Publisher's Solutions Ch 6

Managerial Accounting: Tools for Business Decision-Making, Third Canadian Edition Weygandt, Kimmel, Kieso, Aly

Solutions Manual © 2012 John Wiley & Sons Canada, Ltd. Unauthorized copying, distribution, or transmission of this page is prohibited

6-1

CHAPTER 6

Decision-Making: Cost-Volume-Profit

ASSIGNMENT CLASSIFICATION TABLE

Study Objectives

Questions

Brief

Exercises

Do It!

Exercises

A & B

Problems

* 1. List the five components of

cost-volume-profit analysis

and describe the essential

features of a cost-volume-

profit statement.

1, 2, 3, 4, 6 2 17 24, 27, 30 40A, 43A,

54B, 55B

* 2. Explain what the

contribution margin is and

how it can be expressed.

7, 8, 9 1, 2, 8, 11 15, 16,

17, 19

24, 25, 26, 27,

30, 36

40A – 48A,

50A – 52A,

53B – 56B,

58B, 59B,

61B – 66B

* 3. Identify the three ways to

determine the break-even

point.

5, 10, 11,

12

3, 4, 10,

13, 14

15, 16,

18, 19

20, 23, 25, 28,

29, 33, 34, 35,

36

39A – 46A,

48A – 51A,

53B – 65B

* 4. State the formulas for

determining the sales

required to earn the target

operating income before

and after tax.

14 5, 7 16, 19 20, 21, 26, 33 39A, 40A,

42A, 46A,

48A, 49A,

53B,56B,

58B – 63B

* 5. Define margin of safety,

and state the formulas for

calculating it.

13 6 16, 18,

19

23, 29, 30, 38 41A, 42A,

45A, 46A,

51A, 56B,

59B, 61B,

64B, 65B

* 6. Understand how to apply

basic cost-volume-profit

concepts in a changing

business environment.

18 43A, 45A,

46A, 57B,

61B



6-2

Study Objectives

Questions

Brief

Exercises

Do It!

Exercises

A & B

Problems

* 7. Explain the term “sales mix” and its effect on break-even sales.

20, 21, 22 12, 13, 14 19 22, 32, 33, 34, 35, 36

52A, 66B

* 8. Understand how cost

structure and operating

leverage affects

profitability. (Appendix

6A)

15, 16, 17,

18,19

8, 9, 10 31, 37, 38 49A, 51A,

64B, 65B



6-3

ASSIGNMENT CHARACTERISTICS TABLE

Problem

Number

Description

Difficulty

Level

Time

Allotted (min.)

39A Calculate the break-even point in units and target income after tax.

Moderate 20–30

40A Determine variable and fixed costs, calculate the break-

even point, prepare a CVP graph, and determine operating income.

Moderate 25–35

41A Determine the contribution margin ratio, break-even point

in dollars, and margin of safety. Moderate 20–30

42A Determine the contribution margin ratio, break-even point

in dollars, margin of safety and sales required to earn target operating income under alternative scenarios.

Moderate 25–35

43A Calculate the break-even point under alternative courses

of action. Simple 25–35

44A Determine the break-even point in dollars and units, and

target income. Moderate 25–35

45A Calculate the break-even point and margin of safety

ratio, and prepare a CVP income statement before and after changes in the business environment.

Moderate 20–30

46A Calculate the break-even point and margin of safety

ratio, and prepare a CVP income statement before and after changes in the business environment.

Moderate 35-40

47A Determine the contribution margin ratio. Simple 10-15

48A Determine the contribution margin, break-even point, and

target operating income. Simple 25-35

49A Determine the contribution margin, break-even point,

target sales, and degree of operating leverage. Moderate 25-35

50A Determine the contribution margin, break-even point in

units, and target income. Simple 15-20

51A Calculate the break-even point, margin of safety ratio,

and the degree of operating leverage and evaluate its impact on financial results.

Moderate 25-35



6-4

Problem

Number

Description

Difficulty

Level

Time

Allotted (min.)

52A Determine the sales mix under different scenarios. Simple 15-20

53B Determine the contribution margin, break-even point, and target sales after taxes.

Moderate 20–30

54B Determine variable and fixed costs, calculate the break-

even point, prepare a CVP graph, and determine operating income.

Moderate 25–35

55B Determine variable and fixed costs and operating

income. Simple 10–15

56B Prepare a CVP income statement, and calculate the

break-even point, contribution margin ratio, margin of safety ratio, and sales for target operating income.

Moderate 20–30

57B Calculate the break-even point under alternative courses

of action. Moderate 20–30

58B Determine the break-even point in dollars and target

income. Moderate 20–30

59B Calculate the break-even point and margin of safety ratio,

and prepare a CVP income statement before and after changes in the business environment.

Simple 20–30

60B Determine the break-even point and target income. Simple 20–30

61B Calculate the break-even point and margin of safety ratio,

and prepare a CVP income statement before and after changes in business environment.

Moderate 25–35

62B Determine the contribution margin ratio, break-even point

in dollars, and target sales. Moderate 25–35

63B Determine the contribution margin, break-even point in

dollars, and sales. Simple 10–15

64B Calculate the break-even point, the margin of safety, and

the degree of operating leverage under various scenarios.

Moderate 25–35

65B Calculate the break-even point, the margin of safety and

the degree of operating leverage under various scenarios.

Moderate 25–35

© 2

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Correlation Chart between Bloom’s Taxonomy, Study Objectives and End-of-Chapter Exercises and Problems

Study Objective Knowledge Comprehension Application Analysis Synthesis Evaluation

*1. List the five components of

cost-volume-profit analysis and

describe the essential features

of a cost-volume-profit income

statement.

Q2, Q4 Q1

Q6

BE2

E24

P55B

Q3

E27

E30

P40A

P54B

P43A

*2. Explain what the contribution

margin is and how it can be

expressed.

Q7 Q8

Q9

BE1

BE2

BE8

BE11

E24

E25

E26

E36

P41A

P42A

P55B

E27

E30

P40A

P44A

P47A

P50A

P51A

P54B

P56B

P58B

P61B

P62B

P63B

P64B

P65B

P66B

P43A

P45A

P46A

P48A

P52A

P53B

P59B

*3. Identify the three ways to

determine the break-even point.

Q5,

Q10

Q12

Q11

BE3

BE4

BE10

BE13

BE14

E20

E25

E36

P41A

P42A

P55B

E23

E28

E29

E33

E34

E35

P39A

P40A

P44A

P49A

P50A

P51A

P54B

P56B

P58B

P60B

P61B

P62B

P63B

P64B

P65B

P43A

P45A

P46A

P48A

P53B

P57B

P59B

*4. State the formulas for

determining sales required to

earn the target operating income

before and after taxes.

Q14

BE5

BE7

E20

E21

E26

P42A

E33

P39A

P40A

P49A

P56B

P58B

P60B

P61B

P62B

P63B

P46A

P48A

P53B

P59B

*5. Define margin of safety, and

state the formulas for

calculating it.

Q13

BE6

P41A

P42A E23

E29

E30

P51A

P56B

P61B

P64B

P65B

E38

P45A

P46A

P59B

* 6. Understand how to apply basic

cost-volume-profit concepts in

a changing environment.

P61B P43A

P45A

P46A

P57B

P59B

7. Explain the term “sales mix”

and its effect on break-even

sales.

Q22 Q21 BE12

BE13

BE14

E22

E32

E36

E33

E34

E35

P66B

P52A

**8. Understand how cost structure

and operating leverage affects

profitability. (Appendix 6A)

Q16, Q18 Q15, Q17, Q19 BE8

BE10

BE9

E37

P49A

P51A

P64B

P65B

E31

E38



6-5

ANSWERS TO QUESTIONS

1. CVP or cost-volume-profit analysis is the study of the effects of changes in costs and volume on

a company’s profit.

*2. Managers use CVP analysis to make decisions involving break-even point, sales required to

reach a target operating income, margin of safety, the most profitable sales mix, allocation of

limited resources, and operating leverage.

3. Both types of income statements report the same amount of operating income. But the format

used to reach operating income differs. A traditional income statement’s format consists of:

Sales revenue – cost of goods sold = gross profit; Gross profit – selling and administrative expenses =

operating income.

A CVP income statement’s format consists of:

Sales revenue – variable expenses = contribution margin; Contribution margin – fixed expenses =

operating income.

4. The CVP income statement isolates variable costs from fixed costs while the traditional income

statement does not. The CVP format indicates contribution margin in total and frequently on a per

unit basis as well. This format facilitates calculation of break-even point and target operating

income. It also highlights how changes in sales volume or cost structure affect operating income.

5. If the selling price is reduced but variable and fixed costs remain unchanged, the break-even point

will increase.

6. No. Only two of the basic components of cost-volume-profit (CVP) analysis, unit selling price and

variable cost per unit, relate to unit data. The other components, volume, total fixed costs, and

sales mix are not based on per-unit amounts.

7. There is no truth in Andrea’s statement. Contribution margin is sales less variable costs. It is the

revenue that remains to cover fixed costs and to produce profit for the company.

8.

RICE COMPANY

CVP (Partial) Income Statement

Sales

$900,000

Less: Variable costs ($500,000 × .70) + ($200,000 × .70) 490,000

Contribution margin $410,000

9. Contribution margin per unit is $15 ($40 – $25). The contribution margin ratio is 37.5% ($15 ÷

$40).

*10. Disagree. Knowledge of the break-even point is useful to management in deciding whether to

introduce new product lines, change sales prices on established products, and enter new market

areas. Break-even (CVP) analysis can also be expanded to determine target operating incomes.



6-6

Questions Chapter 6 (Continued)

*11. Break-even sales in dollars is determined by dividing total fixed costs by the contribution margin

ratio, so the break-even point is $22,000 ÷ 25% = $88,000.

*12. (a) The break-even point involves the plotting of three lines over the full range of activity: the

total revenue line, the total fixed cost line, and the total cost line. The break-even point is

determined at the intersection of the total revenue and total cost lines.

(b) The break-even point in units is obtained by drawing a vertical line from the break-even

point to the horizontal axis. The break-even point in sales dollars is obtained by drawing a

horizontal line from the break-even point to the vertical axis.

13. (a) Margin of safety is the difference between actual or expected sales and sales at the break-

even point.

(b) 1,600 × $12 = $19,200; $19,200 – $13,440 = $5,760; $5,760 ÷ $19,200 = 30%.

14. At break-even sales, the contribution margin is equal to fixed costs, or $240,000. To determine

target operating income in sales, first calculate the contribution margin ratio: $240,000 ÷

$600,000 = 40%. The sales volume to achieve operating income of $60,000 is: (Fixed costs +

target operating income) ÷ contribution margin ratio.

Or $240,000 + $60,000 = $750,000

0.4

*15. Cost structure refers to the proportion of fixed costs versus variable costs that a company incurs.

Cost structure can have a considerable effect on a company’s break-even point. If two

companies have the same level of sales dollars and exactly the same amount of expenses, but

opposite cost structures, their break-even points will be very different. The company with a larger

proportion of fixed costs will have a much higher break-even point than the one with a larger

proportion of variable costs.

*16. Operating leverage measures how sensitive operating income is to a specific percentage change

in the sales volume. In highly leveraged firms—those with high fixed costs and low variable

costs—small changes in sales volume result in large changes in net profit. Firms with low

leverage—low fixed costs and high variable costs—are not affected as much by changes in sales

volume. Firms can increase their operating leverage by altering their cost structure (i.e.,

converting variable expenses to fixed expenses or vice versa).

