16 12 1 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 20 Contribution 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 60 179 200 or 32 300 12 500 0 25 179 200 3 Sales 5 60 35 000 196 000 Variable costs 4 20 35 000 147 000 Contribution margin 49 000 Fixed costs44 800 Operating income 4 200 4 Margin of safety 196 000 179 200 16 800 5 Break even in units 44 800 6 20 4 20 22 400 boxes New operating income 6 20 31 500 4 20 31 500 44 800 195 300 132 300 44 800 18 200 Yes operating income will increase by 14 000 18 200 4 200 531531531 16 13 1 Variable cost ratio 126 000 315 000 0 40 Contribution margin ratio 189 000 315 000 0 60 2 46 000 0 60 27 600 3 Break even revenue 63 000 0 60 105 000 Margin of safety 315 000 105 000 210 000 4 Revenue 63 000 90 000 0 60 255 000 5 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 60 238 333 Sales 238 333 Less Variable expenses 238 333 0 40 95 333 Contribution margin 143 000 Less Fixed expenses 63 000 Income before income taxes 80 000 Income taxes 80 000 0 30 24 000 Net income 56 000 532532532 16 14 1 Operating income Revenue 1 Variable cost ratio Fixed cost 0 20 Revenue Revenue 1 0 40 24 000 0 20 Revenue 0 60 Revenue 24 000 0 40 Revenue 24 000 Revenue 60 000 Sales 60 000 Variable expenses 60 000 0 40 24 000 Contribution margin 36 000 Fixed expenses 24 000 Operating 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 6 000 units must be sold Let X equal number of units then Operating income Price Variable cost Fixed cost 0 20 10 X 10 4 X 24 000 2X 6X 24 000 4X 24 000 X 6 000 buckets 0 25 10 X 6X 24 000 2 50X 6X 24 000 3 50X 24 000 X 6 857 buckets Sales 6 857 10 68 570 Variable expenses 6 857 4 27 428 Contribution margin 41 142 Fixed expenses 24 000 Operating 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 operating income will be slightly different due to rounding 533533533 16 14 Concluded 3 Net income 0 20Revenue 1 0 40 0 3333Revenue 0 3333Revenue Revenue 1 0 40 24 000 0 3333Revenue 0 60Revenue 24 000 0 2667Revenue 24 000 Revenue 89 989 16 15 1 Company A 100 000 50 000 2 Company B 300 000 50 000 6 2 Company ACompany B X 50 000 1 0 80 X 250 000 1 0 40 X 50 000 0 20X 250 000 0 60 X 250 000X 416 667 Company B must sell more than Company A to 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 Company A s increase because Company B has a higher degree of operating leverage 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 revenue must cover only variable costs and 60 percent of Company B s revenue above break even is profit whereas only 20 percent of Company A s revenue above break even is profit 534534534 16 16 1 VariableUnits inPackage ProductPrice Cost CM Mix CM Scientific 25 12 131 13 Business20911555 Total 68 500 000 20 000 25 2 000 000 100 000 20 X 1 080 000 145 000 68 X 1 225 000 68 X 18 015 packages 18 015 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 0 544 535535535 16 17 1 Sales mix is 2 1 Twice as many videos are sold as equipment sets 2 VariableSales ProductPrice Cost CM Mix Total CM Videos 12 4 82 16 Equipment sets156919 Total 25 Break even packages 70 000 25 2 800 Break even videos 2 2 800 5 600 Break even equipment sets 1 2 800 2 800 3 Switzer Company Income Statement For Last Year Sales 195 000 Less Variable costs 70 000 Contribution margin 125 000 Less Fixed costs 70 000 Operating income 55 000 Contribution margin ratio 125 000 195 000 0 641 or 64 1 Break even sales revenue 70 000 0 641 109 204 4 Margin of safety 195 000 109 204 85 796 536536536 16 18 1 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 VariableSales ProductPrice Cost CM Mix Total CM Videos 12 4 82 16 Equipment sets156919 Yoga mats18135420 Total 45 Break even packages 118 350 45 2 630 Break even videos 2 2 630 5 260 Break even equipment sets 1 2 630 2 630 Break even yoga mats 4 2 630 10 520 3 Switzer Company Income Statement For the Coming Year Sales 555 000 Less Variable costs 330 000 Contribution margin 225 000 Less Fixed costs 118 350 Operating income 106 650 Contribution margin ratio 225 000 555 000 0 4054 or 40 54 Break even revenue 118 350 0 4054 291 934 4 Margin of safety 555 000 291 934 263 066 537537537 16 19 1 Contribution margin unit 410 000 100 000 4 10 Contribution margin ratio 410 000 650 000 0 6308 Break even units 295 200 4 10 72 000 units Break even revenue 72 000 6 50 468 000 or 295 200 0 6308 467 977 Difference due to rounding error in calculating the contribution margin ratio 2 The break even point decreases X 295 200 P V X 295 200 7 15 2 40 X 295 200 4 75 X 62 147 units Revenue 62 147 7 15 444 351 3 The break even point increases X 295 200 6 50 2 75 X 295 200 3 75 X 78 720 units Revenue 78 720 6 50 511 680 538538538 16 19 Concluded 4 Predictions of increases or decreases in the break even point can be made without computation for price changes or for variable cost changes If both change then the unit contribution margin must be known before and after to predict the effect on the break even point Simply giving the direction of the change for each individual component is not sufficient For our example the unit contribution changes