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CHAPTER 6

Cost-Volume-Profit Analysis: Additional Issues

ASSIGNMENT CLASSIFICATION TABLE

Learning Objectives QuestionsBrief

Exercises Do It! ExercisesA

ProblemsB

Problems

1. Describe the essential features of a cost-volume-profit income statement.

1, 2, 3, 4 1, 2, 3, 4, 5, 6

1 1A, 2A 1B, 2B

2. Apply basic CVP concepts. 2, 4, 5, 6 1, 2, 3, 4, 5, 6

2 1, 2, 3, 4, 5

1A, 2A, 6A 1B, 2B, 6B

3. Explain the term sales mix and its effects on break-even sales.

7, 8, 9 7, 8, 9, 10 3 6, 7, 8, 9, 10

4A 4B

4. Determine sales mix when a company has limited resources.

10, 11 11, 15 4 11, 12, 13 3A 3B

5. Understand how operating leverage affects profitability.

12, 13, 14, 15, 16

12, 13, 14 14, 15, 16 5A, 6A 5B, 6B

*6. Explain the difference between absorption costing and variable costing.

17 16, 17, 18 17, 18, 19 7A, 8A 7B, 8B

*7. Discuss net income effects under absorption costing versus variable costing.

19, 20, 21, 22

19 18 7A, 8A 7B, 8B

*8. Discuss the merits of absorption versus variable costing for management decision making.

18 8A 8B

Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only) 6-1

ASSIGNMENT CHARACTERISTICS TABLE

ProblemNumber Description

DifficultyLevel

TimeAllotted (min.)

1A Compute break-even point under alternative courses of action.

Moderate 20–30

2A Compute break-even point and margin of safety ratio, and prepare a CVP income statement before and after changes in business environment.

Moderate 20–30

3A Determine sales mix with limited resources. Simple 10–15

4A Determine break-even sales under alternative sales strategies and evaluate results.

Moderate 20–30

5A Compute degree of operating leverage and evaluateimpact of operating leverage on financial results.

Moderate 20–30

6A Determine contribution margin, break-even point, target sales, and degree of operating leverage.

Moderate 20–30

*7A Prepare income statements under absorption costing and variable costing for a company with beginning inventory, and reconcile differences.

Moderate 20–30

*8A Prepare absorption and variable costing income statements and reconcile differences between absorption and variable costing income statements when sales level and production level change. Discuss relative usefulness of absorption costing versus variable costing.

Moderate 20–30

1B Compute break-even point under alternative courses of action.

Moderate 20–30

2B Compute break-even point and margin of safety ratio, and prepare a CVP income statement before and after changes in business environment.

Moderate 20–30

3B Determine sales mix with limited resources. Simple 10–15

4B Determine break-even sales under alternative sales strategies and evaluate results.

Moderate 20–30

5B Compute degree of operating leverage and evaluateimpact of operating leverage on financial results.

Moderate 20–30

6B Determine contribution margin, break-even point, target sales, and degree of operating leverage.

Moderate 20–30

*7B Prepare income statements under absorption costing and variable costing for a company with beginning inventory, and reconcile differences.

Moderate 20–30

*8B Prepare absorption and variable costing income statements and reconcile differences between absorption and variable costing income statements when sales level and production level change. Discuss relative usefulness of absorption costing versus variable costing.

Moderate 20–30

6-2 Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only)

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

Learning Objective Knowledge Comprehension Application Analysis Synthesis Evaluation

*1. Describe the essential features of a cost-volume-profit income statement.

Q6-1Q6-3

Q6-2Q6-4

BE6-2BE6-3BE6-4BE6-5BE6-6

DI6-1P6-1AP6-2AP6-1BP6-2B

BE6-1P6-1AP6-2AP6-1BP6-2B

*2. Apply basic CVP concepts. Q6-2Q6-4Q6-5Q6-6

BE6-2BE6-3BE6-4BE6-5BE6-6DI6-2E6-1

E6-2E6-3E6-4E6-5P6-1AP6-2AP6-4A

P6-6AP6-1BP6-2BP6-4BP6-6B

BE6-1P6-1AP6-2AP6-6AP6-1BP6-2B

P6-6B

*3. Explain the term sales mix and its effects on break-even sales.

Q6-7Q6-8

Q6-8Q6-9

BE6-7BE6-8BE6-9BE6-10

DI6-3E6-6E6-7E6-8

E6-9E6-10P6-4AP6-4B

E6-6E6-7E6-8P6-4A

P6-4B

*4. Determine sales mix when a company has limited resources.