*17. The replacement of manual labour with automated equipment will increase a firm’s fixed costs

and decrease its variable costs. This will increase operating leverage, but at the same time, will

also raise the break-even point.

*18. Operating leverage is measured in degrees, and can be calculated by dividing the total

contribution margin by operating income.

*19. Acorn Company’s operating income would increase by twice the amount as Oak Company’s with

the same percentage increase in sales volume. For example, if both companies experienced an



6-7

Questions Chapter 6 (Continued)

increase of 10% in sales volume, Acorn Company would have an 80% increase in operating

income, while Oak Company would only achieve a 40% increase. This would be the case if both

companies are operating above break-even.

20. Sales mix means the proportions in which a company’s products are sold, relative to each other.

The break-even point in a multi-product company is determined by calculating a weighted-

average contribution margin ratio. The proportions of high margin versus low margin products

sold will raise or lower the break-even point accordingly.

21. If the sales mix shifts so the company is selling more of the lower- priced tires which have a lower

contribution margin, the weighted average contribution margin ratio will be lowered, which will, in

turn, raise the break-even point.

22. To calculate the break-even point for a company that has many products, contribution margin will

frequently be determined based on sales information for divisions or product lines, rather than

individual products.



6-8

SOLUTIONS TO BRIEF EXERCISES BRIEF EXERCISE 6-1 1. (a) $250 ($750 – $500) (b) 33.33% ($250 ÷ $750)

2. (c) $315 ($450 – $135) (d) 30 % ($135 ÷ $450)

3. (e) $2,000 ($400 ÷ 20%) (f) $1,600 ($2,000 – $400)

BRIEF EXERCISE 6-2

FONTILLAS MANUFACTURING INC. CVP Income Statement

For the Quarter Ended March 31, 2012 Sales ...................................................................... $2,500,000 Variable costs ($850,000 + $140,000 + $70,000) . 1,060,000 Contribution margin ............................................. 1,440,000 Fixed costs ($450,000 + $65,000 + $90,000) ........ 605,000 Operating income ................................................. $ 835,000

BRIEF EXERCISE 6-3 (a) $650Q = $350Q + $180,000 + $0 $300Q = $180,000 Q = 600 units (b) Contribution margin per unit is $300 ($650 – $350) Q = $180,000 ÷ $300 Q = 600 units



6-9

BRIEF EXERCISE 6-4 Contribution margin ratio = [($30 – $18) ÷ $30] = 40% Required sales in dollars = $40,000 ÷ 40% = $100,000 BRIEF EXERCISE 6-5 If variable costs are 55% of sales, the contribution margin ratio is ($1 – $0.55) ÷ $1 = 45%. X = ($210,000 + $80,000) ÷ 45% X = $644,444 BRIEF EXERCISE 6-6 (a) Margin of safety in dollars = $1,200,000 – $840,000 = $360,000 (b) Margin of safety ratio = $360,000 ÷ $1,200,000 = 30% BRIEF EXERCISE 6-7 Contribution margin per unit is $10.00 ($24.00 – $14.00). $10Q = $130,000 + .10($130,000 + $14Q) $10Q = $143,000 + $1.4Q X = 16,628 units (rounded) Proof: $24Q – $14Q – $130,000 = .10($130,000 + $14Q) $24(16,628) – $14(16,628) – $130,000 = .10($130,000 + $14(16,628)) $166,280 – $130,000 = $36,280 (rounded) *BRIEF EXERCISE 6-8

The degree of operating leverage is calculated by dividing the total contribution margin by operating income. To determine the contribution margin, multiply the degree of operating leverage by the operating income. Delta Corp: $50,000 × 1.4 = $70,000 Epsilon Co.: $50,000 × 5.6 = $280,000



6-10

*BRIEF EXERCISE 6-9

Operating leverage— Before the purchase: $160,000 ÷ $40,000 = 4.0 After the purchase: $240,000 ÷ $40,000 = 6.0 By replacing variable expenses with fixed expenses (depreciation), Sanjay’s Shingle Corporation is increasing its operating leverage. That is, before the purchase, the percentage increase in operating income will be 4 times the percentage increase in sales volume. After the purchase, it will be 6 times. By changing its cost structure, Sanjay’s will have greater benefits (increased income) if revenues increase, but also greater risks (decreased income) if revenues decrease. An increase in operating leverage will also result in a higher break-even point, which might be riskier for Sanjay’s if the market is uncertain.

*BRIEF EXERCISE 6-10 Break-even for Finch Co.: $50,000 ÷ ($90,000 ÷ $150,000) = $83,3341 Break-even for Sparrow Co.: $95,000 ÷ ($135,000 ÷ $150,000) = $105,5561

Sparrow Co. is more highly leveraged, so their break-even point will be higher. This is risky in an unstable market, but could result in higher returns once they reach break-even. Finch Co. has taken a more conservative approach. They will reach break-even faster, but their income on sales above that point will be less. 1 rounded to the nearest dollar



6-11

BRIEF EXERCISE 6-11

Sales mix %: Bedroom: $500,000 ÷ ($500,000 + $750,000) = 40% Dining Room: $750,000 ÷ ($500,000 + $750,000) = 60%

Contribution margin ratio: Bedroom: $250,000 ÷ $500,000 = 50% Dining Room: $300,000 ÷ $750,000 = 40%

Weighted-average contribution margin ratio: (40% × 50%) + (60% × 40%) = 44%

BRIEF EXERCISE 6-12

Models

Per unit: A12 B22 C124

Sales $50.00 $100.00 $400.00

Less: variable costs $40.00 $70.00 $300.00

Contribution margin $10.00 $30.00 $100.00

Sales mix 60% 25% 15%

Weighted-average unit

contribution margin = ($10 × 60%) + ($30 × 25%) + ($100 × 15%)

= $28.50 BRIEF EXERCISE 6-13

Break-even in units = Fixed costs ÷ per unit contribution margin Break-even in units = $199,500 ÷ $28.50 = 7,000 units 4,200 units of A12 (7,000 × 60%) 1,750 units of B22 (7,000 × 25%) 1,050 units of C124 (7,000 × 15%) 7,000



6-12

BRIEF EXERCISE 6-14

Weighted-average contribution margin ratio = (30% × 10%) + (50% × 20%) + (20% × 45%) = 22% Break-even in sales dollars = $440,000 ÷ 22% = $2,000,000 Birthday: $2,000,000 × 30% = $600,000 Standard tapered: $2,000,000 × 50% = $1,000,000 Large scented: $2,000,000 × 20% = $400,000



6-13

SOLUTIONS TO DO IT! REVIEW DO IT! REVIEW 6-15

(a) $250Q = $160Q + $135,000 + $0 $90Q = $135,000 Q = 1,500 units (b) Contribution margin per unit is $90 ($250 – $160) Q = $135,000 ÷ $90 Q = 1,500 units

DO IT! REVIEW 6-16

(a) Contribution margin ratio is 1/3 [($30 – $20) ÷ $30] Q = $200,000 ÷ 1/3 Q = $600,000 (b) Margin of safety ratio is 20%

($750,000 – $600,000) ÷ $750,000

(c) Sales dollars to earn $120,000 operating income: ($200,000 + $120,000) ÷ 1/3 = $960,000

DO IT! REVIEW 6-17 (a)

NAYLOR MANUFACTURING INC.

CVP Income Statement

For the Month ended January 31, 2012

Total Per Unit

Sales (8,000 units) $400,000 $50

Variable costs 240,000 30

Contribution margin 160,000 $20

Fixed expenses 140,000

Operating income $ 20,000



6-14

DO IT! REVIEW 6-17 (Continued) (b) $160,000 ÷ 8,000 = $20 Contribution margin per unit (c) $20 ÷ $50 = 40% Contribution margin ratio DO IT! REVIEW 6-18 (a) Assuming no changes (1) Break-even point in units: $150,000 ÷ $22.50 = 6,667 (rounded) (2) Contribution margin ratio: $22.50 ÷ $50.00 = 45% Break-even point in dollars: $150,000 ÷ 45% = $333,333 (3) Margin of safety: $450,000 – $333,333 = $116,667 (b) Assuming changes to sales price and volume New contribution margin: ($50 × .9) – $27.50 = $17.50 (1) Break-even point in units: $150,000 ÷ $17.50 = 8,572 (rounded) (2) Contribution margin ratio: $17.50 ÷ $45.00 = 38.89% (rounded) Break-even point in dollars: $150,000 ÷ 38.89% = $385,703 (3) Margin of safety: [$45 × (9,000 × 1.3)] – $385,703 = $140,797 Lowering the selling price with no change in variable costs will result

in a lower contribution margin. This causes the break-even point to increase by 1,905 units. The 30% increase in sales is not enough to compensate for the higher break-even point, as shown by an increase in the margin of safety.

DO IT! REVIEW 6-19

(a) Sales mix: Basic: 60% (840 ÷ 1,400)

Basic Plus: 25% (350 ÷ 1,400)

Premium: 15% (210 ÷ 1,400)



6-15

DO IT! REVIEW 6-19 (Continued) (b) [60% × ($250 – $195)] + [25% × ($400 – $288)] + [15% × ($800 – $416)] = $33.00 + $28.00 + $57.60 = $118.60 (c) Break-even point: $140,000 ÷ $118.60 = 1,180 units (rounded) (d) Break-even units by model:

Basic: 708 (60% × 1,180)

Basic Plus: 295 (25% × 1,180)

Premium: 177 (15% × 1,180)



6-16

SOLUTIONS TO EXERCISES EXERCISE 6-20 (a) Sales revenue $750,000 ($250 × 300 × 10 months) Variable costs 150,000 ($50 × 300 × 10 months) Contribution margin 600,000 Fixed costs 450,000 Operating income $150,000 (b) $450,000 ÷ ($250 – $50) = 2,250 units to break-even (c) Unit sales for 6 months: 300 × 6 = 1,800 1,800 × (S – $50) – $450,000 = $30,000 Selling price would need to be $316.67 (rounded) EXERCISE 6-21 (a) If variable cost ratio is 30%, then contribution margin ratio is 70%. [($56,000 + $140,000) ÷ 0.70] = $280,000 (b) Sales revenue $280,000 [from (a)] Variable costs 84,000 [$280,000 × 0.30]

Contribution margin 196,000 Fixed costs 56,000

Operating income $140,000

EXERCISE 6-22

Weighted-average contribution margin = (0.15 × $120) + (0.60 × $60) + (0.25 × $40) = $64 Break-even in units = $5,440,000 ÷ $64 = 85,000 Destroyer: 85,000 × 15% = 12,750 units Voyager: 85,000 × 60% = 51,000 units Rebel: 85,000 × 25% = 21,250 units



6-17

EXERCISE 6-23 (a) (1) Contribution margin per room = $50 – ($5 + $25) Contribution margin per room = $20 Contribution margin ratio = $20 ÷ $50 = 40% Fixed costs = $10,000 + $2,000 + $1,000 + $500 = $13,500 Break-even point in rooms = $13,500 ÷ $20 = 675 (2) Break-even point in dollars = 675 rooms × $50 per room = $33,750 per month OR Fixed costs ÷ Contribution margin ratio = $13,500 ÷ 0.40 = $33,750 per month (b) (1) Margin of safety in dollars: Planned activity = 30 rooms per day × 30 days = 900 rooms per month Expected rental revenue = 900 rooms × $50 = $45,000 Margin of safety in dollars = $45,000 – $33,750 = $11,250

(2) Margin of safety ratio: $11,250 = 25%

$45,000 EXERCISE 6-24 (a) (1) At break even, fixed costs = contribution margin = $105,000 $350,000 – $105,000 = $245,000 variable costs

Variable cost per unit = $245,000 ÷ ($350,000 ÷ $7.00) = $4.90 (2) $105,000 ÷ $350,000 = 30% contribution margin ratio (b) The increase in sales is $70,000 ($420,000 – $350,000) Increase in contribution margin = $70,000 × 0.30 = $21,000 Increase in fixed costs would be $21,000, the same as the increase

in contribution margin at break-even.



