# Chapter 25 Cost-Volume-Profit Analysis Questions

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1 Chapter 25 Cost-Volume-Profit Analysis Questions 1. Cost-volume-profit analysis is used to accomplish the first step in the planning phase for a business, which involves predicting the volume of activity, costs to be incurred, revenues to be received, and profits to be earned. 2. A variable cost is one that varies proportionately with the volume of activity that drives the cost. Examples in a manufacturing setting include direct materials and direct labour (when the workers are paid for completed units). 3. Variable costs per unit stay the same because each unit consumes the same amount of variable costs within the relevant range of activity. That is, variable costs per unit remain constant as volume increases. 4. Fixed costs per unit decrease because the total amount of fixed costs remains the same while being divided among more units within the relevant fixed cost range of activity. 5. A step-wise cost remains constant over a limited range of production, after which it increases by a lump-sum amount, then remains constant over another limited range of production, and so on. A curvilinear cost gradually changes in a nonlinear relationship to volume changes. 6. A CVP analysis for a manufacturing company is greatly simplified by an assumption that the production and sales volumes are equal. 7. The first is that individual costs classified as fixed or variable may not behave precisely in those patterns; some variations of individual components may tend to offset each other. The second is that management can assume that costs are either fixed or variable within the relevant range of operations. 8. By assuming a relevant range, management can more justifiably assume fixed and variable relationships between costs and volume, and between revenue and volume. The assumption also limits the alternative strategies to those that call for a volume that falls within the relevant range. 9. Estimated line of cost behaviour, high-low method, least-squares regression. 10. A scatter diagram can be used to display past costs and volumes. Then, management (assisted by the accountant) can attempt to identify the fixed and variable components of the total cost being graphed. 11. At break-even, profits are zero. Break-even is the point where sales equals fixed plus variable costs. 12. The line shows the total cost, which equals the sum of the fixed and variable costs at all volumes within the period s capacity. Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 160 Fundamental Accounting Principles, Eleventh Canadian Edition

2 13. Fixed costs are depicted as a horizontal line on a CVP chart because they remain the same at all volumes within the relevant range. 14. Company A has a contribution margin ratio of 50% ([\$20,000 \$10,000] \$20,000), and Company B has a contribution margin ratio of 80% ([\$20,000 \$4,000] \$20,000). Thus, compared to Company A, Company B will make more profit on each additional dollar of sales. 15. Margin of safety. 16. The primary variable costs in making hats are cloth, thread, cardboard, and direct labour. The costs of operating the plant and equipment are fixed because regardless of production levels these product costs are incurred. 17. A 65% increase in production would be viewed as a substantial increase in production. When this occurs, the sales and cost structure changes. The sales value, fixed costs, and variable costs are likely to change as production moves out of the relevant range. Variable cost per unit may go down, and fixed cost in total is likely to increase due to, for example, more space needed to manage the increase in production. Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

3 QUICK STUDY Quick Study 25-1 Series 1 Variable cost Series 2 Fixed cost Series 3 Step-wise cost Quick Study 25-2 (a) Fixed (d) Fixed (b) Variable (e) Probably mixed (c) Variable (f) Variable Quick Study 25-3 (a) Fixed (b) Mixed (c) Variable Quick Study 25-4 Fixed costs = \$3,000 Variable costs = \$8,000 \$3,000 3,500 0 = \$ Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 162 Fundamental Accounting Principles, Eleventh Canadian Edition

4 Quick Study 25-5 Total cost = \$15,000 + \$6(9,000 units) = \$69,000 Quick Study 25-6 (a) Contribution margin per unit = \$50 \$30 = \$20 (b) Break-even point in units = Quick Study 25-7 (a) Contribution margin ratio = \$225,000 \$20 \$50 \$30 \$50 = 11,250 units = 40% (b) Break-even point in dollars = Quick Study 25-8 The correct answer is b. \$225,000 40% = \$562,500 Quick Study 25-9 Before-tax income = \$630,000 (1.40) = \$1,050,000 Income taxes = \$1,050, = \$420,000 \$225,000 + \$630,000 + \$420,000 = 63,750 units \$50 \$30 Quick Study Break-even point in composite units = \$835,120 \$85 = 9,825 units Mixers at break-even point = 3 9,825 = 29,475 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