Q6-11 Q6-10 BE6-11BE6-15DI6-4

E6-11E6-12E6-13

P6-3AP6-3B

E6-11E6-12E6-13

P6-3AP6-3B

*5. Understand how operating leverage affects profitability.

Q6-12Q6-13Q6-15

Q6-14 Q6-16BE6-12BE6-13BE6-14

E6-14E6-15E6-16P6-5A

P6-6A P6-5B

E6-14E6-15E6-16P6-5A

P6-6AP6-5BP6-6B

**6. Explain the difference between absorption costing and variable costing.

Q6-17 BE6-16BE6-17BE6-18E6-17

E6-18E6-19P6-7AP6-8A

P6-7BP6-8B

E6-18E6-19P6-7AP6-8A

P6-7BP6-8B

*7. Discuss net income effects under absorption costing versus variable costing.

Q6-19Q6-20Q6-21

Q6-22 Q6-19BE6-19E6-18

P6-7AP6-8AP6-7B

P6-8B P6-7AP6-8AP6-7B

P6-8B

**8. Discuss the merits of absorption versus variable costing for management decision making.

Q6-18 P6-8AP6-8B

Broadening Your Perspective BYP6-7 BYP6-4BYP6-5

BYP6-1BYP6-2

BYP6-6BYP6-9

BYP6-3BYP6-8BYP6-10

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 net 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 net income. But the format used to reach net income differs.A traditional income statement’s format consists of:Sales revenue – cost of goods sold = gross profit; Gross profit – selling and administrative expenses = net income.A CVP income statement’s format consists of:Sales revenue – variable expenses = contribution margin; Contribution margin – fixed expenses = net 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 net income. It also highlights how changes in sales volume or cost structure affect net income.

5. WHEAT COMPANYCVP Income Statement

Sales........................................................................................................... $900,000Variable costs ($500,000 X .75) + ($200,000 X .75).................................. 525,000 Contribution margin.................................................................................... $375,000

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

7. Sales mix is the relative percentage of each product sold when a company sells more than one product. Sales mix changes the calculation of the break-even point because the fixed costs must be divided by the weighted-average unit contribution margin.

8. The 150,000-mile tire has a higher unit contribution margin, that is, each tire sold covers a larger amount of fixed costs. Therefore, if the sales mix shifts away from the 150,000-mile tire to the 50,000-mile tire, the company will have to sell more total tires in order to break-even.

9. If a company has many products, the break-even point is calculated using sales information for divisions or product lines, rather than individual products. The weighted-average contribution margin ratio is computed by multiplying the sales mix percentage of each product line by the contribution margin ratio of each product line, and then summing the results. Total break-even sales in dollars is then calculated by dividing the company’s total fixed costs by the weighted-average contribution margin ratio. Finally, to determine the amount of sales generated by each product line at the break-even point, multiply the total break-even sales by the sales mix percentage of each product line.


Questions Chapter 6 (Continued)

10. Contribution margin per unit of limited resource is determined by dividing the contribution margin per unit of the product by the number of units of the limited resource required to produce the product.

11. The theory of constraints is a specific approach used to identify and manage constraints to achieve the company’s goals. According to this theory, a company must continually identify its constraints and find ways to reduce or eliminate them, where appropriate. Examples of constraints would be production bottlenecks or poorly trained workers.

12. Cost structure refers to the relative proportion of fixed costs versus variable costs that a company incurs. Companies that rely heavily on fixed costs will have higher break-even points.

13. Operating leverage refers to the extent to which a company’s net income reacts to a given change in sales. A company can increase its operating leverage by increasing its reliance on fixed costs.

14. Typically manual labor is considered a variable cost. Depreciation on factory equipment is a fixed cost. Therefore, if a company replaces manual labor with automated factory equipment it will increase its operating leverage, and increase its break-even point.

15. The degree of operating leverage is a measure of a company’s relative operating leverage. It is calculated by dividing the contribution margin by net income at a particular level of sales.

16. Pine’s degree of operating leverage of 8 versus Fir’s measure of 4 tells us that Pine will experience twice (8 ÷ 4) the increase (or decrease) in net income for a given increase(decrease) in sales as Fir.

*17. Under absorption costing, both variable and fixed manufacturing costs are considered to be product costs. Under variable costing, only variable manufacturing costs are product costs and fixed manufacturing costs are expensed when incurred.

*18. (a) The rationale for variable costing centers on the purpose of fixed manufacturing costs, which is to have productive facilities available for use. Since these costs are incurred whether a company operates at zero or 100% capacity, it is argued that they should be expensed when they are incurred. Variable costing is useful in product costing internally by management and it is useful in controlling manufacturing costs.