6-18

EXERCISE 6-25

(a) Total Per unit %

Sales ($30 × 2,600) $78,000 $30 100%

Variable costs (60% of sales) 46,800 18 60%

Contribution margin $31,200 $12 40%

(b) Break-even point in dollars =

$24,000 = $60,000

0.40

Break-even point in units =

$24,000 = 2,000 units

$12

EXERCISE 6-26 (a) $150Q = $90Q + $570,000 + $150,000 $60Q = $720,000 Q = 12,000 units OR

(b) Units needed in 2013 =

$570,000 + $210,000*

$150 – $90

= 13,000 units

*$150,000 + $60,000 = $210,000 desired profit

(c) Use the equation:

Sales = variable costs + fixed costs + operating income 12,000X = (12,000 × $90) + $570,000 + $210,000 Selling price (X) would have to be $155

$570,000 + $150,000

$150 – $90



6-19

EXERCISE 6-27

Current selling price = $310,000 ÷ 5,000 units = $62 1. Increase selling price to $68.20 ($62 × 110%). Operating income = ($68.20 × 5,000) – $217,000 – $70,000 = $54,000.

2. Reduce variable costs to 65% of sales. Operating income = $310,000 – ($310,000 × 0.65) – $70,000 = $38,500. 3. Reduce fixed costs by $10,000. Operating income = $310,000 – $217,000 – $60,000 = $33,000.

Alternative 1, increasing selling price, will produce the highest operating income. EXERCISE 6-28

(a) (1) Contribution margin ratio = $27,500 ÷ $50,000 = 55% Break-even point in dollars = $22,000 ÷ 0.55 = $40,000 (2) Round trip revenue per fare = $50,000 ÷ 400 = $125 Contribution margin in fares = $27,500 ÷ 400 = $68.75 Break-even point in fares = $22,000 ÷ $68.75 = 320

(b) At the break-even point fixed costs and contribution margin are equal. Therefore, the contribution margin at the break-even point would be $22,000.

(c) New fare = $125 × 0.90 = $112.50 New variable costs = ($22,500 ÷ 400) × 1.20 = $67.50

New contribution margin per unit = $112.50 – $67.50 = $45

New operating income = ($45 × 480) – $22,000 = ($400)

The new fare should not be adopted as it would put them below break-

even.



6-20

EXERCISE 6-29

(a)

$3,200

Sales Line

DO

LL

AR

S (

00

0)

2,800

Total Cost Line

2,400

Break-even Point

2,000

1,600

1,200

800

Fixed Cost Line

400

100 200 300 400 500 600 700 800 Number of Units (in thousands)

(b) (1) Break-even sales in units: $4Q = $2.40Q + $800,000 + $0 $1.60Q = $800,000 Q = 500,000 units (2) Break-even sales in dollars: 500,000 units × $4 per unit = $2,000,000

(c) (1) Margin of safety in dollars: $2,500,000 – $2,000,000 = $500,000 (2) Margin of safety ratio: $500,000 ÷ $2,500,000 = 20%



6-21

EXERCISE 6-30 (a) Income statement without changes: VOLMAR COMPANY

CVP Income Statement (Unchanged) For the Year Ended December 31, 2012

Total Per Unit

Sales (50,000 × $25) ..................................... Variable costs ................................................ Contribution margin ...................................... Fixed costs .................................................... Operating income ..........................................

$1,250,000 600,000

650,000 500,000 $ 150,000

$25.00 12.00 $13.00

(b) Income statement with changes: Proposed selling price per unit = $25.00 – ($2.40 × 0.50) = $23.80 Expected variable cost per unit = $12.00 – ($12.00 × 0.20) = $9.60 Expected level of sales = 50,000 × 110% = 55,000 New fixed costs = $500,000 + $50,000 = $550,000 VOLMAR COMPANY

CVP Income Statement (with changes) For the Year Ended December 31, 2012

Total Per Unit

Sales (55,000 × $23.80) ................................. Variable costs (55,000 × $9.60) ..................... Contribution margin ...................................... Fixed costs ($500,000 + $50,000) ................. Operating income ..........................................

$1,309,000 528,000 781,000 550,000 $231,000

$23.80 9.60 $14.20



6-22

*EXERCISE 6-31 (a) (1) Old-Fashioned: Operating leverage = $120,000 ÷ $100,000 = 1.2 Contribution margin ratio = $120,000 ÷ $400,000 = 30% (2) Mech-Apple: Operating leverage = $260,000 ÷ $100,000 = 2.6 Contribution margin ratio = $260,000 ÷ $400,000 = 65% Mech-Apple will be more sensitive to changes in sales volume,

because after reaching their break-even point, 65 cents from every sales dollar goes to profit. Old-Fashioned will only receive 30 cents from every sales dollar towards profit.

(b) (1) Old-Fashioned: 10% × 1.2 = 12% decrease, or $12,000 Mech-Apple: 10% × 2.6 = 26% decrease, or $26,000 (2) Old-Fashioned: 5% × 1.2 = 6% increase, or $6,000 Mech-Apple: 5% × 2.6 = 13% increase, or $13,000 (c) The investment banker should not make her decision solely on the

information provided. Other factors, such as the market situation, should be considered, because this will impact the profitability of the companies.

For example, Mech-Apple will benefit from its high degree of operating

leverage, but only if it is above break-even. With its current cost structure, it has a much higher break-even point than Old-Fashioned has, and carries a much higher risk in an unstable market. Profitability will not be as great for Old-Fashioned, with an operating leverage of only 1.2, but with a lower break-even point it will achieve profitability much faster.



6-23

EXERCISE 6-32 Weighted-average contribution margin per unit = (30% × $35) + (50% × $25) + (20% × $50) = $33 Break-even in units = $4,620,000 ÷ $33 = 140,000 units Lawn mowers: 140,000 × 30% = 42,000 units Weed-trimmers: 140,000 × 50% = 70,000 units Chain saws: 140,000 × 20% = 28,000 units 140,000 EXERCISE 6-33 (a) Weighted average contribution margin ratio: (60% × 20%) + (40% × 60%) = 36% Break-even = $18,000,000 ÷ 0.36 = $50,000,000 Oil changes: 60% × $50,000,000 = $30,000,000 Brake repairs: 40% × $50,000,000 = $20,000,000 (b) Desired operating income per outlet = $66,000 Required sales = (fixed costs + desired operating income) ÷ CM ratio = ($60,000 + $66,000) ÷ 36% = $350,000 of which 60% or $210,000 should be oil changes, and 40%, or $140,000 should be brake repairs. EXERCISE 6-34 (a) Weighted average contribution margin ratio: (0.80 × 10%) + (0.20 × 60%) = 20% Break-even sales = $12,000,000 ÷ 0.20 = $60,000,000



6-24

EXERCISE 6-34 (Continued) Distributed as follows— Pouches: 0.80 × $60,000,000 = $48,000,000 Non-standard: 0.20 × $60,000,000 = $12,000,000 (b) New weighted average contribution margin ratio: (0.20 × 10%) + (0.80 × 60%) = 50% Break-even sales = $12,000,000 ÷ 0.50 = $24,000,000 Distributed as follows— Pouches: 20% × $24,000,000 = $4,800,000 Non-standard: 80% × $24,000,000 = $19,200,000 EXERCISE 6-35

(a) Weighted average contribution margin per unit: (40% × $40) + (50% × $20) + (10% × $70) = $33

Break-even in units = $660,000 ÷ $33 = 20,000 units

(b) Shoes: 20,000 × 40% = 8,000 units Gloves: 20,000 × 50% = 10,000 units Range-Finder: 20,000 × 10% = 2,000 units

(c) Operating income = total contribution margin – fixed costs [(8,000 × $40) + (10,000 × $20) + (2,000 × $70)] – $660,000 = $0 EXERCISE 6-36 (a) Percentage of sales: TV Division $800,000 ÷ $1,000,000 = 80% DVD Division $200,000 ÷ $1,000,000 = 20% Contribution margin: TV Division $240,000 ÷ $800,000 = 30% DVD Division $40,000 ÷ $200,000 = 20%



6-25

EXERCISE 6-36 (Continued) (b) Weighted average contribution margin ratio: (0.80 × 30%) + (0.20 × 20%) = 28% (c) Break-even = $140,000 ÷ 0.28 = $500,000 (d) TV Division: 80% × $500,000 = $400,000 DVD Division: 20% × $500,000 = $100,000

*EXERCISE 6-37

(a) Operating Leverage:

Billings Co: $280,000 ÷ $100,000 = 2.8

Bozeman Co: $480,000 ÷ $100,000 = 4.8 Billings Co. has an operating leverage of 2.8, which means that for

every percentage increase in sales (above break-even) the company’s operating income will increase by 2.8 times the percent. It also means the company has a lower break-even point.

It would be the opposite for Bozeman. They have a much higher break-

even point, but past that, their operating income will increase by a percentage that is 4.8 times the percentage increase in sales.

(b)

Billings and Bozeman Companies CVP Income Statement

Billings Bozeman Sales revenue $660,000 $660,000 Variable costs 352,000 132,000

Contribution margin 308,000 528,000 Fixed costs 180,000 380,000

Operating income $128,000 $148,000



6-26

*EXERCISE 6-37 (Continued)

(c) Operating leverage is a measure of the sensitivity of operating income to changes in the level of sales. The degree of operating leverage is determined by the cost structure of an organization. Billings Co. has a lower measure, meaning it has more variable costs than fixed costs. This is preferable during a time of economic stability—they are able to reach break-even quickly, but the return on sales will be lower than a company with higher leverage. With a 10% increase in sales, they achieved a $28,000 increase in operating income. (10% × 2.8 O.L. = 28% increase in sales; or $100,000 × 1.28 = $128,000.)

The low variable costs and high fixed costs for Bozeman Co. results in

a higher operating leverage, and will lead to a much higher contribution margin from sales; however, their break-even point is much higher as well. Compared to Billings, a 10% increase in sales for Bozeman lead to a $48,000 increase in operating income—$20,000 more operating income on the same $60,000 increase in sales. This is a good cost structure to have if you are certain you will reach break even.

*EXERCISE 6-38

(a) Operating leverage: Manual System: $300,000 ÷ $100,000 = 3.0 Computerized System: $600,000 ÷ $100,000 = 6.0

(b) For any increase in sales, Computerized System would produce a higher operating income, because it has a higher operating leverage.

(c) To determine margin of safety, first calculate the sales at break-even: Manual System: $200,000 ÷ ($300,000 ÷ $1,500,000) = $1,000,000 Computerized System: $500,000 ÷ ($600,000 ÷ $1,500,000) = $1,250,000 Margin of Safety: Manual: $1,500,000 – $1,000,000 = $500,000 Computerized: $1,500,000 – $1,250,000 = $250,000 Manual System has two times the safety margin that Computerized

System has, so would be in a far better position to withstand a greater decline in sales before operating at a loss.