5 EXERCISES Exercise f 2. c 3. d 4. a 5. b 6. e Exercise 25-2 Sales Variable Cost Fixed Cost Total Cost Net Income Contribution Margin \$4,000 \$3,000 \$600 \$3,600 \$400 \$1,000 2,800 1, , , ,800 4,400 5,240 Exercise 25-3 Series A Curvilinear cost Series B Mixed cost Series C Variable cost Series D Step-wise cost Series E Fixed cost Exercise 25-4 a. 1. Fixed cost 2. Mixed cost 3. Step-wise cost 4. Variable cost 5. Curvilinear cost b. (1) 3 (2) 5 (3) 1 (4) 4 (5) 2 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 164 Fundamental Accounting Principles, Eleventh Canadian Edition

6 Exercise 25-5 (20 minutes) The cost appears to be a mixed cost. Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

8 Exercise 25-7 (15 minutes) Sales CGS High level of activity \$450,000 \$235,000 Low level of activity 420, ,000 Change observed \$ 30,000 \$ 9,000 Variable cost element: Change in CGS \$9,000 Change in Sales = \$30,000 = \$0.30 per sales dollar Fixed cost element: Total cost at the high level of activity \$235,000 Less variable cost element (\$0.30 \$450,000) 135,000 Fixed cost element \$100,000 Exercise 25-8 (15 minutes) Selling & Administration Sales Expenses High level of activity \$450,000 \$108,000 Low level of activity Change observed 420,000 \$ 30, ,000 \$ 2,000 Variable cost element: Change in Expenses = \$2,000 Change in Sales \$30,000 = \$ per sales dollar Fixed selling and administration expenses: Total cost at the high level of activity... \$108,000 Less variable cost element (\$ \$450,000)... 30,015 Fixed selling and administration expenses... \$ 77,985 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

9 Exercise 25-9 (20 minutes) KEATING COMPANY Forecasted Income Statement For Month Ended January 2002 Sales... \$500,000 Variable costs: Variable cost of goods sold*... \$150,000 Variable selling and administrative expenses** 33,350 Total variable costs... \$183,350 Contribution margin... \$316,650 Fixed costs: Cost of goods sold... \$100,000 Selling and administrative expenses... 77,985 Total fixed costs... \$177,985 Income before taxes... \$138,665 Income taxes (35% rate)... 48,533 Net income... \$ 90,132 *\$0.30 \$500,000 = \$150,000 **\$ \$500,000 = \$33,350 Exercise (15 minutes) a. Contribution margin per unit = \$ \$88.20 = \$29.40 per unit b. Contribution margin ratio = \$29.40 \$ = 25% c. Break-even point in units = \$441,000 \$29.40 = 15,000 units d. Break-even point in dollars = \$441,000 25% = \$1,764,000 or = 15,000 units \$ = \$1,764,000 Exercise Income Sales (15,000 \$117.60)... \$1,764,000 Variable costs (15,000 \$88.20)... 1,323,000 Contribution margin ,000 Fixed costs ,000 Net income... \$ 0 Sales (in dollars) to break even with increased fixed costs: Break-even = (original fixed costs + new amount) contribution margin ratio = (\$441,000 + \$63,000) 25% = \$2,016,000 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 168 Fundamental Accounting Principles, Eleventh Canadian Edition

10 Exercise Pre-tax income = After-tax income (1 tax rate) = \$530,000 (1 0.4) = \$530, = \$883,333 Income taxes = Pre-tax income tax rate = \$883, = \$353,333 a. Fixed + Net + Income costs income taxes Unit sales at target income level = Contribution margin = \$441,000 + \$530,000 + \$353,333 \$29.40 = 45,045 units (rounded) b. Fixed + Net + Income costs income taxes Dollar sales at target income level = Contribution ratio = \$441,000 + \$530,000 + \$353,333 25% = \$5,297,332 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

11 Exercise a. Recall that: Net income = Sales revenue Variable costs Fixed costs Income taxes. Given that we are working with pre-tax income, we can ignore income taxes. Therefore, we can rewrite the above equation as follows: Desired pre-tax net income = Total contribution margin Fixed costs Assume desired sales dollars is S. Therefore, 0.18S = 0.25S - \$441,000 (desired pre-tax income is 18% of sales revenues; contribution margin ratio is 25% of sales revenues) Therefore, 0.07S = \$441,000, and S = \$441, = \$6,300,000. Monroe Company must generate sales revenues of \$6,300,000 to earn a pre-tax income equal to 18% of sales. b. Desired sales in units = \$6,300,000 \$ = approximately 53,572 units Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 170 Fundamental Accounting Principles, Eleventh Canadian Edition