(b) Variable costing cannot be used for financial reporting purposes because it does not follow generally accepted accounting principles.

*19. One way to compute the difference is as follows:

Ending inventory X Fixed manufacturing overhead cost per unit 8,500 X $5 = $42,500

Absorption costing will report a $42,500 higher net income than variable costing because a portion of the fixed manufacturing overhead costs are deferred in inventory.


Questions Chapter 6 (Continued)

*20. If production equals sales in any given period, the net incomes under both methods will be equal. In this case, there is no increase in the ending inventory. So fixed manufacturing overhead costs in the current period are not deferred to future periods through the ending inventory.

*21. If production is greater than sales, absorption costing net income will be greater than variable costing net income. Absorption costing net income is higher because some of the fixed manufacturing overhead costs will be deferred in the inventory account until the products are sold.

*22. In the long run, neither method will produce a higher net income amount. Over a long period of time, sales can never exceed production, nor production exceed sales by significant amounts. For this reason, over the lifetime of a corporation, variable costing and absorption costing will tend to yield the same net income amounts.


SOLUTIONS TO BRIEF EXERCISES

BRIEF EXERCISE 6-1

1. (a) $70 = ($250 – $180)(b) 28% ($70 ÷ $250)

2. (c) $200 = ($500 – $300)(d) 60% ($300 ÷ $500)

3. (e) $1,100 = ($330 ÷ 30%)(f) $770 ($1,100 – $330)

BRIEF EXERCISE 6-2

HAMBY INC.Income Statement

For the Quarter Ended March 31, 2014

Sales......................................................................... $2,000,000Variable expenses

Cost of goods sold.......................................... $760,000Selling expenses............................................. 95,000Administrative expenses................................ 79,000

Total variable expenses.......................... 934,000Contribution margin................................................ 1,066,000Fixed expenses

Cost of goods sold.......................................... 600,000Selling expenses............................................. 60,000Administrative expenses................................ 66,000

Total fixed expenses............................... 726,000Net income............................................................... $ 340,000

BRIEF EXERCISE 6-3

Contribution margin ratio = [($250,000 – $175,000) ÷ $250,000] = 30%Required sales in dollars = $120,000 ÷ 30% = $400,000


BRIEF EXERCISE 6-4

(a) $400Q = $250Q + $210,000 + $0$150Q = $210,000

Q = 1,400 units

(b) Contribution margin per unit $150, or ($400 – $250)X = $210,000 ÷ $150X = 1,400 units

BRIEF EXERCISE 6-5

X = .60X + $210,000 + $60,000.40X = $270,000

X = $675,000

BRIEF EXERCISE 6-6

Margin of safety = $1,200,000 – $960,000 = $240,000Margin of safety ratio = $240,000 ÷ $1,200,000 = 20%

BRIEF EXERCISE 6-7

ModelSales Mix

PercentageUnit Contribution

MarginWeighted-Average Unit

Contribution MarginA12B22

C124

60%15%25%

$10 ($50 – $40)$30 ($100 – $70)

$100 ($400 – $300)

$ 6.00 4.50 25.00$35.50


BRIEF EXERCISE 6-8

Total break-even = ($213,000 ÷ $35.50*) = 6,000 units

*Computed in BE 6-7

Sales UnitsUnits of A12 = .60 X 6,000 = 3,600Units of B22 = .15 X 6,000 = 900Units of C124 = .25 X 6,000 = 1,500

6,000

BRIEF EXERCISE 6-9

(a) Weighted-average contribution = (.30 X .20) + (.50 X .20) + ( .20 X .45) = .25 margin ratio

(b) Total break-even point = ($440,000 ÷ .25) = $1,760,000 in dollars

Birthday $1,760,000 X .30 = $ 528,000Standard tapered $1,760,000 X .50 = 880,000Large scented $1,760,000 X .20 = 352,000

$1,760,000

BRIEF EXERCISE 6-10

(a) Sales MixBedroom Division $500,000 ÷ $1,250,000 = .40Dining Room Division $750,000 ÷ $1,250,000 = .60

(b) Weight-average contribution = $575,000 = .46margin ratio $1,250,000

OR

Contribution Margin RatioBedroom Division ($275,000 ÷ $500,000) = .55Dining Room Division ($300,000 ÷ $750,000) = .40

Weighted-average contribution margin ratio = (.55 X .40) + (.40 X .60) = .46


BRIEF EXERCISE 6-11

Product A Product B

Contribution margin per unit (a)Machine hours required (b)Contribution margin per unit of limited resource [(a) ÷ (b)]

$12.0 2$ 6

$15 3$ 5

BRIEF EXERCISE 6-12

Degree of operating leverage (old) = $200,000 ÷ $40,000 = 5

Degree of operating leverage (new) = $240,000 ÷ $40,000 = 6

If Sam’s sales change, the resulting change in net income will be 1.2 times (6 ÷ 5) higher with the new machine than under the old system.

