Cost Volume -Profit Analysis

Copyright © 2005 by McGraw-Hill Ryerson Limited. All rights reserved. 160 Fundamental Accounting Principles, Eleventh Canadian Edition

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 McGraw-Hill Ryerson Limited. All rights reserved. Solutions Manual for Chapter 25 161

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.


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

$8,000 – $3,000 Variable costs = 3,500 – 0 = $1.4286


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

$225,000 (b) Break-even point in units = $20 = 11,250 units

Quick Study 25-7 $50 – $30 (a) Contribution margin ratio = $50 = 40%

$225,000 (b) Break-even point in dollars = 40% = $562,500

Quick Study 25-8 The correct answer is b.

Quick Study 25-9 Before-tax income = $630,000 ÷ (1 – .40) = $1,050,000 Income taxes = $1,050,000 × .40 = $420,000 $225,000 + $630,000 + $420,000

$50 – $30 = 63,750 units

Quick Study 25-10 $835,120 Break-even point in composite units = $85 = 9,825 units

Mixers at break-even point = 3 × 9,825 = 29,475


EXERCISES

Exercise 25-1 1. 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 1,960 840 2,800 - 0 - 840 6,200 960 840 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


Exercise 25-5 (20 minutes)

The cost appears to be a mixed cost.


Exercise 25-6

The cost appears to be a step-variable cost.


Exercise 25-7 (15 minutes) Sales CGS High level of activity $450,000 $235,000 Low level of activity 420,000 226,000 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 420,000 106,000 Change observed $ 30,000 $ 2,000 Variable cost element: Change in

Expenses

$2,000 Change in Sales

= $30,000

= $0.0667 per sales dollar

Fixed selling and administration expenses: Total cost at the high level of activity...................... $108,000 Less variable cost element ($0.0667 × $450,000) ... 30,015 Fixed selling and administration expenses ............ $ 77,985


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 **$0.0667 × $500,000 = $33,350

Exercise 25-10 (15 minutes) a. Contribution margin per unit = $117.60 – $88.20 = $29.40 per unit b. Contribution margin ratio = $29.40 ÷ $117.60 = 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 × $117.60 = $1,764,000

Exercise 25-11 Income

Sales (15,000 × $117.60) ......................................... $1,764,000 Variable costs (15,000 × $88.20) ........................ 1,323,000 Contribution margin ........................................... 441,000 Fixed costs .......................................................... 441,000 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


Exercise 25-12 Pre-tax income = After-tax income ÷ (1 – tax rate) = $530,000 ÷ (1 – 0.4) = $530,000 ÷ 0.6 = $883,333 Income taxes = Pre-tax income × tax rate = $883,333 × 0.4 = $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


Exercise 25-13

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 = $441,000 ÷ 0.07 = $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 ÷ $117.60 = approximately 53,572 units


Exercise 25-14 Sales (60,000 × $175).............................................. $10,500,000 Variable costs (60,000 × $100)............................... 6,000,000 Contribution margin ............................................... 4,500,000 Fixed costs.............................................................. 441,000 Net income before taxes ........................................ 4,059,000 Income taxes (40% × $4,059,000) .......................... (1,623,600) Net income after taxes ........................................... $ 2,435,400

Exercise 25-15 (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 25-16 a. (i) Sales $12,000,000 Sales price = units = 80,000 = $150 per unit

Selling price per unit............................................... $ 150 Less: contribution margin per unit........................ (40) Variable costs per unit............................................ $ 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


Exercise 25-17 (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 25-18 (a) Selling price per composite unit 10 windows @ $70 per unit .............................................. $ 700 3 doors @ $450 per unit ................................................... 1,350 Selling price per composite unit ..................................... $2,050 (b) Variable costs per composite unit 10 windows @ $40 per unit .............................................. $ 400 3 doors @ $290 per unit ................................................... 870 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 × 1,250 .................................. 12,500 units Doors: 3 × 1,250................................... 3,750 units


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


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 2 ................................................................ 0 25,000 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) ............. 133,000 186,200 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 approxi-mations are reasonably close to these more precisely determined amounts.