12 Exercise Sales (60,000 \$175)... \$10,500,000 Variable costs (60,000 \$100)... 6,000,000 Contribution margin... 4,500,000 Fixed costs ,000 Net income before taxes... 4,059,000 Income taxes (40% \$4,059,000)... (1,623,600) Net income after taxes... \$ 2,435,400 Exercise (a) Sales = Fixed costs + Variable costs + Pre-tax income Sales = \$600,000 + \$375,000 + \$150,000 Sales = \$1,125,000 (b) Total contribution = Sales Variable costs Total contribution = \$1,125,000 \$375,000 = \$750,000 Unit sales = Total contribution Contribution margin = \$750,000 \$75 per unit = 10,000 units Exercise a. (i) Sales \$12,000,000 Sales price = = units 80,000 = \$150 per unit Selling price per unit... \$ 150 Less: contribution margin per unit... Variable costs per unit... \$ (40) 110 Total variable costs (\$110 80,000 units)... \$ 8,800,000 (ii) Sales... \$12,000,000 Less variable costs... (8,800,000) Less pre-tax income... (2,400,000) Fixed costs... \$ 800,000 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

13 Exercise (a) Dollar sales = Fixed costs + Target pre-tax income Contribution rate = 600,000 + \$240,000 75% = \$1,120,000 (b) Sales... \$1,120,000 Less fixed costs... (600,000) Less pre-tax income... (240,000) Variable costs... \$ 280,000 Exercise (a) Selling price per composite unit 10 \$70 per unit... \$ \$450 per unit... 1,350 Selling price per composite unit... \$2,050 (b) Variable costs per composite unit 10 \$40 per unit... \$ \$290 per unit Variable costs per composite unit... \$1,270 (c) Break-even point in composite units = Fixed costs Contribution margin per composite unit = \$975,000 \$2,050 \$1,270 = 1,250 units (d) Unit sales of windows and doors at break-even point: Windows: 10 1, ,500 units Doors: 3 1, ,750 units Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 172 Fundamental Accounting Principles, Eleventh Canadian Edition

14 PROBLEMS Problem 25-1A (45 minutes) Parts 1 & 2 Note to Instructor answers to Parts 3 and 4 will vary among students because they will be based on imprecise visual placements of the estimated line of cost behaviour. The better predictions of total fixed costs will fall in the range between \$20,000 and \$30,000. The predicted variable cost per sales dollar should fall between \$0.60 and \$0.70. According to a least-squares regression, the following coefficients apply in this case: Fixed costs = \$24,928 Variable cost = \$0.665 per sales dollar Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

15 Problem 25-1A (concluded) Part 3 Using the scatter diagram and the vertical intercept, a good approximate answer for the predicted monthly fixed cost is \$25,000. Assessing the variable cost requires determining the slope of the line. The slope can be estimated by dividing the difference between two costs on the line by the difference between the two sales levels associated with those costs. At sales of \$200,000, it appears that the total cost will equal approximately \$158,000. And, at sales of \$0, the total cost will equal the fixed costs, which are about \$25,000. Using these two data points, we can estimate the variable cost as follows: Point Sales Total Cost 1... \$200,000 \$158, ,000 Differences... \$200,000 \$133,000 Slope = Difference in Total Cost Difference in Sales = \$133,000 = \$0.665 per sales dollar \$200,000 Part 4 Then, these factors can be used to predict the total costs that will be incurred at sales levels of \$200,000 and \$280,000: Sales Level \$200,000 \$280,000 Fixed cost... \$ 25,000 \$ 25,000 Variable cost (\$0.665 sales dollar) , ,200 Total cost... \$158,000 \$211,200 Note according to the least-squares estimated line of cost behaviour, the predicted total costs at these given sales levels would be \$157,928 and \$211,128. The above approximations are reasonably close to these more precisely determined amounts. Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 174 Fundamental Accounting Principles, Eleventh Canadian Edition

16 Problem 25-2A Part 1 (a) Contribution margin per unit = \$480 \$180 = \$300 Break-even point in units = Fixed costs Contribution margin per unit = \$300,000 \$300 = 1,000 units (b) Contribution ratio = \$300 \$480 = 62.5% Part 2 Break-even point in dollars = Fixed costs Contribution ratio = \$300, % = \$480,000 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