BRIEF EXERCISE 6-13

Break-even point in dollars:

Logan Co. Morgan Co.

$60,000 ÷ ($120,000 ÷ $200,000) $90,000 ÷ ($150,000 ÷ $200,000)= $100,000 = $120,000

Morgan Company’s cost structure relies much more heavily on fixed costs than that of Logan Co. As result, Morgan has a higher contribution margin ratio of .75 ($150,000 ÷ $200,000) versus .60 ($120,000 ÷ $200,000), for Logan Co. Morgan also has much higher fixed costs to cover. Its break-even point is therefore higher than that of Logan Co.

BRIEF EXERCISE 6-14

Degree of operating leverage = Contribution margin ÷ Net income

Montana Corp. 1.6 = Contribution margin ÷ $50,000Contribution margin = $50,000 X 1.6 = $80,000

APK Co. 5.4 = Contribution margin ÷ $50,000Contribution margin = $50,000 X 5.4 = $270,000


BRIEF EXERCISE 6-15

Product 1 Product 2

Contribution margin per unit (a)Machine hours required (b)Contribution margin per unit of limited resource [(a) ÷ (b)]

$ 42 .15

$280

$ 35 .10

$350

Product 2 has a higher contribution margin per limited resource, even though it has a lower contribution margin per unit. Given that machine hours are limited to 2,000 per month, Ger Corporation should produce Product 2.

*BRIEF EXERCISE 6-16

Variable CostingDirect materials $14,400 Direct labor 25,600 Variable manufacturing overhead 32,400 Total product costs $72,400


Absorption CostingDirect materials $14,400 Direct labor 25,600 Variable manufacturing overhead 32,400 Fixed manufacturing overhead 12,000 Total product costs $84,400


(a) Absorption Costing.......Direct materials................................................................. $20

Direct labor........................................................................ 14Variable manufacturing overhead................................... 15Fixed manufacturing overhead ($128,000 ÷ 8,000)......... 16 Total manufacturing cost per unit................................... $65


*BRIEF EXERCISE 6-18 (Continued)

(b) Variable CostingDirect materials............................................... $20Direct labor...................................................... 14Variable manufacturing overhead.................. 15Total manufacturing cost per unit................. $49


MEMO

To: Chief financial officer

From: Student

Re: Absorption and variable costing

Under absorption costing, fixed manufacturing overhead is a product cost, while under variable costing, fixed manufacturing overhead is a period cost (expensed as incurred).

Since units produced (50,000) exceeded units sold (48,000) last month, income under absorption costing will be higher than under variable costing. Some fixed overhead (2,000 units X $4 = $8,000) will be assigned to ending inventory and therefore not expensed under absorption costing, whereas all fixed overhead is expensed under variable costing. Therefore, absorption costing net income will be higher than variable costing net income by $8,000.


SOLUTIONS TO DO IT! REVIEW EXERCISES

DO IT! 6-1

AMANDA INC.Income Statement

For the Month Ended January 31, 2014

Sales (10,000 units)........................................... $400,000Variable expenses

Cost of goods sold...................................... $184,000Selling expenses......................................... 40,000Administrative expenses............................ 16,000

Total variable expenses....................... 240,000 Contribution margin 160,000Fixed expenses

Cost of goods sold...................................... $ 70,000Selling expenses......................................... 30,000Administrative expenses............................ 50,000

Total fixed expenses............................ 150,000 Net income......................................................... $ 10,000

Contribution margin per unit: $160,000 ÷ 10,000 units = $16 per unit.Contribution margin ratio: $160,000 ÷ $400,000 = 40% or $16 ÷ $40 = 40%.

DO IT! 6-2

(a) Break-even point in units is 7,500 units ($150,000 ÷ $20).Break-even point in sales dollars is $375,000 ($150,000 ÷ .40*).The margin of safety in dollars is $75,000 ($450,000 – $375,000).

*$20 ÷ $50.

(b) Break-even point in units is 8,333 units (rounded) ($150,000 ÷ $18*).Break-even point in sales dollars is $400,000 ($150,000 ÷ .375**).The margin of safety in dollars is $118,400 ($518,400*** – $400,000).