6-27

SOLUTIONS TO PROBLEMS-SET A

PROBLEM 6-39A

(a) Variable cost per unit =

($75,000 + $90,000 + $45,000 + $60,000) ÷ 15,000 = $18

Total fixed costs = $30,000 + $40,000 = $70,000

Contribution margin per unit = $38 – $18 = $20

Units at break even = $70,000 ÷ $20 = 3,500

(b) New Contribution margin per unit = $43 – $18 = $25

Target operating income = ($70,000 + $25,000) ÷ $25 = 3,800

(c) Operating income before taxes = $30,000 ÷ (1.00 – 0.40) = $50,000

Let X = selling price per unit

Sales = variable costs + fixed costs + desired income before tax

7,500X = ($18 × 7,500) + $70,000 + $50,000

7,500X = $255,000

X = $34 per unit

(d) Let X = selling price per unit

9,000X = ($18 × 9,000) + $70,000 + 0.30(9,000X)

9,000X = $232,000 + 2,700X

6,300X = $232,000

X = $36.825

Proof: (small rounding error)

Sales revenue (9,000 × $36.825) $331,428

Less: variable costs (9,000 × $18.00) 162,000

Contribution margin 169,428

Less: fixed costs 70,000

Operating income before tax ($331,428 × 0.30) $99,428



6-28

PROBLEM 6-40A

(a) Variable cost per haircut =

($2.00 + $0.60 + $0.40) = $3.00

Total fixed costs =

[$3,900 + (3 × $1,900) + $700 + $500 + $300 + $100] = $11,200

(b) Contribution margin per unit = $11 – $3 = $8

Units at break-even = $11,200 ÷ $8 = 1,400

Sales at break-even = $11 × 1,400 = $15,400

(c) CVP graph:

(d)

Total contribution margin – fixed costs = operating income

[($8 × 1,700) – $11,200] = $2,400



6-29

PROBLEM 6-41A

(a) Contribution ratio = Contribution margin ÷ Sales

($50 – $30) ÷ $50 = 40%

(b) Break-even in dollars: $30,000 ÷ 40% = $75,000

(c) Margin of safety = (2,800 × $50) – $75,000 = $65,000

$65,000 ÷ $50 = 1,300 margin of safety in units

(d) Current unit contribution margin $50 – $30 = $20

Total current contribution margin is $20 × 2,800 = $56,000

New contribution margin is [$56,000 + ($56,000 × 0.60)] = $89,600

Total sales required: $89,600 ÷ 40% = $224,000

Proof: Before After

Sales revenue $140,000 $224,000

Less: variable costs 84,000 134,400

Contribution margin $ 56,000 $ 89,600



6-30

PROBLEM 6-42A

(a) Number of units sold: $500,000 ÷ $50 = 10,000 units

Variable cost per unit:

Direct materials $90,000

Direct labour 60,000

Manufacturing overhead 20,000

Selling expenses 20,000

Administrative expenses 10,000

$200,000

Number of units 10,000

$20

Fixed costs: ($30,000 + $20,000 + $10,000) = $60,000 Contribution margin per unit: $50 – $20 = $30

(1)Monthly break-even in units: ($60,000 ÷ 12) ÷ $30 = 167 units (rounded)

(2)Monthly break-even in dollars: 167 × $50 = $8,350 (rounded) (b) Contribution margin ratio: $30 ÷ $50 = 60% Annual break-even: $60,000 ÷ 0.60 = $100,000 Margin of safety ratio: ($500,000 – $100,000) ÷ $500,000 = 80% Annual profit: $500,000 – $200,000 – $60,000 = $240,000 (c) 20% increase in selling price: $50 × 0.20 = $10 per unit Increase in contribution margin and profit: 10,000 × $10 = $100,000 Percent increase in profit: $100,000 ÷ $240,000 = 41.67% (rounded) (d) Increase in fixed costs: $60,000 × 0.20 = $12,000 Increase in CM required to cover increased fixed costs: $12,000 Increase in unit sales required: $12,000 ÷ $30 = 400 units Percent increase in unit sales: 400 ÷ 10,000 = 4%



6-31

PROBLEM 6-42A (Continuing) (e) Before tax operating income: $360,000 ÷ (100% – 40%) = $600,000 Target operating income after tax: ($60,000 + $600,000) ÷ 0.60 = $1,100,000 Proof:

Sales $1,100,000 100%

Variable costs 440,000 40%

Contribution margin 660,000 60%

Fixed costs 60,000

Operating income before tax 600,000

Tax at 40% 240,000

Operating income after tax $ 360,000



6-32

PROBLEM 6-43A

(a) Contribution margin = $1,600,000 – $1,040,000 = $560,000

CM ratio = $560,000 ÷ $1,600,000 = 35%

Break-even in dollars = $840,000 ÷ 0.35 = $2,400,000

(b) (1) New selling price: ($1,600,000 ÷ 64,000) × 1.40 = $35

Contribution margin = ($35 × 64,000) – $1,040,000 = $1,200,000

CM ratio = $1,200,000 ÷ $2,240,000 = 54%


(2) New variable costs = $1,040,000 + (0.05 × $1,600,000) = $1,120,000

New fixed costs = $840,000 – $200,000 + $30,000 = $670,000

CM = $1,600,000 – $1,120,000 = $480,000

CM ratio = $480,000 ÷ $1,600,000 = 30%


Proof:

Sales $2, 233,333

Less: variable costs (70% of sales) 1,563,333



Operating income before tax —

(c) Alternative 1 is the recommended course of action using break-even analysis because it has the lower break-even point.



6-33

PROBLEM 6-44A

(a) Sales (40,000 × $90) $3,600,000

Less: Variable costs (40,000 × $60) 2,400,000

Contribution margin

1,200,000

Less: Fixed costs 810,000


(b) Contribution margin ratio = $1,200,000 ÷ $3,600,000 = 33.33%

Break-even point in dollars = $810,000 ÷ 33.33% = $2,430,000 (rounded) Contribution margin per unit = $90 – $60 = $30 Break-even point in units = $810,000 ÷ $30 = 27,000 units

(c) Because fixed costs do not change, we can find the maximum by using contribution margin.

Current level: 40,000 × $30 = $1,200,000 Next levels: 55,000 × $25 = $1,375,000 70,000 × $20 = $1,400,000 85,000 × $15 = $1,275,000 100,000 × $10 = $1,000,000

Maximum contribution margin is $1,400,000; less fixed costs of $810,000 means maximum profit is $590,000. This can be achieved by selling 70,000 units at $80 each ($20 CM plus $60 variable costs).

(d) At a selling price of $80: Breakeven = $810,000 ÷ $20 = 40,500 units or $3,240,000



6-34

PROBLEM 6-45A

(a) (1) Contribution margin per unit = $40 – $22 = $18


(2) New selling price per unit = $38

New fixed costs = $270,000 + $34,000 = $304,000

New contribution margin per unit = $38 – $22 = $16

Break-even in units = $304,000 ÷ $16 = 19,000

(b) (1) Margin of safety = ($40 × 20,000) – ($40 × 15,000) = $200,000

Margin of safety ratio = $200,000 ÷ $800,000 = 25%

(2) Margin of safety = ($38 × 24,000) – ($38 × 19,000) = $190,000

Margin of safety ratio = $190,000 ÷ $912,000 = 20.83%

(c) VALUE SHOE STORE

CVP Income Statement For the Year Ended December 31, 2012

Current New

Sales $800,000 $912,000

Less: Variable costs 440,000 528,000

Contribution margin 360,000 384,000

Less: Fixed costs 270,000 304,000

Operating income before tax $90,000 $80,000

No, the changes should not be made because operating income will be lower than the operating income currently earned. In addition, the break-even point would be higher and the margin of safety percentage would decrease.



6-35

PROBLEM 6-46A

(a) (1) Contribution margin Current Year

Sales ($16 per unit) $1,600,00

Less: variable costs

Direct materials ($5.11 per unit) $511,000

Direct labour ($2.85 per unit) 285,000

Manufacturing overhead (70% × $360,000) 252,000

Selling expenses (40% × $240,000) 96,000

Administrative expenses (20% × $280,000) 56,000 1,200,000


Contribution margin Projected Year

Sales (100,000 × 110% × $16) $1,760,000


Direct materials(110,000 × $5.11) $562,100

Direct labour (110,000 × $2.85) 313,500

Manufacturing overhead (110,000 × $2.52) 277,200

Selling expenses (110,000 × $0.96) 105,600

Administrative expenses (110,000 × $0.56) 61,600 1,320,000


(2) Fixed costs—Current Year

Manufacturing overhead (30% × $360,000) $108,000


Administrative expenses (80% × $280,000) 224,000

$476,000

(b) Contribution margin per unit = $400,000 ÷ 100,000 = $4


Break-even in dollars = 119,000 × $16 = $1,904,000



6-36

PROBLEM 6-46A (Continued)

(c) Contribution margin ratio: $400,000 ÷ $1,600,000 = 25%

Target income = ($476,000 + $310,000) ÷ 0.25 = $3,144,000

(d) Safety of margin ratio = ($3,144,000 – $1,904,000) ÷ $3,144,000

Safety of margin ratio = 39.44%

(e) (1) Contribution margin With changes

Sales $1,600,000




Manufacturing overhead (30% × $360,000) 108,000


Administrative expenses 56,000 1,072,000


(2) Contribution margin ratio = $528,000 ÷ $1,600,000 = 33%

(3) Fixed costs—with changes

Manufacturing overhead $252,000



$500,000

Break-even in sales = $500,000 ÷ 0.33 = $1,515,151



6-37

PROBLEM 6-46A (Continued) By incorporating the changes, the break-even sales declined—which means the company’s overall risk is decreased. It will not take them as long to reach break-even as before, so they will show profits sooner. However, the changes actually had opposing effects. Reducing variable costs increases the contribution margin ratio, but also leads to a higher break-even point because of higher fixed costs (purchase of equipment). On the other hand, moving to commissioned sales increases variable costs and lowers fixed costs resulting in a lower contribution margin ratio and a lower break-even point.



6-38

PROBLEM 6-47A

(a) (1) Sales $1,300,000 Less: Contribution margin $117,000 Direct material 400,000 Direct labour 500,000 Variable MOH 100,000 1,117,000 Variable selling and admin costs $183,000

(2) Sales $1,300,000 Less: Gross profit $200,000 Direct material 400,000 Direct labour 500,000 Variable MOH 100,000 1,200,000 Fixed manufacturing overhead $100,000

(3) Contribution margin ratio = $117,000 ÷ $1,300,000 = 9.0%

CM at breakeven = $1,350,000 × 0.09 = $121,500

Less: fixed manufacturing overhead 100,000 Fixed selling and admin expense $ 21,500

(b) Incremental sales = $1,300,000 × 15% = $195,000 Incremental contribution margin = $195,000 × 9% = $17,550 rounded. The maximum increased advertising expenditure would be equal to the

incremental contribution margin earned on the increased sales, which is $17,550. The company is initially operating below break even, so the contribution margin will all go to both profits and additional fixed costs in this situation. The other fixed costs are irrelevant to this decision, because they would be incurred whether or not the advertising expenditure is increased.