17 Problem 25-2A (concluded) Part 3 GROVE COMPANY Product A Income Statement at Break-Even Point Sales (1,000 units \$480)... \$480,000 Costs: Fixed costs... \$300,000 Variable costs (1,000 units \$180) , ,000 Net income... \$ 0 Part 4 Pre-tax target income = After-tax target income (1 tax rate) = \$231,000 (1.3) = \$330,000 Income tax = \$330,000 30% = \$99,000 Necessary sales level = (Fixed costs + Target income + Taxes) Contribution rate = (\$300,000 + \$231,000 + \$99,000) 62.5% = \$630, % = \$1,008,000 Part 5 Contribution margin at predicted sales = Sales Contribution rate = \$1,200, % = \$750,000 Pre-tax income Income taxes = Contribution margin Fixed costs = \$750,000 \$300,000 = \$450,000 = Pre-tax income Tax rate = 450,000 30% = \$135,000 After-tax income = Pre-tax income Income taxes = \$450,000 \$135,000 = \$315,000 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 176 Fundamental Accounting Principles, Eleventh Canadian Edition

18 Problem 25-3A Part 1 Price per unit... \$750,000 15,000 = \$50 Variable costs per unit... \$450,000 15,000 = \$30 Contribution margin per unit... \$50 \$30 = \$20 Contribution ratio... (\$20 \$50) = 40% Fixed costs... = \$384,000 Break-even point... \$384,000 40% = \$960,000 Part 2 New variable costs per unit... \$30 (\$30 50%) = \$15 New contribution margin per unit \$50 \$15 = \$35 New contribution ratio... \$35 \$50 = 70% New fixed costs... \$384,000 + \$120,000 = \$504,000 New break-even point... \$504,000 70% = \$720,000 Part 3 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

19 Problem 25-3A (concluded) Part 4 MORGAN COMPANY Forecasted Income Statement For Year Ended December 31, 2005 Sales (15,000 \$50)... \$750,000 Variable costs (15,000 \$15) ,000 Contribution margin... \$525,000 Fixed (\$384,000 + \$120,000) ,000 Income before income taxes... \$ 21,000 Income taxes (\$21,000 30%)... Net income... 6,300 \$ 14,700 Part 5 Pre-tax target income = After-tax target income (1 tax rate) = \$147,000 (1.30) = \$210,000 Income tax = \$210,000 30%...= \$63,000 Necessary sales level = (Fixed costs + Target income + Taxes) Contribution rate = (\$504,000 + \$147,000 + \$63,000) 70% = \$714,000 70% = \$1,020,000 Unit sales = \$1,020,000 \$50 = 20,400 units MORGAN COMPANY Forecasted Income Statement For Year Ended December 31, 2005 Sales (20,400 \$50)... \$1,020,000 Variable (20,400 \$15) ,000 Contribution margin... \$ 714,000 Fixed ,000 Income before income taxes \$ 210,000 Income taxes (\$210,000 30%)... 63,000 Net income... \$ 147,000 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 178 Fundamental Accounting Principles, Eleventh Canadian Edition

20 Problem 25-4A Part 1 Product A Product B Part 2 Sales... \$800,000 \$800,000 Units sold... 50,000 50,000 Selling price per unit... \$ \$ Variable costs \$560,000 \$100,000 Variable cost per unit... \$ \$ 2.00 Contribution margin per unit... \$ 4.80 \$ Contribution ratio % 87.5% Fixed costs... Break-even (fixed costs contribution rate) \$100,000 \$333,333 \$560,000 \$640,000 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

21 Problem 25-4A, Part 2 (concluded) Part 3 Income statements, assuming that the sales volume falls to 33,000 units: Per Unit Units Product A Product B Sales... \$16.00 \$ ,000 33,000 \$528,000 \$528,000 Fixed costs... \$100,000 \$560,000 Variable costs... \$ , ,600 \$ ,000 66,000 Total costs... \$469,600 \$626,000 Income before taxes... \$ 58,400 \$ (98,000) Income taxes (32%)... (18,688) (31,360) Net income... \$ 39,712 \$ (129,360) Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 180 Fundamental Accounting Principles, Eleventh Canadian Edition