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% Break-even point in dollars = Fixed costs ÷ Contribution ratio = $300,000 ÷ 62.5% = $480,000 Part 2


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) .............................................. 180,000 480,000 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% = $630,000 ÷ 62.5% = $1,008,000 Part 5 Contribution margin at predicted sales = Sales × Contribution rate = $1,200,000 × 62.5% = $750,000 Pre-tax income = Contribution margin – Fixed costs = $750,000 – $300,000 = $450,000 Income taxes = Pre-tax income × Tax rate = 450,000 × 30% = $135,000 After-tax income = Pre-tax income – Income taxes = $450,000 – $135,000 = $315,000


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


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) .............................................................. 225,000 Contribution margin.............................................................................. $525,000 Fixed ($384,000 + $120,000) ................................................................ 504,000 Income before income taxes ............................................................... $ 21,000 Income taxes ($21,000 × 30%).............................................................. 6,300 Net income ............................................................................................ $ 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) ......................................................................... 306,000 Contribution margin.............................................................................. $ 714,000 Fixed ...................................................................................................... 504,000 Income before income taxes.......................................................... ...... $ 210,000 Income taxes ($210,000 × 30%) ........................................................... 63,000 Net income ............................................................................................ $ 147,000


Problem 25-4A Part 1 Product A Product B Sales ................................................................ $800,000 $800,000 Units sold ........................................................ 50,000 50,000 Selling price per unit ...................................... $ 16.00 $ 16.00 Variable costs ...................... ........................... $560,000 $100,000 Variable cost per unit ..................................... $ 11.20 $ 2.00 Contribution margin per unit ......................... $ 4.80 $ 14.00 Contribution ratio ........................................... 30.0% 87.5% Fixed costs ...................................................... $100,000 $560,000 Break-even (fixed costs ÷ contribution rate) $333,333 $640,000

Part 2


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 33,000 $528,000 $16.00 33,000 $528,000 Fixed costs ..................................................... $100,000 $560,000 Variable costs ................................................. $11.20 33,000 369,600 $ 2.00 33,000 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)


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 ............................................................... $16.00 64,000 $1,024,000 $16.00 64,000 $1,024,000 Fixed costs ..................................................... $ 100,000 $ 560,000 Variable costs ................................................. $11.20 64,000 716,800 $ 2.00 64,000 128,000 Total costs ...................................................... $ 816,800 $ 688,000 Income before taxes ...................................... $ 207,200 $ 336,000 Income taxes (32%) ........................................ 66,304 107,520 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.


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 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 Plan 2 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

Part 2


Problem 25-5A (concluded)

Part 3

KIRBY COMPANY Forecasted Income Statement

Per Unit Units Plan 1 Plan 2 Sales ............................................................ $16.00 35,000 $560,000 $20.00 31,500 $630,000 Fixed costs .................................................. $300,000 $300,000 Variable costs .............................................. $ 4.00 35,000 140,000 $ 4.00 31,500 126,000 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


Problem 25-6A 1. Sales ................................................................ $1,400,000 Variable costs: Cost of sales ............................................... $840,000 Commissions .............................................. 210,000 1,050,000 Contribution margin ....................................... $ 350,000 Contribution margin ratio (CMR) = $ 350,000 $1,400,000 = 25% Fixed costs ........................................... $14,000 CMR ...................................................... ÷ .25 Estimated break-even point ................ $56,000 2. Variable cost ratios Cost of sales .................................... 60% Commissions ................................... 5% 65% CMR = 100% – 65% = 35% Fixed costs Sales manager ............................................................. $ 84,000 Three salespeople @ $42,000...................................... 126,000 Administrative .............................................................. 14,000 $224,000 Fixed costs ....................................................................... $224,000 CMR .................................................................................. ÷ .35 Estimated break-even point............................................. $640,000 3. 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 .................................................................................. ÷ .20 Estimated sales volume .................................................. $1,750,000


Problem 25-6A (concluded) 4. Total costs with agents = Total costs with company’s own force receiving 20% commission x = sales volume .80x + $14,000 = .65x + $224,000 .15x = $210,000 x = $1,400,000

Problem 25-7A (a) $1,680,000 – (560,000 + 700,000 + 140,000 + VSA) = $140,000 Variable selling and administrative expense (VSA) = $140,000 (b) $1,680,000 – (560,000 + 700,000 + 140,000 + FMO) = $140,000 Fixed manufacturing overhead (FMO) = $140,000 (c) Contribution margin ratio = $140,000 ÷ 1,680,000 = 8.33% At break-even, contribution margin = Fixed selling and administrative + Fixed manufacturing overhead Break-even point = $1,890,000 Contribution margin = 1,890,000 × .083333 = 157,500 157,500 = FSA + 140,000 Fixed selling and administrative = $17,500 (d) Maximum increased advertising expenditure = 1,680,000 × .25 × .083333 = $35,000

The amount that advertising expenditures can be increased and the company be just as profitable as before is the amount of the increased contribution arising from the increase in sales. The fixed manufacturing overhead and the fixed selling and administrative expenses are irrelevant in this case.