6-39

PROBLEM 6-48A

(a) Contribution margin per unit = $750 – $450 = $300

Break-even = $180,000 ÷ $300 = 600 units.

Before tax target operating income = $360,000 ÷ (1 – 0.25) = $480,000

Target operating income = ($180,000 + $480,000) ÷ 300 = 2,200

units.

(b) (1) Reduce selling price by $60; sell 3,400 units

Sales (400 × $750) + (3,000 × $690) $2,370,000

Variable costs (3,400 × $450) 1,530,000




Tax at 25% 165,000

Operating income after tax $495,000

(2) Reduce variable costs by $20; selling price by $40;

sell 2,800 more units

Sales (400 × $750) + (2,800 × $710) $2,288,000

Variable costs:

(400 × $450) + (2,800 × $430) 1,384,000




Tax at 25% 181,000




6-40


(3) Reduce fixed costs by $20,000; lower selling price by 5% ($750 × 5% = $37.50); sell 2,900 units

Sales (400 × $750) + (2,500 × $712.50) $2,081,250

Variable costs (2,900 × $450) 1,305,000




Tax at 25% 154,063


To achieve its desired operating income, the company should select the second alternative where the sales price is reduced by $40, and 2,500 units are sold during the remainder of the year. This alternative results in the highest operating income and exceeds the company’s desired operating income after taxes.



6-41

PROBLEM 6-49A

(a) Reformat the income statement to CVP format. All amount are in $000s.

Sales $78,000

Variable costs ($36,660 + $14,040) 50,700


Less: Fixed costs ($7,940 + $10,260) 18,200


Contribution margin ratio = $27,300 ÷ $78,000 = 35% Break-even point = $18,200 ÷ 0.35 = $52,000 (b) If a hired workforce replaces sales agents, commissions will be reduced to 10% of sales, or $7,800; but fixed costs will increase by $6,240. All amount are in $000s.

Sales $78,000

Variable costs ($36,660 + $7,800) 44,460


Less: Fixed costs ($18,200 + $6,240) 24,440


Contribution margin ratio = $33,540 ÷ $78,000 = 43% Break-even point = $24,440 ÷ 0.43 = $56,837 (rounded) (c) Operating leverage = contribution margin ÷ operating income Current situation: from part (a) $27,300,000 ÷ $9,100,000 = 3.00 Proposed situation: from part (b) $33,540,000 ÷ $9,100,000 = 3.69 (rounded)



6-42


The calculations indicate that at a sales level of $78 million, a percentage change in sales and contribution margin will result in 3.00 times that percentage change in operating income if Olin continues to use sales agents. If they choose to employ their own, the change in operating income will be 3.69 times the percentage change in sales.

The higher contribution margin per dollar of sales and higher fixed costs from Olin employing their own agents gives them more operating leverage. This will result in greater benefits (increases in operating income) if revenues increase, but greater risks (decreases in operating income) if revenues decline. It will also increase their break-even point, which could be risky in an unstable market.

(d) The sales level at which operating incomes will be identical is called the point of indifference. This would be when the cost of the network of agents (18% of sales) is exactly equal to the cost of paying employees 10% commission along with additional fixed costs of $6.24 million. None of the other costs are relevant, because they will not change between alternatives.

Let the sales volume = S

18% × S = (8% × S) + 7,800,000

0.18S = 0.08S + $7,800,000 0.10S = $7,800,000

S = $78,000,000

This confirms what is shown in parts (a) and (b) of this question—the operating income under both scenarios is $9,100,000 and the sales are $78 million.



6-43

PROBLEM 6-50A

(a) Sales (50,000 × $180) $9,000,000

Variable costs (50,000 × $80) 4,000,000

Contribution margin 5,000,000

Less: Fixed costs 4,000,000

Operating income before tax $1,000,000

(b) Break-even = $4,000,000 ÷ ($180 – $80) = 40,000 units (c) Incremental contribution margin = 5,000 × $100 = $500,000 Incremental cost = $400,000 New operating income = $1,000,000 + ($500,000 – $400,000) = $1,100,000



6-44

*PROBLEM 6-51A

Contribution margin ratio: Old Company: $220,000 ÷ $400,000 = 55% New Company: $320,000 ÷ $400,000 = 80% (a) Break-even point in dollars: Old Company: $170,000 ÷ 0.55 = $309,090 New Company: $270,000 ÷ 0.80 = $337,500 Margin of safety ratio: Old Company: ($400,000 – $309,090) ÷ $400,000 = 22.73% New Company: ($400,000 – $337,500) ÷ $400,000 = 15.63% (b) Degree of operating leverage: Old Company: $220,000 ÷ $50,000 = 4.4 New Company: $320,000 ÷ $50,000 = 6.4

Operating leverage measures the impact any increase or decrease in sales will have on a company’s operating income. In this situation, any percentage increase in sales for Old Company will result in an increase in operating income equal to 4.4 times that percentage. For New Company, it would be equal to 6.4 times that percentage. In the current situation, New Company stands to gain much more from sales increases than Old Company.

The opposite effect will occur with any declines in sales. In this case, Old Company is in a better position because its income will decrease by a smaller amount in relation to any decreases in sales.



6-45


(c) New income statements with a 20% increase in sales:

Old New

Company Company

Sales $480,000 $480,000

Variable costs 216,000 96,000




(d) New income statements with a 20% decrease in sales:

Old New

Company Company

Sales $320,000 $320,000




Operating income (loss) $6,000 $(14,000)

(e) New Company, with its high ratio of fixed costs to variable costs is highly leveraged, and stands to add 6.4 times any percentage sales increases to its operating income, compared to Old Company, which has less leverage. But the same cost structure that gives New Company the greater benefits from increased sales has also given it a higher break-even point. Another risk is that any decreases in sales will have the same, but opposite impact—causing a faster decline in profits.

Simply stated, it will take New Company longer to reach break-even, but after that the return on sales will be much greater. Old Company will start to earn a profit sooner (lower break-even point), but the impact on operating income from any increases in sales will be less. Alternatively, any benefit becomes a risk if the company is losing sales.



6-46

PROBLEM 6-52A

(a) Weighted average contribution margin ratio: (10% × 60%) + (60% × 30%) + (10% × 50%) + (20% × 80%) = 45%

Target operating income = ($1,200,000 + $150,000) ÷ 45% = $3,000,000 Appetizers: 10% × $3,000,000 = $300,000 Entrees: 60% × $3,000,000 = $1,800,000 Desserts: 10% × $3,000,000 = $300,000 Beverages: 20% × $3,000,000 = $600,000

(b) New weighted average contribution margin ratio: (20% × 60%) + (30% × 10%) + (10% × 50%) + (40% × 80%) = 52% New fixed costs = $1,200,000 × 150% = $1,800,000 Target income = ($1,800,000 + $150,000) ÷ 52% = $3,750,000 Appetizers: 20% × $3,750,000 = $750,000 Entrees: 30% × $3,750,000 = $1,125,000 Desserts: 10% × $3,750,000 = $375,000 Beverages: 40% × $3,750,000 = $1,500,000

(c) Revised weighted average contribution margin ratio: (10% × 60%) + (60% × 10%) + (10% × 50%) + (20% × 80%) = 33% Target income = ($1,800,000 + $150,000) ÷ 33% = $5,909,090 Appetizers: 10% × $5,909,090 = $590,909 Entrees: 60% × $5,909,090 = $3,545,454 Desserts: 10% × $5,909,090 = $590,909 Beverages: 20% × $5,909,090 = $1,181,818

By changing the mix and the contributions from some of the products, Terry has increased her break-even point, and will have to accomplish $750,000 more in sales to make the same income. If her predictions do not work out, and the mix stays the same, she will need to almost double her sales to make the same income. She will only benefit if her new scheme works so well that sales increase more than $750,000. At which point, she would be earning 52% contribution margin—the greatest amount of all three scenarios.



6-47

SOLUTIONS TO PROBLEMS-SET B

PROBLEM 6-53B

(a) Contribution margin per unit = $600 – $300 = $300

Units at break even = $150,000 ÷ $300 = 500 units

Operating income before taxes = $360,000 ÷ (1.00 – 0.25) = $480,000

Target operating income = ($150,000 + $480,000) ÷ $300 = 2,100 units

(b) (1) Reduce selling price by $60; additional 2,700 units sold

Sales (400 × $600) + (2,700 × $540) $1,698,000

Variable costs (3,100 × $300) 930,000




Tax at 25% 154,500


(2) New variable cost is $280; reduce selling price by $40; additional

2,500 units sold

Sales (400 × $600) + (2,500 × $560) $1,640,000

Variable costs: (400 × $300) + (2,500 × 280) 820,000




Tax at 25% 167,500




6-48

PROBLEM 6-53B (Continued)

(3) Reduce fixed costs by $20,000, lower selling price by 5%

($600 × 5% = $30), sell 2,200 more units

Sales (400 × $600) + (2,200 × $570) $1,494,000

Variable costs (2,600 × $300) 780,000




Tax at 25% 146,000


To achieve its desired operating income, the company should select the second alternative where the sales price is reduced by $40, and 2,500 units are sold during the remainder of the year. This alternative results in the highest operating income and exceeds the company’s desired operating income after taxes.



6-49

PROBLEM 6-54B

(a) Variable costs (per haircut) Fixed costs (per month) Barbers’ commission $5.50

Barber supplies .30 Utilities .20 Total variable cost per haircut $6.00

Barbers’ salaries $5,000 Manager’s extra salary 500 Advertising 200 Rent 900 Utilities 175 Magazines 25 Total fixed $6,800

(b) $10.00X = $6.00X + $6,800 $ 4.00X = $6,800 X = 1,700 haircuts

1,700 haircuts X $10 = $17,000

(c)

18 Break-even Point

Sales Line

DO

LL

AR

S (

00

0)

15

Total Cost Line

12

9

Fixed Cost Line 6

3

300 600 900 1,200 1,500 1,800 Number of Haircuts (d) Net income = $19,000 – [($6.00 X 1,900) + $6,800] = $800



6-50

PROBLEM 6-55B

(a) Break-even sales = Sales – Margin of Safety

Break-even sales = $600,000 – $300,000 = $300,000

(b) If contribution margin ratio is 40%, then variable cost ratio is 60%

Variable costs = 60% × $600,000 = $360,000

(c) At break-even, contribution margin = fixed costs

Contribution margin at break-even = $300,000 × 40% = $120,000

Therefore, Fixed costs = $120,000

(d) Sales $500,000 100%

Variable costs 300,000 60%






6-51

PROBLEM 6-56B

(a) Number of units sold: $500,000 ÷ $40 = 12,500 units

Variable cost per unit:



Manufacturing overhead 30,000



$300,000

Number of units 12,500

$24

Fixed costs: ($40,000 + $30,000 + $20,000) = $90,000 Contribution margin per unit: $40 – $24 = $16 Monthly break-even in units: ($90,000 ÷ 12) ÷ $16 = 469 units (rounded) Monthly break-even in dollars: 469 × $40 = $18,760 (rounded) (b) Contribution margin ratio: $16 ÷ $40 = 40% Annual break-even: $90,000 ÷ 0.40 = $225,000 Margin of safety ratio: ($500,000 – $225,000) ÷ $500,000 = 55% Annual profit: $500,000 – $300,000 – $90,000 = $110,000 (c) 30% increase in selling price: $40 × 0.30 = $12 per unit Increase in contribution margin and profit: 12,500 × $12 = $150,000 Percent increase in profit: $150,000 ÷ $110,000 = 136% (rounded) (d) Increase in fixed costs: $90,000 × 0.30 = $27,000 Increase in CM required to cover increased fixed costs: $27,000 Increase in unit sales required: $27,000 ÷ $16 = 1,687 units (rounded) Percent increase in unit sales: 1,687 ÷ 12,500 = 13.5%