22 Problem 25-4A (concluded) Part 4 Income statements, assuming that the sales volume increases to 64,000 units: Per Unit Units Product A Product B Sales... \$ ,000 \$1,024,000 \$ ,000 \$1,024,000 Fixed costs... \$ 100,000 \$ 560,000 Variable costs... \$ , ,800 \$ , ,000 Total costs... \$ 816,800 \$ 688,000 Income before taxes... \$ 207,200 \$ 336,000 Income taxes (32%)... 66, ,520 Net income... \$ 140,896 \$ 228,480 Part 5 If sales were to greatly decrease, Product B would suffer the greater loss because it would lose more contribution per unit than Product A. At zero sales, Product B would have a loss equal to its fixed costs of \$560,000, while Product A s loss would be only \$100,000. Part 6 A factor that could cause Product A to have lower fixed costs might be a labour arrangement that pays workers for units produced. Another might be that the sales representatives work totally on commission. Managers may be compensated with a share of the profits instead of salaries. The fixed costs for Product B may be higher because of a salary structure that is not based on production or sales. Another factor may be that assets used in the production of Product A are leased and rent is based on the amount of usage. Product B s assets may be owned or under a lease agreement based on time, not the amount of usage. Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

23 Problem 25-5A Part 1 New variable costs: Materials cost... \$4.00 (1 60%) = \$1.60 Direct labour... \$3.00 (1 40%) = \$1.80 Overhead variable costs... = \$0.40 Selling and admin. costs... = \$0.20 Total variable costs... = \$4.00 Plan 1 Plan 2 Part 2 Selling price... = \$16.00 Contribution margin per unit \$16.00 \$4.00 = \$12.00 Contribution ratio... \$12.00 \$16.00 = 75% Total fixed costs... = \$300,000 Break-even point (dollars).. \$300,000 75% = \$400,000 Selling price... \$16.00 (1 + 25%) = \$20.00 Contribution margin per unit \$20.00 \$4.00 = \$16.00 Contribution ratio... \$16.00 \$20.00 = 80% Total fixed costs... = \$300,000 Break-even point (dollars).. \$300,000 80% = \$375,000 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 182 Fundamental Accounting Principles, Eleventh Canadian Edition

24 Problem 25-5A (concluded) Part 3 KIRBY COMPANY Forecasted Income Statement Per Unit Units Plan 1 Plan 2 Sales... \$ ,000 \$560,000 \$ ,500 \$630,000 Fixed costs... \$300,000 \$300,000 Variable costs... \$ , ,000 \$ , ,000 Total costs... \$440,000 \$426,000 Income before taxes... \$120,000 \$204,000 Income taxes (30%)... 36,000 61,200 Net income... \$ 84,000 \$142,800 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

25 Problem 25-6A 1. Sales... \$1,400,000 Variable costs: Cost of sales... \$840,000 Commissions ,000 1,050,000 Contribution margin... \$ 350,000 Contribution margin ratio (CMR) = \$ 350,000 \$1,400,000 = 25% Fixed costs... \$14,000 CMR Estimated break-even point... \$56, Variable cost ratios Cost of sales... 60% Commissions... 5% 65% CMR = 100% 65% = 35% Fixed costs Sales manager... \$ 84,000 Three \$42, ,000 Administrative... 14,000 \$224,000 Fixed costs... \$224,000 CMR Estimated break-even point... \$640, Target income before income tax... \$336,000 Fixed costs... 14,000 \$350,000 Variable cost ratios Cost of sales... 60% Commissions... 20% 80% CMR = 100% 80%... 20% Target income + fixed costs... \$ 350,000 CMR Estimated sales volume... \$1,750,000 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 184 Fundamental Accounting Principles, Eleventh Canadian Edition

27 Problem 25-8A Part 1 5 units of \$55 per unit = \$275 4 units of \$85 per unit = units of \$110 per unit = 220 Selling price of a composite unit = \$835 5 units of \$40 per unit = \$200 4 units of \$60 per unit = units of \$80 per unit = 160 Variable cost of a composite unit = \$600 Contribution margin of a composite unit = \$835 \$600 = \$235 Contribution margin ratio = \$235 \$835 = 28.14% Break-even point in dollars = \$150, % = \$533,049 Break-even point in composite units = \$150,000 \$235 = 639 composite units Units of Red at break-even point: = 3,195 units Units of White at break-even point: = 2,556 units Units of Blue at break-even point: = 1,278 units Part 2 Under the new plan, there would be no change in selling prices. The fixed costs would increase by \$20,000 to \$170,000 per year. 5 units of (\$40 \$10) per unit = \$150 4 units of (\$60 \$20) per unit = units of (\$80 \$10) per unit = 140 Variable cost of a composite unit = \$450 Contribution margin of a composite unit = \$835 \$450 = \$385 Contribution margin ratio = \$385 \$835 = 46.11% Break-even point in dollars = \$170, % = \$368,683 Break-even point in composite units = \$170,000 \$385 = 442 composite units Units of Red at break-even point: = 2,210 units Units of White at break-even point: = 1,768 units Units of Blue at break-even point: = 884 units Part 3 When a business invests in capital assets, as in this problem, the risk of doing business changes. The break-even point decreased, making it easier to make a profit. However, the commitment of fixed resources is higher, therefore increasing the amount of loss in a business failure. Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 186 Fundamental Accounting Principles, Eleventh Canadian Edition