Problem 25-8A Part 1 5 units of Red @ $55 per unit = $275 4 units of White @ $85 per unit = 340 2 units of Blue @ $110 per unit = 220 Selling price of a composite unit = $835 5 units of Red @ $40 per unit = $200 4 units of White @ $60 per unit = 240 2 units of Blue @ $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 = $150,000 ÷ 28.14% = $533,049 Break-even point in composite units = $150,000 ÷ $235 = 639 composite units Units of Red at break-even point: 639 × 5 = 3,195 units Units of White at break-even point: 639 × 4 = 2,556 units Units of Blue at break-even point: 639 × 2 = 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 Red @ ($40 – $10) per unit = $150 4 units of White @ ($60 – $20) per unit = 160 2 units of Blue @ ($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 = $170,000 ÷ 46.11% = $368,683 Break-even point in composite units = $170,000 ÷ $385 = 442 composite units Units of Red at break-even point: 442 × 5 = 2,210 units Units of White at break-even point: 442 × 4 = 1,768 units Units of Blue at break-even point: 442 × 2 = 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.


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)....................... 45 75 Total cost................................................................. $135 $165


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 = $30,000 ÷ 33.33% = $90,009

Part 2


Problem 25-2B (concluded) Part 3

Sales (400 units @ $225)........................................ $90,000 Variable costs (400 units @ $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 – ($18 × 72.22%) = $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 .................. $300,000 ÷ 68.75% = $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) ......................................... 250,000 550,000 Income before income taxes ................................. 250,000 Income taxes ($250,000 × 40%) ............................. 100,000 Net income .............................................................. $150,000


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% = $800,000 ÷ 68.75% = $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) ........................................... 363,640 663,640 Income before income taxes ..................................... $ 500,008 Income taxes ($500,008 × 40%) ................................. 200,003 Net income .................................................................. $ 300,005 (Net income is greater than $300,000 due to rounding up in units from Part 4.)


Problem 25-4B Part 1

Product L Product M Sales ..................................................................... $3,000,000 $3,000,000 Units sold ............................................................. 120,000 120,000 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

Part 2 Income statements, assuming that the sales volume falls to 104,000 units: Per Unit Units Product L Product M

Sales ................................ $25.00 × 104,000 $2,600,000 $25.00 × 104,000 $2,600,000 Variable costs ................. $15.00 × 104,000 1,560,000 $5.00 × 104,000 520,000 Contribution margin ....... 1,040,000 2,080,000 Fixed costs...................... 600,000 1,800,000 Income before taxes....... 440,000 280,000 Income tax (35%) ............ 154,000 98,000 Net income ...................... $ 286,000 $ 182,000


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 ................................ $25.00 × 190,000 $4,750,000 $25.00 × 190,000 $4,750,000 Variable costs ................. $15.00 × 190,000 2,850,000 $ 5.00 × 190,000 950,000 Contribution margin ....... 1,900,000 3,800,000 Fixed costs ...................... 600,000 1,800,000 Income before taxes ....... 1,300,000 2,000,000 Income tax (35%) ............ 455,000 700,000 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.


Problem 25-5B Part 1 Priced at $25.00 per unit (old plan):

Bulk material cost per unit ................................. $1,000,000 ÷ 100,000 = $10.00 Packaging cost per unit ...................................... $100,000 ÷ 100,000 = $1.00 Total variable costs per unit............................... $10.00 + $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 ................................. $10.00 × 80% = $8.00 Packaging cost per unit ...................................... $1.00 × 125% = $1.25 Total variable costs per unit............................... $8.00 + $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 ................................................. $1,250,000 ÷ 53.75% = $2,325,581