6-52

PROBLEM 6-56A (Continuing) (e) Before tax income: $360,000 ÷ (100% – 40%) = $600,000 Target sales: ($90,000 + $600,000) ÷ 0.40 = $1,725,000 Proof:

Sales $1,725,000 100%

Variable costs 1,035,000 60%


Fixed costs 90,000


Tax at 40% 240,000

Operating income after tax $ 360,000



6-53

PROBLEM 6-57B

(a) Prepare a CVP income statement:

DELGADO MANUFACTURING CVP Income Statement For the Year Ending December 31, 2012

Net sales (60,000 units at $25 ea.) $1,500,000 100%


Cost of goods sold $930,000

Selling & admin ($65,000 + $55,000) 120,000 1,050,000 70%


Less: fixed costs

Cost of goods sold $420,000

Selling & admin ($355,000 + $65,000) 420,000 840,000

Operating income before tax $(390,000)

Contribution margin ratio = ($450,000 ÷ $1,500,000) = 30%

Sales at break even = $840,000 ÷ 0.30 = $2,800,000

(b) (1) Increase selling price by 40% or $10

Sales increase by $10 × 60,000 = $600,000 to $2,100,000

CM increases by $600,000 to $1,050,000

New CM ratio = $1,050,000 ÷ $2,100,000 = 50%


(2) Variable costs increase by 4% × $1,500,000 = $60,000

Contribution margin decreases by $60,000 to $390,000

Fixed costs decrease by $170,000 to $670,000

New CM ratio = $390,000 ÷ $1,500,000 = 26%




6-54


(3) Variable costs decrease by $255,000 [$930,000 – ($1,350,000 ÷ 2)]

Contribution margin increases by $255,000 to $705,000

Fixed costs increase by $255,000 to $1,095,000

New CM ratio = $705,000 ÷ $1,500,000 = 47%

Sales at break even = $1,095,000 ÷ 0.47 = $2,329,787

It appears obvious that they should go with Alternative (1), which reduces the break–even point significantly lower than Alternative (2) or (3). However, Alternative (1) is still very risky, and may not be the right choice either. For Alternative (1) the break-even point is still higher than the sales achieved in 2012, so Delgado would be in a position where they would have to increase their total sales by $180,000 just to break-even at the same time as they are raising their prices by 40%. Unless they have a very good sense of how the market will react to a price increase, they would be wise to start looking for even more alternatives.



6-55

PROBLEM 6-58B

(a) Variable cost per haircut =

($6.00 + $1.50 + $0.50 + $0.25) = $8.25

Total fixed costs =

[($1,500 + $500) + (4 × $1,500) + $500 + $1,000 + $300 + $50] = $9,850

(1) CM per haircut = $15.00 – $8.25 = $6.75

Sales in units at break-even = $9,850 ÷ $6.75 = 1,460 (rounded)

(2) Selling price per haircut = $15.00

Sales in dollars at break-even = 1,460 × $15.00 = $21,900

(3) Monthly capacity = 5 barbers × 20 haircuts per day × 24 days

Monthly capacity = 2,400 haircuts

Ratio of BE to capacity = 1,460 ÷ 2,400 = 60.83%

(b) Sales $22,500 (1,500 × $15)

Variable costs 12,375 (1,500 × $8.25)



Operating income $275

(c) Target operating income = ($9,850 + $4,000) ÷ $6.75 = 2,052 units

(d) Profit in March = (1,600 × $6.75) – $9,850 = $950

Profit in April has to be $4,000 + ($4,000 – $950) = $7,050

Target operating income = ($9,850 + $7,050) ÷ $6.75 = 2,504 units

It is not possible, since capacity is 2,400 haircuts per month, and John

would have to give 2,504 haircuts in April to bring his target operating

income to $4,000 for each month (March and April combined).



6-56

PROBLEM 6-59B

(a) Current break-even point: where Q = the number of pairs of shoes

$30Q = $15Q + $210,000

$15Q = $210,000

Q = 14,000 pairs of shoes

After proposed changes—

New selling price per pair = $28

New fixed costs = $210,000 + $24,000 = $234,000

New break-even point: where Q = the number of pairs of shoes

$28Q = $15Q + $234,000

$13Q = $234,000

Q = 18,000 pairs of shoes

(b) Current situation—

Margin of safety in units = 16,000 – 14,000 = 2,000

Margin of safety ratio = 2,000 ÷ 16,000 = 12.5%

After proposed changes—

Margin of safety in units = 20,000 – 18,000 = 2,000

Margin of safety ratio = 2,000 ÷ 20,000 = 10%

(c) THRIFTY SHOE STORE CVP Income Statement

Current After

Sales $480,000 $560,000

Less: Variable costs 240,000 300,000






6-57


The proposed changes will raise the break-even point by 4,000 units, reduce income by $4,000 and narrow the margin of safety by 2.5%. The recommendation is not to accept the proposed changes.



6-58

PROBLEM 6-60B

(a) Variable costs Total Per unit

Direct materials $32,000 $ 4.00

Direct labour 40,000 5.00

Variable overhead 20,000 2.50

Selling and Admin 24,000 3.00

$116,000 $14.50

Fixed costs

Fixed overhead $30,000

Selling and Admin 33,000

$63,000

Current break-even point: where Q = the number of units

$35Q = $14.50Q + $63,000

$20.50Q = $63,000

Q = 3,073 units

(b) Target operating income in units: where Q = the number of units

$37.50Q = $14.50Q + $63,000 + $22,000

$23Q = $85,000

Q = 3,696 units

(c) Before tax operating income = $28,000 + (1.00 – 0.30) = $40,000

Target selling price: where P = unit selling price

7,500P = (7,500 × $14.50) + $63,000 + $40,000

7,500P = $211,750

P = $28.23



6-59


(d) Let the unit price be P

Before tax profit = 30% × (9,000 x P)

9,000P = (9,000 × $14.50) + $63,000 + [30% × (9,000 × P)]

9,000P = $130,500 + $63,000 + 2,700P

P = $30.71



6-60

PROBLEM 6-61B

(a) Current Projected

Year Year

Sales (100,000 units) $2,000,000 2,400,0007

Less: Variable costs

Direct materials 600,000 720,0007

Direct labour 340,000 408,0007

Manufacturing overhead 96,0001 115,2007

Selling expenses 120,0002 144,0007

Administrative expenses 150,0003 180,0007

Total variable costs 1,306,000 1,567,200

(1) Contribution margin 694,000 832,800

Less: Fixed costs

Manufacturing overhead4 384,000 384,000

Selling expenses5 280,000 280,000

Administrative expenses6 350,000 350,000

(2) Total fixed costs 1,014,000 1,014,000

Operating income (loss) $(320,000) $(181,200)

1 $480,000 × 20% 5 $400,000 × 70% 2 $400,000 × 30% 6 $500,000 × 70% 3 $500,000 × 30% 7 Current year × 1.2 4 $480,000 × 80%

(a) Contribution margin ratio = $694,000 ÷ $2,000,000 = 34.7%

(b) Break-even in sales = $1,014,000 ÷ 0.347 = $2,922,190 (rounded) Per unit contribution margin = $694,000 ÷ 100,000 units = $6.94

Break-even in units = $1,014,000 ÷ $6.94 = 146,110 units (rounded)



6-61

(c)


Sales to meet target operating income:

= ($1,014,000 + $374,000) ÷ 0.347 = $4,000,000

(d) Margin of safety = $4,000,000 – $2,922,190 = $1,077,810

Margin of safety ratio = $1,077,810 ÷ $4,000,000 = 26.94%

(e) New costs: Variable Fixed

Direct materials (no change) $600,000

Direct labour ($340,000 – $140,000) 200,000

MOH $480,000—10%; 90% 48,000 $432,000

Selling expenses $400,000—80%; 20% 320,000 80,000

Admin expenses (no change) 150,000 350,000

Total $1,318,000 $862,000

(1) Contribution margin = $2,000,000 – $1,318,000 = $682,000

(2) Contribution margin ratio = $682,000 ÷ $2,000,000 = 34.1%

(3) Break-even in sales dollars = $862,000 ÷ 0.341 = $2,527,859

The break-even point in dollars declined from $2,922,190 to $2,527,859. This means that overall the company’s risk has declined because it doesn’t have to generate as much in sales. The two changes actually had opposing effects on the break-even point. By changing to a more commission based approach for compensating its sales staff the company reduced its fixed costs, and therefore reduced its break-even point. In contrast, the purchase of the new equipment increased the company’s fixed costs (by increasing its equipment depreciation) and reduced its variable direct labour cost, both of which would increase the break-even point.



6-62

PROBLEM 6-62B

(a) Redo the pro forma income statement in CVP format

Sales $1,000,000 100%

Variable costs ($600,000 + $150,000) 750,000 75%



Operating income before taxes 240,000

Income tax expense (25%) 60,000


Break-even in sales, where S = sales in dollars

1.00S = 0.75S + $10,000 + $0

0.25S = $10,000

S = $40,000

(b) Switch from outside sales agents to their own salespeople:

Variable costs would decrease by: $1,000,000 × 10% = $100,000

Fixed costs would increase by: $60,000 + (3 × $30,000) = $150,000

Sales

$1,000,000 100%

Variable costs ($750,000 – $100,000) 650,000 65%


Less: Fixed costs ($10,000 + $150,000) 160,000

Operating income before taxes 190,000

Income tax expense (25%) 47,500



1.00S = 0.65S + $160,000 + $0

0.35S = $160,000



6-63

S = $457,143


(c) Increase outside sales commissions to 20%

Variable costs would increase by: $1,000,000 × 5% = $50,000

CM will decrease by $50,000 to $200,000

New contribution margin will be $200,000 ÷ $1,000,000 = 20%


1.00S = 0.80S + $10,000 + $240,000

0.20S = $250,000

S = $1,250,000

(d) Identical operating income would arise when sales are equal. Let sales be S.

Sales for option (1)—employ own salespeople

S = $600,000 + (5% × S) + $160,000 + $240,000

Sales for option (2)—go with outside agents and 20%

S = $600,000 + (20% × S) + $10,000 + $240,000

Or to simplify

0.05S + $160,000 = 0.20S + $10,000

$150,000 = 0.15S

$1,000,000 = S

Proof: (d)(1) (d)(2)

Sales $1,000,000 $1,000,000



Less: fixed costs 160,000 10,000




6-64

PROBLEM 6-63B

(a) Sales (90,000 units) $3,150,000 $35.00 100%

Variable costs 1,350,000 $15.00 43%

Contribution margin 1,800,000 $20.00 57%


Operating income $1,000,000

Break-even = $800,000 ÷ $20.00 = 40,000 units

(b) 10% increase in sales = 99,000 units

New CM = 99,000 × $20 = $1,980,000

New income = $1,980,000 – $800,000 = $1,180,000

(c) New unit purchase price = $35 × 1.3 = $45.50

New unit CM = $45.50 – $15.00 = $30.50

New CM ratio: $30.50 ÷ $45.50 = 67%

Sales for target operating income =

($800, 000 + $1,000,000) ÷ 0.67 = $2,686,5671 1rounded

Proof:

Sales (59,045 × $45.50) $2,686,547

Less: variable costs (59,045 × $15.00) 885,675



Operating income before tax $1,000,000



6-65

*PROBLEM 6-64B

Contribution margin ratio: Retro Company— $200,000 ÷ $500,000 = 40% Modern Company— $400,000 ÷ $500,000 = 80% (a) Break-even point in dollars: Retro Company— $140,000 ÷ 0.40 = $350,000 Modern Company— $340,000 ÷ 0.80 = $425,000 Margin of safety ratio: Retro Company— ($500,000 – $350,000) ÷ $500,000 = 30% Modern Company— ($500,000 – $425,000) ÷ $500,000 = 15% (b) Degree of operating leverage: Retro Company— $200,000 ÷ $60,000 = 3.33 Modern Company— $400,000 ÷ $60,000 = 6.67

Operating leverage measures the impact any increase or decrease in sales will have on a company’s operating income. In this situation, any percentage increase in sales for Retro Company will result in 3.33 times that percentage increase in operating income. In the current situation, Modern Company, with an operating leverage of 6.67, stands to increase its operating income by twice the factor of Retro.