28 ALTERNATE PROBLEMS Problem 25-1B Parts 1 & 2 Part 3 Using the scatter diagram and the vertical intercept, a good approximate answer for the predicted monthly fixed cost is \$90 and.30 for variable cost. Part 4 Then, these factors can be used to predict the total costs that will be incurred at sales levels of \$150 and \$250. \$150 \$250 Fixed cost... \$ 90 \$ 90 Variable cost (\$0.30 sales dollar) Total cost... \$135 \$165 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

29 Problem 25-2B Part 1 (a) Contribution margin = \$225 \$150 = \$75 Break-even point in units = Fixed costs Contribution margin = \$30,000 \$75 = 400 units (b) Contribution margin ratio = \$75 \$225 = 33.33% Break-even point in dollars = Fixed costs Contribution margin ratio = \$30, % = \$90,009 Part 2 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 188 Fundamental Accounting Principles, Eleventh Canadian Edition

30 Problem 25-2B (concluded) Part 3 Sales (400 \$225)... \$90,000 Variable costs (400 \$150)... 60,000 Contribution margin... 30,000 Fixed costs... 30,000 Net income... 0 Problem 25-3B Part 1 Price per unit... \$800,000 50,000 = \$16.00 Variable costs per unit... \$900,000 50,000 = \$18.00 Contribution margin per unit... \$16 \$18 = \$ 2 Contribution margin ratio... (\$ 2 \$16) = not applicable Fixed costs... = \$100,000 Break-even point... Capital will never break even because variable cost is greater than selling price per unit. Part 2 New variable costs per unit... \$18 (\$ %) = \$5 New contribution margin per unit \$16 \$5 = \$11 New contribution margin ratio... \$11 \$16 = 68.75% New fixed costs... \$100,000 + \$200,000 = \$300,000 New break-even point... \$300, % = \$436,364 Part 3 CAPITAL COMPANY Forecasted Income Statement For Year Ended December 31, 2005 Sales (50,000 \$16)... \$800,000 Costs: Fixed (\$100,000 + \$200,000)... \$300,000 Variable (50,000 \$5) , ,000 Income before income taxes ,000 Income taxes (\$250,000 40%) ,000 Net income... \$150,000 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

31 Problem 25-3B (continued) Part 4 Pre-tax target income = After-tax target income (1 tax rate) = \$300,000 (1 0.40) = \$500,000 Income tax = \$500,000 40% = \$200,000 Necessary sales level = (Fixed costs + Target income + Taxes) Contribution margin ratio = (\$300,000 + \$300,000 + \$200,000) 68.75% = \$800, % = \$1,163,637 Unit sales = \$1,163,637 \$16 = 72,728 units Part 5 CAPITAL COMPANY Forecasted Income Statement For Year Ended December 31,2005 Sales (72,728 \$16)... \$1,163,648 Costs: Fixed... \$300,000 Variable (72,728 \$5) , ,640 Income before income taxes... \$ 500,008 Income taxes (\$500,008 40%) ,003 Net income... \$ 300,005 (Net income is greater than \$300,000 due to rounding up in units from Part 4.) Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 190 Fundamental Accounting Principles, Eleventh Canadian Edition

32 Problem 25-4B Part 1 Part 2 Product L Product M Sales... \$3,000,000 \$3,000,000 Units sold , ,000 Selling price per unit... \$25 \$25 Variable costs... \$1,800,000 \$600,000 Variable cost per unit... \$15 \$5 Contribution margin per unit... \$10 \$20 Contribution margin ratio... 40% 80% Fixed costs... \$ 600,000 \$1,800,000 Break-even (fixed costs contribution margin ratio)... \$1,500,000 \$2,250,000 Income statements, assuming that the sales volume falls to 104,000 units: Per Unit Units Product L Product M Sales... \$ ,000 \$2,600,000 \$ ,000 \$2,600,000 Variable costs... \$ ,000 1,560,000 \$ , ,000 Contribution margin... 1,040,000 2,080,000 Fixed costs ,000 1,800,000 Income before taxes , ,000 Income tax (35%) ,000 98,000 Net income... \$ 286,000 \$ 182,000 Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