Part 2

WHITE COMPANY Forecasted Income Statement

Per Unit Units Old Plan New Plan Sales ................................ $25.00 100,000 $2,500,000 $20.00 180,000 $3,600,000 Fixed costs...................... $1,250,000 $1,250,000 Variable costs: Product ........................ $10.00 100,000 1,000,000 $ 8.00 180,000 1,440,000 Packaging .................... $ 1.00 100,000 100,000 $ 1.25 180,000 225,000 Total costs....................... $2,350,000 $2,915,000 Income before taxes....... $ 150,000 $ 685,000 Income taxes (30%) ........ 45,000 205,500 Net income ...................... $ 105,000 $ 479,500

Return on sales............... 4.2% 13.3%


Problem 25-6B Part 1 Sales ................................................................ $1,960,000 Variable costs: Cost of sales ............................................... $1,176,000 Commissions .............................................. 235,200 1,411,200 Contribution margin ....................................... $ 548,800 Contribution margin ratio (CMR) = $548,800 $1,960,000 = 28% Fixed costs ........................................... $21,100 CMR ...................................................... ÷ .28 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 salespeople @ $48,000...................................... 144,000 Administrative .............................................................. 21,100 $272,700 Fixed costs ....................................................................... $272,700 CMR .................................................................................. ÷ .36 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 .................................................................................. ÷ .25 Estimated sales volume .................................................. $1,960,000


Problem 25-6B (continued) d. Total costs with agents = Total costs with company’s own force receiving 15% commission x = sales volume .75x + $21,100 = .64x + $272,700 .11x = $251,600

x = $2,287,273

Problem 25-7B (a) $910,000 – (280,000 + 350,000 + 70,000 + VSA) = $182,000 Variable selling and administrative expense (VSA) = $ 28,000 (b) $910,000 – (280,000 + 350,000 + 70,000 + FMO) = $ 70,000 Fixed manufacturing overhead (FMO) = $140,000 (c) Contribution margin ratio = $182,000 ÷ 910,000 = 20% At break-even, contribution margin = Fixed selling and administrative + Fixed manufacturing overhead Break-even point = $1,050,000 Contribution margin = 1,050,000 × .2 = 210,000 210,000 = FSA + 140,000 Fixed selling and administrative = $ 70,000 (d) Maximum increased advertising expenditure = 910,000 × .3 × .2 = $54,600

The amount that advertising expenditures can be increased and the company be just as profitable as before is the amount of the increased contribution arising from the increase in sales. The fixed manufacturing overhead and the fixed selling and administrative expenses are irrelevant in this case.


Problem 25-8B Part 1 Break-even analysis assuming new machine is not acquired: 2 units of Product 1 @ $225 per unit = $ 450 5 units of Product 2 @ $150 per unit = 750 8 units of Product 3 @ $120 per unit = 960 Selling price of a composite unit = $2,160 2 units of Product 1 @ $120 per unit = $ 240 5 units of Product 2 @ $102 per unit = 510 8 units of Product 3 @ $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 = $793,800 ÷ 37.5% = $2,116,800 Break-even point in composite units = $793,800 ÷ $810 = 980 composite units Units of Product 1 at break-even point: 980 × 2 = 1,960 units Units of Product 2 at break-even point: 980 × 5 = 4,900 units Units of Product 3 at break-even point: 980 × 8 = 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 1 @ $120 per unit = $ 240 5 units of Product 2 @ ($102 – $18) per unit = 420 8 units of Product 3 @ ($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: 900 × 2 = 1,800 units Units of Product 2 at break-even point: 900 × 5 = 4,500 units Units of Product 3 at break-even point: 900 × 8 = 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.


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 8.40 10.08 Variable overhead 4.20 6.72 Variable selling 2.80 22.40 2.80 27.44 Contribution margin $19.60 $14.56 (i) $3,416,000 + $700,000 = 210,000 units 19.60 (ii) $1,848,000 + $700,000 = 175,000 units 14.56 (b) $22.40X + $4,116,000 = $27.44X + $2,548,000

$ 5.04X = $1,568,000 X = 311,111 units


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.


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 25-4 1. NIKE Reebok

Variable costs: Materials 100,000 100,000 Direct labour 300,000 340,000 Factory rent Total variable costs 400,000 440,000 Fixed costs: Factory rent 30,000 10,000 Factory equipment 50,000 60,000 Total fixed costs 80,000 70,000 Total cost 480,000 510,000 Sales in units 10,000 10,000 Cost per unit $48 $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.