from 4 10 to 4 40 so the break even point in units will decrease Break even units 295 200 7 15 2 75 67 091 Now let s look at the break even point in revenues We might expect that it too will decrease However that is not the case in this particular example Here the contribution margin ratio decreased from about 63 percent to just over 61 5 percent As a result the break even point in revenues has gone up Break even revenue 67 091 7 15 479 701 5 The break even point will increase because more units will need to be sold to cover the additional fixed expenses Break even units 345 200 4 10 84 195 units Revenue 547 268 539539539 16 20 1 0 5 000 10 000 15 000 20 000 25 000 30 000 35 000 05001 0001 5002 0002 5003 0003 500 Units Sold Dollars Break even point 2 500 units line is total revenue and x line is total costs 540540540 16 20 Continued 2 a Fixed costs increase by 5 000 0 5 000 10 000 15 000 20 000 25 000 30 000 35 000 40 000 05001 0001 5002 0002 5003 0003 5004 000 Units Sold Dollars Break even point 3 750 units 541541541 16 20 Continued b Unit variable cost increases to 7 0 10 000 20 000 30 000 40 000 50 000 05001 0001 5002 0002 5003 0003 5004 000 Units Sold Dollars Break even point 3 333 units 542542542 16 20 Continued c Unit selling price increases to 12 0 10 000 20 000 30 000 40 000 50 000 05001 0001 5002 0002 5003 0003 5004 000 Units Sold Dollars Break even point 1 667 units 543543543 16 20 Continued d Both fixed costs and unit variable cost increase 0 10 000 20 000 30 000 40 000 50 000 60 000 70 000 01 0002 0003 0004 0005 0006 0007 0008 000 Units Sold Dollars Break even point 5 000 units 544544544 16 20 Continued 3 Original data 10 000 0 10 000 05001 0001 5002 0002 5003 0003 5004 000 Break even point 2 500 units 545545545 16 20 Continued a Fixed costs increase by 5 000 15 000 0 15 000 05001 0001 5002 0002 5003 0003 5004 000 Break even point 3 750 units 546546546 16 20 Continued b Unit variable cost increases to 7 10 000 0 10 000 05001 0001 5002 0002 5003 0003 5004 000 Break even point 3 333 units 547547547 16 20 Continued c Unit selling price increases to 12 10 000 0 10 000 05001 0001 5002 0002 5003 0003 5004 000 Break even point 1 667 units 548548548 16 20 Concluded d Both fixed costs and unit variable cost increase 15 000 0 15 000 01 0002 0003 0004 0005 0006 0007 000 Break even point 5 000 units 4 The first set of graphs is more informative since these graphs reveal how costs change as sales volume changes 549549549 16 21 1 Unit contribution margin 1 060 000 50 000 21 20 Break even units 816 412 21 20 38 510 units Operating income 30 000 21 20 636 000 2 CM ratio 1 060 000 2 500 000 0 424 or 42 4 Break even point 816 412 0 424 1 925 500 Operating income 200 000 0 424 243 588 328 388 3 Margin of safety 2 500 000 1 925 500 574 500 4 1 060 000 243 588 4 352 operating leverage 4 352 20 0 8704 0 8704 243 588 212 019 New operating income level 212 019 243 588 455 607 5 Let X Units 0 10 50 X 50 00X 28 80X 816 412 5X 21 20X 816 412 16 20X 816 412 X 50 396 units 6 Before tax income 180 000 1 0 40 300 000 X 816 412 300 000 21 20 52 661 units 550550550 16 22 1 VariableSalesPackage ProductPrice Cost CM Mix CM Vases 40 30 102 20 Figurines704228128 Total 48 Break even packages 30 000 48 625 Break even vases 2 625 1 250 Break even figurines 625 2 The new sales mix is 3 vases to 2 figurines VariableSalesPackage ProductPrice Cost CM Mix CM Vases 40 30 103 30 Figurines704228256 Total 86 Break even packages 35 260 86 410 Break even vases 3 410 1 230 Break even figurines 2 410 820 16 23 1 d 2 c 3 a 4 d 5 e 6 b 7 c 551551551 PROBLEMS 16 24 1 Unit contribution margin 825 000 110 000 7 50 Break even point 495 000 7 50 66 000 units CM ratio 7 50 25 0 30 Break even point 495 000 0 30 1 650 000 or 25 66 000 1 650 000 2 Increased CM 400 000 0 30 120 000 Less Increased advertising expense40 000 Increased operating income 80 000 3 315 000 0 30 94 500 4 Before tax income 360 000 1 0 40 600 000 Units 495 000 600 000 7 50 146 000 5 Margin of safety 2 750 000 1 650 000 1 100 000 or 110 000 units 66 000 units 44 000 units 6 825 000 330 000 2 5 operating leverage 20 2 5 50 profit increase 552552552 16 25 1 Sales mix Squares 300 000 30 10 000 units Circles 2 500 000 50 50 000 units SalesTotal ProductP V P V Mix CM Squares 30 10 201 20 Circles5010405200 Package 220 100 000 10 000 10 500 000 50 000 10 Break even packages 1 628 000 220 7 400 packages Break even squares 7 400 1 7 400 Break even circles 7 400 5 37 000 2 Contribution margin ratio 2 200 000 2 800 000 0 7857 0 10Revenue 0 7857Revenue 1 628 000 0 6857Revenue 1 628 000 Revenue 2 374 216 3 New mix SalesTotal ProductP V P V Mix CM Squares 30 10 203 60 Circles5010405200 Package 260 Break even packages 1 628 000 260 6 262 packages Break even squares 6 262 3 18 786 Break even circles 6 262 5 31 310 CM ratio 260 340 0 7647 3 30 5 50 340 revenue per package 0 10Revenue 0 7647Revenue 1 628 000 0 6647Revenue 1 628 000 Revenue 2 449 225 553553553 16 25 Concluded 4 Increase in CM for squares 15 000 20 300 000 Decrease in CM for circles 5 000 40 200 000 Net increase in total contribution ma