33 Problem 25-4B (continued) Part 3 Income statements, assuming that the sales volume increases to 190,000 units: Per Unit Units Product L Product M Sales... \$ ,000 \$4,750,000 \$ ,000 \$4,750,000 Variable costs... \$ ,000 2,850,000 \$ , ,000 Contribution margin... 1,900,000 3,800,000 Fixed costs ,000 1,800,000 Income before taxes... 1,300,000 2,000,000 Income tax (35%) , ,000 Net income... \$ 845,000 \$1,300,000 Part 4 If sales were to greatly increase, Product M would experience the greater increase in profit because it would experience a much greater contribution for each additional unit sold. Part 5 A factor that could cause Product L to have lower fixed costs might be a labour arrangement that pays workers for units produced. Another might be that the sales representatives work totally on commission. Managers may be compensated with a share of the profits instead of salaries. The fixed costs for Product M may be higher because of a salary structure that is not based on production or sales. Another factor may be that assets used in the production of Product L are leased and rent is based on the amount of usage. Product M s assets may be owned or under a lease agreement based on time, not the amount of usage. Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 192 Fundamental Accounting Principles, Eleventh Canadian Edition

34 Problem 25-5B Part 1 Priced at \$25.00 per unit (old plan): Bulk material cost per unit... \$1,000, ,000 = \$10.00 Packaging cost per unit... \$100, ,000 = \$1.00 Total variable costs per unit... \$ \$1.00 = \$11.00 Contribution margin per unit... \$25.00 \$11.00 = \$14.00 Contribution margin ratio... \$14.00 \$25.00 = 56% Fixed costs per year... = \$1,250,000 Break-even point... \$1,250,000 56% = \$2,232,143 Priced at \$20.00 per unit (new plan): Bulk material cost per unit... \$ % = \$8.00 Packaging cost per unit... \$ % = \$1.25 Total variable costs per unit... \$ \$1.25 = \$9.25 Contribution margin per unit... \$20.00 \$9.25 = \$10.75 Contribution margin ratio... \$10.75 \$20.00 = 53.75% Fixed costs per year... = \$1,250,000 Break-even point... \$1,250, % = \$2,325,581 Part 2 WHITE COMPANY Forecasted Income Statement Per Unit Units Old Plan New Plan Sales... \$25.00 \$ , ,000 \$2,500,000 \$3,600,000 Fixed costs... \$1,250,000 \$1,250,000 Variable costs: Product... \$ ,000 1,000,000 \$ ,000 1,440,000 Packaging... \$ , ,000 \$ , ,000 Total costs... \$2,350,000 \$2,915,000 Income before taxes... \$ 150,000 \$ 685,000 Income taxes (30%)... Net income... 45,000 \$ 105, ,500 \$ 479,500 Return on sales % 13.3% Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

35 Problem 25-6B Part 1 Sales... \$1,960,000 Variable costs: Cost of sales... \$1,176,000 Commissions ,200 1,411,200 Contribution margin... \$ 548,800 Contribution margin ratio (CMR) = \$548,800 \$1,960,000 = 28% Fixed costs... \$21,100 CMR Estimated break-even point... \$75,357 Part 2 a. Variable cost ratios Cost of sales... 60% Commissions... 4% 64% CMR = 100% 64% = 36% b. Fixed costs Sales manager... \$107,600 Three \$48, ,000 Administrative... 21,100 \$272,700 Fixed costs... \$272,700 CMR Estimated break-even point... \$757,500 c. Target income before income tax... \$468,900 Fixed costs... 21,100 \$490,000 Variable cost ratios Cost of sales... 60% Commissions... 15% 75% CMR = 100% 75%... 25% Target income + fixed costs... \$ 490,000 CMR Estimated sales volume... \$1,960,000 Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 194 Fundamental Accounting Principles, Eleventh Canadian Edition