The opposite effect will occur with any declines in sales. In this case, Retro Company is in a better position because its income will decrease by a smaller amount in relation to any decreases in sales.



6-66


(c) New income statements with a 25% increase in sales:

Retro Modern

Sales $625,000 $625,000





(d) New income statements with a 25% decrease in sales:

Retro Modern

Sales $375,000 $375,000




Operating income (loss) $10,000 $(40,000)

(e) Modern Company, with its high ratio of fixed costs to variable costs is highly leveraged, and stands to add 6.67 times any percentage sales increases to its operating income, compared to Retro Company, which has less leverage. But the same cost structure that gives Modern Company the greater benefits from increased sales has also given it a higher break-even point. Another risk is that any decreases in sales will have the same, but opposite impact—causing a faster decline in profits.

Simply stated, it will take Modern Company longer to reach break-even, but after that the return on sales will be much greater. Retro Company will start to earn a profit sooner (lower break-even point), but the impact on operating income from any increases in sales will be less. Alternatively, any benefit becomes a risk if the company is losing sales.



6-67

*PROBLEM 6-65B

(a) Sales (10,000 × $480) $4,800,000 $480.00 100.0%

Variable costs (10,000 × $180) 1,800,000 $180.00 37.5%

Contribution margin 3,000,000 $300.00 62.5%



(b) Contribution margin ratio = $300 ÷ $480 = 62.5%

Break-even in sales dollars = $2,200,000 ÷ 0.625 = $3,520,000

Margin of safety ratio = ($4,800,000 – $3,520,000) ÷ $4,800,000 = 26.67%

Operating leverage = $3,000,000 ÷ $800,000 = 3.75

(c) Sales (10,000 × $480) $4,800,000 $480.00 100.0%

Variable costs (10,000 × $80) 800,000 $80.00 16.7%

Contribution margin 4,000,000 $400.00 83.3%



(d) Contribution margin ratio = $400 ÷ $480 = 83.3%

Break-even in sales dollars = $3,200,000 ÷ 0.833 = $3,841,5371

Margin of safety ratio = ($4,800,000 – $3,841,537) ÷ $4,800,000 = 19.97%

Operating leverage = $4,000,000 ÷ $800,000 = 5.00

1rounded (e) By automating the system, ComfortCraft increases their contribution

margin ratio, so that the return on every dollar of sales will be greater than before the automation ($0.833 compared to $0.625). This is also reflected in an increased degree of operating leverage. However, they also raise their break-even point—so, it will take them longer to start earning profits, but after that, their profits will raise significantly faster than under the manual system. A cost structure that has a higher level of fixed costs could be adopted when a company is operating within a stable marketplace, and is not adverse to a higher level of risk.



6-68

PROBLEM 6-66B

(a) Weighted average contribution margin ratio: (10% × 50%) + (55% × 30%) + (10% × 60%) + (25% × 75%) = 46.25% Target sales = ($400,000 + $155,000) ÷ 46.25% = $1,200,000

Appetizers: 10% × $1,200,000 = $120,000 Entrees: 55% × $1,200,000 = $660,000 Desserts: 10% × $1,200,000 = $120,000 Beverages: 25% × $1,200,000 = $300,000

(b) New weighted average contribution margin ratio: (15% × 50%) + (30% × 15%) + (15% × 60%) + (40% × 75%) = 51% New fixed costs = $400,000 × 150% = $600,000 Target sales = ($600,000 + $155,000) ÷ 51% = $1,480,392 Appetizers: 15% × $1,480,392 = $222,059 Entrees: 30% × $1,480,392 = $444,117 Desserts: 15% × $1,480,392 = $222,059 Beverages: 40% × $1,480,392 = $592,157

(c) Revised weighted average contribution margin ratio: (10% × 50%) + (55% × 15%) + (10% × 60%) + (25% × 75%) = 38% Target sales = ($600,000 + $155,000) ÷ 38% = $1,986,842 Appetizers: 10% × $1,986,842 = $198,684 Entrees: 55% × $1,986,842 = $1,092,763 Desserts: 10% × $1,986,842 = $198,684 Beverages: 25% × $1,986,842 = $496,711

By changing the mix and the contributions from some of the products, Debbie has increased her break-even point, and will have to accomplish almost $300,000 more in sales to make the same income. If her predictions are incorrect, and the mix stays the same, she will need to increase sales almost $800,000 to make the same income. She would only benefit if her new scheme worked so well that sales increased more than $300,000. At that point, she would be earning 51% contribution margin—the greatest amount of all three scenarios.



6-69

SOLUTIONS TO CASES

CASE 6-67

(a) (1) Capital–Intensive

Variable cost per unit = $4.00 + $5.00 + $2.00 + $2.00 = $13.00

Contribution margin = $30.00 – $13.00 = $17.00

Fixed costs = $2,508,000 + $502,000 = $3,010,000

Break-even in units = $3,010,000 ÷ $17.00 = 177,059 units (rounded)

(2) Labour–Intensive

Variable cost per unit = $6.00 + $9.00 + $5.00 + $2.00 = $22.00

Contribution margin = $30.00 – $22.00 = $8.00

Fixed costs = $538,000 + $502,000 = $1,040,000

Break-even in units = $1,040,000 ÷ $8.00 = 130,000 units

(b) Clay Company would be indifferent between the two manufacturing

methods at the volume (Q) where total costs are equal.

$13Q + $3,010,000 = $22Q + $1,040,000 $9Q = $1,970,000 Q = 218,889 units

(c) Clay should employ the capital-intensive manufacturing method if they are working in fairly stable market conditions and are certain they will pass 177,059 units in sales. The labour-intensive method is more suitable in a more risky market because the break-even point is lower, and it takes less time to start earning a profit. If Clay is certain they will exceed 177,059 units in sales, then the capital-intensive method would be preferred, as the return on each $1.00 sold will be greater than with the capital-intensive method.



6-70

CASE 6-68

(a) Unit contribution margin = $28 – ($18 + $6) = $4.00

Income last year:

Sales (260,000 units) $7,280,000 $ 28.00 100.0%

Variable costs 6,240,000 $ 24.00 85.7%

Contribution margin 1,040,000 $ 4.00 14.3%



Income required this year:

Fixed costs ($700,000 – $60,000) $ 640,000

Plus: Target operating income 340,000

Contribution margin needed 980,000

Less: CM earned (60,000 × $4) 240,000

Total CM left to be earned $ 740,000

Contribution required on remaining sales:

Let CM = contribution margin per unit

Let Q = 240,000 – 60,000 = 180,000 units

180,000 × CM = $740,000

CM = $4.11 per unit



6-71

CASE 6-68 (Continued)

(b) Current New

Sales (260,000 × $28) $7,280,000 $7,280,000

Variable costs

(260,000 × $24) 6,240,000

(260,000 × $11.00*) 2,860,000

Contribution margin 1,040,000 4,420,000

Total fixed costs 700,000 3,200,000

Operating income $340,000 $1,220,000

* $6.00 + $5.00

Current New

Operating leverage (CM ÷ Operating income) 3.06 3.62

With a 10% increase in sales, operating

income will increase by…………… 30.6% 36.2%

Increase in operating income $104,040 $ 441,640

Previous operating income 340,000 1,220,000

New operating income $444,040 $1,661,640 With a 20% decrease in sales, operating

income will decrease by ………….. 61.2% 72.4%

Decrease in operating income $(208,080) $ (883,280)

Previous operating income 340,000 1,220,000

New operating income $131,920 $336,720



6-72


MEMO

To: President From: Cost analyst

Subject: Proposed Cost Structure

As you can see from the above analysis, a move to the new cost structure has potential benefits, but it is also considerably more risky. Should sales volume increase by 10% over this year, the new cost structure will generate an increase in operating income of 36.2% of the present operating income, compared to approximately 30.6% of the present operating income under the current cost structure. However, should sales volume decrease by 20% from this year's, under the old structure the decline is 61.2%, while under the proposed structure the decline is 72.4%. In general, a move to a structure with high fixed costs and low variable costs is much more sensitive to upswings and downswings in sales volume. If there is a high probability of sales volume increases in the future, the changes are probably a good idea; if there is some uncertainty about future sales volumes, the changes may not be such a good idea.



6-73

CASE 6-69

(a) Selling price per unit ($1,200,000 ÷ 200,000) = $6.00 Costs: Variable Fixed Total Cost of goods sold (75%; 25%) $600,000 $200,000 $800,000 Selling (50%; 50%) 140,000 140,000 280,000 Administrative (25%; 75%) 40,000 120,000 160,000

Total $780,000 $460,000 $1,240,000

Variable costs per unit are: Cost of goods sold ($600,000 ÷ 200,000) $3.00 Selling ($140,000 ÷ 200,000) 0.70 Administrative ($40,000 ÷ 200,000) 0.20

Total $3.90

Contribution margin per unit ($6.00 – $3.90) = $2.10 Contribution margin ratio ($2.10 ÷ $6.00) = 35%

Break-even point in sales dollars = $460,000 ÷ 35% = $1,314,288 Break-even point in units = $460,000 ÷ $2.10 = 219,048

(b) Variable unit cost = $3.90 + $0.25 = $4.15 Sales volume = 260,000 units (200,000 × 130%)

Sales: (260,000 × $6.25) $1,625,000 Less: variable costs (260,000 × $4.15) 1,079,000

Contribution margin 546,000 Less: fixed costs 460,000

Operating income before tax $86,000

Contribution margin ratio = $546,000 ÷ $1,625,000 = 33.6% Break-even point in sales = $460,000 ÷ 0.336 = $1,369,048

Contribution margin per unit = $6.25 – $4.15 = $2.10 Break-even point in units = $460,000 ÷ $2.10 = 219,048



6-74

CASE 6-69 (Continued) This plan would have no affect on the break-even point in units, but increases break-even point in sales dollars because of the higher selling price.

(c) New variable cost per unit: $3.90 + $0.09 = $3.99 New selling price per unit: $6.00 – $0.30 = $5.70 New fixed costs: $460,000 + $35,000 = $495,000 New sales volume: 200,000 × 160% = 320,000

Sales: (320,000 × $5.70) $1,824,000 Less: variable costs (320,000 × $3.99) 1,276,800

Contribution margin 547,200 Less: fixed costs 495,000

Operating income before tax $52,200

Contribution margin ratio = $547,200 ÷ $1,824,000 = 30% Break-even point in sales = $495,000 ÷ 0.30 = $1,650,000

Contribution margin per unit = $5.70 – $3.99 = $1.71 Break-even point in units = $495,000 ÷ $1.71 = 289,474

(d) Phan’s plan should be accepted. It produces a higher operating income with a lower break-even point than Nguyen’s plan.



6-75

*CASE 6-70

(a) Current approach:

Contribution margin ratio = $800,000 ÷ $2,000,000 = 40%

Automated approach:

Contribution margin ratio = $1,600,000 ÷ $2,000,000 = 80%

The contribution margin ratio under the current approach is equal to

one-half the ratio under the automated approach because of the difference in total variable costs. For the current approach, variable expenses are high, which means the contribution from each dollar of sales is less. With the automated approach, the variable costs are less—leaving considerably more contribution to cover fixed costs.

(b) Current approach:

Break-even point = $200,000 ÷ 0.40 = $500,000

Automated approach:

Break-even point = $600,000 ÷ 0.80 = $750,000

Even though the CM ratio under the automated approach is twice as

much as under the current approach, the fixed costs are three times as much. The result is the break-even point for the automated approach is much higher than for the current approach. So, while under the automated approach the return on sales is greater after the break-even point, it takes a longer time for the company to reach profitable operations.

(c) Current approach:

Margin of safety ratio: ($2,000,000 – $500,000) ÷ $2,000,000 = 75%

Automated approach:

Margin of safety ratio: ($2,000,000 – $750,000) ÷ $2,000,000 = 62.5%



6-76


The current approach is less risky. Their sales can decline by 75% before they would no longer be profitable. Under the automated approach, their margin of safety is only 62.5%.

(d) Current approach:

Degree of operating leverage: $800,000 ÷ $600,000 = 1.33

Automated approach:

Degree of operating leverage: $1,600,000 ÷ $1,000,000 = 1.6

In times of falling sales, the current approach would be preferred. If

there was a 10% decrease in sales, profit under the current approach would decrease by 13.3% compared to 16% under the automated approach.

(e) Current approach: Let S be Sales

Total expenses = 0.60S + $200,000

Automated approach: Let S be Sales

Total expenses = 0.20S + $600,000

Point of indifference is the level of sales where total expenses

under both approaches will be the same:

0.60S + $200,000 = 0.20S + $600,000

0.40S = $400,000

S = $1,000,000

Proof: Current Automated

Sales $1,000,000 $1,000,000



Less: fixed costs 200,000 600,000




6-77

CASE 6-70 (Continued) (f) Issues that need to be considered in automation include: (1) the organization’s tolerance for risk, (2) knowledge of the marketplace and consumer trends, (3) the margin of safety required for regular operations, (4) the impact on the workforce, and (5) the short and long term profit goals for the organization.



6-78

CASE 6-71

(a) Selling price per unit $8.00 100%

Variable costs 4.80 60%

Contribution margin per unit $3.20 40%

Break-even = $880,000 ÷ $3.20 = 275,000 units

(b) For contribution margin ratio to remain at 40%,

variable costs must be 60% of sales.

New variable cost:

Cost of candy ($4.00 × 115%) $4.60

Selling expenses 0.80

$5.40

If $5.40 is 60% of sales, then the new selling price

per box must be $9.00 ($5.40 ÷ 60%)

(c) Now

Sales (780,000 × $8) $6,240,000

Variable costs 3,744,000


Total fixed costs 880,000

Operating income before tax 1,616,000

Operating income tax at 40% 646,400


Required operating income before tax is $1,616,000

Unit selling price = $8.00

Unit variable cost = $5.40

Contribution margin ratio = $2.60 ÷ $8.00 = 32.5%

Required sales to maintain operating income before tax of CASE 6-71 (continued)



6-79

$1,616,000 =

($880,000 + $1,616,000) ÷ 32.5% = $7,680,000



6-80

CASE 6-72

Break-even point = $300,000 ÷ $15.00 = 20,000 units

(b) Before tax income = after tax income ÷ (1 – tax rate)

Before tax income = $247,500 ÷ (1 – .45) = $450,000

Sales = ($300,000 + $450,000) ÷ $15 = 50,000 units

(c) New variable cost per unit = $10 – $5 + $10 = $15

New contribution margin per unit = $25 – $15 = $10

Fixed costs increase by $15,000 ($90,000 ÷ 6 years)

Break-even = ($300,000 + $15,000) ÷ $10 = 31,500 units

(d) Sales = ($315,000 + $825,000) ÷ $10 = 114,000 units

(e) New variable cost = $15, which must be 40% of sales

Selling price per unit = $15 ÷ 40% = $37.50

(a) Total Per Unit %

Sales (75,000 units) $1,875,000 $25.00 100%

Variable costs 750,000 10.00 40%

Contribution margin 1,125,000 $15.00 60%

Total fixed costs 300,000


Operating income tax at 45% 371,250




6-81

CASE 6-73

(a) The stakeholders in this situation are:

Ronnie Fraenze, accountant of Korol Company.

The dislocated personnel of Korol.

The senior management who made the decision. (b) As an accountant, Ronnie has a responsibility to

Communicate information fairly and objectively and

Disclose fully all relevant information that could reasonably be expected to influence an intended user’s understanding of the reports, comments, and recommendations presented.

Ronnie will violate the standards of ethical conduct for accountants if

he fails to inform senior management of his error. He risks losing a promotion and receiving a less favourable performance review if he reveals his error.

(c) Ronnie’s alternatives are:

Keep quiet.

Inform management of his error. Even though it appears there is nothing at stake in this situation, the

actions recommended must be idealistic and ethical. Any individual who is willing to act ethically when there is nothing at stake is more likely to act ethically when there is something to lose.



6-82

CASE 6-74: “All About You” Activity

(a)Overhead costs:

Rent

Utilities (heat. Light, water)

Property and business taxes

Management salaries and benefits

Marketing costs for the station

Sales force base salaries

Variable costs

Costs of production of on-air commercial

Advertising sales commission

(b)The radio station is not profitable if it cannot sell enough advertising

to cover its costs.

To calculate the Break Even point, we would need to know: the selling

price per minute of on-air advertising, the variable cost per minute of on-

air advertising and the total fixed costs of the radio station.

The contribution margin per minute of on-air time is equal to the Per

minute Sales Price less the variable cost per minute.

The Break Even Point occurs when the total Fixed costs are fully

recovered by the contribution per minutes sold. i.e.

Break even point = Total Fixed costs (rent, utilities etc.)

Contribution per minute of air time advertising



6-83

SOLUTION TO WATERWAYS CONTINUING PROBLEM

WCP-6

(Note: All figures are rounded) Part 1: (a) (1) The contribution margin ratio is 30% ($883,920 ÷ $2,937,120):

Waterways Corporation

Contribution Margin Income Statement for Water Control and Timer

For the Year 2012

Unit Cost

Sales (696,000 units) $2,937,120 $4.22 100%

Variable expenses 2,053,200 2.95 70%

Contribution margin 883,920 1.27 30%

Fixed Expenses 683,338

Operating income from product $ 200,582

(2) Break-even point in units = 538,061 units

Fixed expenses $683,338 ÷ Unit CM $1.27 = 538,061 units (rounded)

Break-even point in dollars = $2,277,793

Fixed expenses $683,338 ÷ CM ratio 0.30 = $2,277,793 (rounded)

(3) Margin of safety in dollars = $659,327

Sales $2,937,120 – Break-even in dollars $2,277,793 = $659,327

Margin of safety ratio = 22.45%

Margin of safety in dollars $659,327 ÷ Sales $2,937,120 = 22.45%



6-84

WCP6 (continued)

(4) Waterways would have to sell an additional 15,794 units.

10% increase in operating income = 0.10 × $200,582.00 = $20,058.20

Because Waterways is operating above break-even, any increase in

operating income will also be an equal increase in contribution margin.

Required increase in contribution margin = $20,058.20

Required increase in unit sales = $20,058.20 ÷ $1.27 = 15,794 (rounded)

(5) Waterways is operating above the break-even point, so every dollar

increase in contribution margin means a dollar increase in income.

Since additional sales of 71,090 units will contribute 71,090 × $1.27 =

$90,284.30 margin, operating income will also increase by $90,284.30.

(b) Total Per Unit %

Sales (491,740 units) $13,031,110 $26.50 100%

Variable costs1 9,524,864 19.37 73%

Contribution margin 3,506,246 $ 7.13 27%

Total fixed costs2 2,845,090

Operating income $661,156 1 $6,863,512 + $2,661,352 2 $2,050,140 + $794,950



6-85

WCP6 (continued)

(1) New number of units = 491,740 × 110% = 540,914

New CM per unit = $7.13 + $0.25 – $0.71 = $6.67 CM per unit

Total Per Unit %

Sales (540,914 units) $14,469,450 $26.75 100%

Variable costs 10,861,553 20.08 75%


Total fixed costs 2,845,090

Net income $ 762,807

The changes would create a $101,651 increase in operating income, but

would also decrease the contribution margin ratio from 27% to 25%.

(2) If the average sales price did not increase, the contribution margin ratio

would drop 3% (from 27% to 24%). Profit would decrease by $33,578

($661,156 − $627,578). This definitely would not be in the best interest

of the company.

Total Per Unit %

Sales (540,914 units) $14,334,221 $26.50 100%

Variable costs 10,861,557 20.08 76%


Total fixed costs 2,845,090

Net income $627,574



6-86

WCP6 (continued)

Part 2:

(a) Total units = 450,000 + 1,500,000 + 50,000 = 2,000,000

Sprinklers: 450,000 ÷ 2,000,000 = 22.5%

Valves: 1,500,000 ÷ 2,000,000 = 75%

Controllers: 50,000 ÷ 2,000,000 = 2.5%

(b) Sprinklers Valves Controllers

Sales (540,914 units) $26.50 $11.20 $42.50

Variable costs

Manufacturing $13.96 $ 7.95 $29.75

Selling & Admin 1.30 0.50 3.41

Total variable costs $15.26 $8.45 $33.16

Contribution margin $11.24 $2.75 $9.34

Weighted-Average Unit Contribution Margin

Unit CM Mix % WA Unit CM

Sprinklers $11.24 22.5% $2.53

Valves $2.75 75.0% $2.06

Controllers $9.34 2.5% $0.23

$4.82

(c) Break-even point in units: ($760,000 + $1,600,000) ÷ $4.82 = 489,627



6-87

WCP6 (continued)

Part 3:

Unit Cost

Sales (4,000 units) $170,000 $42.50 100%

Variable expenses1 52,640 13.16 31%

Contribution margin 117,360 $29.34 69%

Fixed expenses2 94,122

Operating income from product $ 23,238

1 $9.75 + $3.41

2 $81,000 + $13,122

(a) Contribution margin ratio (as above) = 69%

Degree of operating leverage = $117,360 ÷ $23,238 = 5 (rounded)

Break-even point in dollars = $94,122 ÷ 0.69 = $136,409 (rounded)

Margin of safety ratio = ($170,000 – $136,409) ÷ $170,000 = 19.76%

(b) If these figures represent the cost structure for the company as a

whole, it suggests that Waterways is well positioned to operate in a

stable market. Although the high proportion of fixed costs means it will

take longer to reach break-even, it also means that for every dollar of

sales above break-even, the company will be receiving a greater return

on the dollar.



6-88

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