37 Problem 25-8B Part 1 Break-even analysis assuming new machine is not acquired: 2 units of Product \$225 per unit = \$ units of Product \$150 per unit = units of Product \$120 per unit = 960 Selling price of a composite unit = \$2,160 2 units of Product \$120 per unit = \$ units of Product \$102 per unit = units of Product \$75 per unit = 600 Variable cost of a composite unit = \$1,350 Contribution margin of a composite unit = \$2,160 \$1,350 = \$810 Contribution margin ratio = \$810 \$2160 = 37.5% Break-even point in dollars = \$793, % = \$2,116,800 Break-even point in composite units = \$793,800 \$810 = 980 composite units Units of Product 1 at break-even point: = 1,960 units Units of Product 2 at break-even point: = 4,900 units Units of Product 3 at break-even point: = 7,840 units Part 2 Break-even analysis assuming purchase of new machine: Under the new plan, there would be no change in selling prices. The fixed costs would increase by \$81,000 to \$874,800 per year. 2 units of Product \$120 per unit = \$ units of Product (\$102 \$18) per unit = units of Product (\$75 \$9) per unit = 528 Variable cost of a composite unit = \$1,188 Contribution margin of a composite unit = \$2,160 \$1,188 = \$972 Contribution margin ratio = \$972 \$2,160 = 45% Break-even point in dollars = \$874,800 45% = \$1,944,000 Break-even point in composite units = \$874,800 \$972 = 900 composite units Units of Product 1 at break-even point: = 1,800 units Units of Product 2 at break-even point: = 4,500 units Units of Product 3 at break-even point: = 7,200 units Part 3 When a business invests in capital assets, as in this problem, there is a change in the riskiness of conducting business. The break-even point decreased, making it easier to make a profit with less sales. However, because of the commitment of higher fixed resources, the risk of loss from business failure is greater. Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 196 Fundamental Accounting Principles, Eleventh Canadian Edition

38 ANALYTICAL & REVIEW PROBLEMS A&R Problem 25-1 (a) Break even = Fixed costs contribution margin per unit CAMS LIPS SP \$42.00 \$42.00 VC: Direct material \$7.00 \$ 7.84 Direct labour Variable overhead Variable selling Contribution margin \$19.60 \$14.56 (i) \$3,416,000 + \$700,000 = 210,000 units (ii) \$1,848,000 + \$700,000 = 175,000 units (b) \$22.40X + \$4,116,000 = \$27.44X + \$2,548,000 \$ 5.04X = \$1,568,000 X = 311,111 units Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

39 A&R Problem 25-2 (20 minutes) a. Three relevant ranges are identified; in terms of percentage of physical capacity utilization, the ranges are OK, KL, and LM. In the three ranges, the total cost has linear relationship with volume, and fixed costs remain constant in the range. b. At lower levels of capacity utilization, costs increase rapidly; as efficiency of operation is reached, costs level off, increasing at a constant lower rate as increases in volume are experienced; when capacity of facility is approached, the rate of cost increase increases due to factors such as machine breakdowns, material shortages, increased waste, etc. Copyright 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 198 Fundamental Accounting Principles, Eleventh Canadian Edition

40 A&R Problem 25-3 (10 minutes) Fixed costs are costs that remain constant, in total, regardless of changes in the level of activity. These costs are a function of capacity; for example, amortization is a function of the amount of capital assets. Since these costs are a function of capacity they are viewed as capacity costs. Variable costs are not affected (per unit of activity) by changes in volume. They are a function of activity and vary with activity. Hence, variable costs are viewed as activity costs. A&R Problem NIKE Reebok Variable costs: Materials 100, ,000 Direct labour 300, ,000 Factory rent Total variable costs 400, ,000 Fixed costs: Factory rent 30,000 10,000 Factory equipment 50,000 60,000 Total fixed costs 80,000 70,000 Total cost 480, ,000 Sales in units Cost per unit 10,000 \$48 10,000 \$51 2. The reason why NIKE is more profitable than Reebok can be explained by the difference in cost structures for each company. NIKE invested more in capital assets than Reebok. Thus, the contribution margin for NIKE is greater than for Reebok. As a result, at sales of 10,000 pairs, the savings in labour more than offsets the \$10,000 of additional investment in capital assets for NIKE. 3. If sales significantly decline, NIKE will be less profitable. The fixed cost for each company stays the same, and NIKE has a greater commitment to fixed costs. Thus, a decrease in total contribution would be greater for NIKE (\$12/pair) than for Reebok (\$9/pair) in a sales downturn, although sales would have to decrease by more than 75% before Reebok would be more profitable than NIKE. Copyright 2005 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter

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