*$50 – (.04 X $50) – 30 = $18.**$18 ÷ $48 = .375

***9,000 + (.20 X 9,000) = 10,800 units, 10,800 units X $48 = $518,400


DO IT! 6-2 (Continued)

The increase in the break-even point from $375,000 to $400,000 indi-cates that management should not implement the proposed change while the increase in the margin of safety from $75,000 to $118,400 indicates that management should implement the proposed change. Since the expected 20% increase in sales volume will result in a con-tribution margin of $194,400 (10,800 X $18) which is only $14,400 more than the current amount, management should be cautious before reducing unit prices.

DO IT! 6-3

(a) The sales mix percentages as a function of units sold is:

Basic Basic Plus Premium750 ÷ 1,500 = 50% 450 ÷ 1,500 = 30% 300 ÷ 1,500 = 20%

(b) The weighted-average unit contribution margin is:

[.50 X ($250 – $195)] + [.3 X ($400 – $288)] + [.20 X ($800 – $416)] = $137.90.

(c) The break-even point in units is: $165,480 ÷ $137.90 = 1,200 units.

(d) The break-even units to produce for each product are:Basic: 1,200 units X 50% = 600 unitsBasic Plus 1,200 units X 30% = 360 unitsPremium: 1,200 units X 20% = 240 units

1,200 units

DO IT! 6-4

(a) The Best binoculars have the highest contribution margin per unit. Thus, ignoring any manufacturing constraints, it would appear that the company should shift toward production of more Best units.


DO IT! 6-4 (Continued)

(b) The contribution margin per unit of limited resource is calculated as:

Good Better Best Contribution margin per unit $40 $150 $420Limited resource consumed per unit .5 = $80 1.5 = $100 6 = $70

(c) The Better binoculars have the highest contribution margin per unit of limited resource, even though they do not have the highest contribution margin per unit. Given the resource constraint, any additional capacity should be used to make Better binoculars.


SOLUTIONS TO EXERCISES

EXERCISE 6-1

(a) 1. Contribution margin per room = $60 – ($8 + $37)Contribution margin per room = $15Contribution margin ratio = $15 ÷ $60 = 25%

Fixed costs = $8,800 + $2,400 + $1,500 + $800 = $13,500Break-even point in rooms = $13,500 ÷ $15 = 900

2. Break-even point in dollars = 900 rooms X $60 per room= $54,000 per month

ORFixed costs ÷ Contribution margin ratio = $13,500 ÷ .25

= $54,000 per month

(b) 1. Margin of safety in dollars:Planned activity = 50 rooms per day X 30 days

= 1,500 rooms per month

Expected rental revenue = 1,500 rooms X $60 = $90,000Margin of safety in dollars = $90,000 – $54,000 = $36,000

2. Margin of safety ratio: $36,000 = 40%$90,000

EXERCISE 6-2

(a) Contribution margin in dollars: Sales = 4,000 X $30 = $120,000Variable costs = $120,000 X .75 = 90,000 Contribution margin $ 30,000

Contribution margin per unit: $30 – $22.50 ($30 X 75%) = $7.50.Contribution margin ratio: $7.50 ÷ $30 = 25%.


EXERCISE 6-2 (Continued)

(b) Break-even sales in dollars: = $67,200.

Break-even sales in units: = 2,240.

(c) Margin of safety in dollars: $120,000 – $67,200 = $52,800.

Margin of safety ratio: $52,800 ÷ $120,000 = 44%.

EXERCISE 6-3

Current selling price = $310,000 ÷ 5,000 unitsCurrent selling price = $62

1. Increase selling price to $68.20 ($62 X 110%).Net income = $341,000* – $210,000 – $75,000 = $56,000.

*($68.20 X 5,000)

2. Reduce variable costs to 58% of sales.Net income = $310,000 – $179,800** – $75,000 = $55,200.

**($310,000 X .58)

3. Reduce fixed costs to $55,000 ($75,000 – $20,000).Net income = $310,000 – $210,000 – $55,000 = $45,000.

Alternative 1, increasing unit sales price, will produce the highest net income.


EXERCISE 6-4

(a) 1. Contribution margin ratio is: $30,000 = 62.5%$48,000

Break-even point in dollars = $20,250 = $32,40062.5%

2. Round-trip fare = $48,000 = $120400 fares

Break-even point in fares = $32,400 = 270 fares$120

(b) At the break-even point fixed costs and contribution margin are equal. Therefore, the contribution margin at the break-even point would be $20,250.

(c) Fare revenue ($108* X 500**) $54,000Variable costs ($18,000 X 1.20) 21,600Contribution margin 32,400Fixed costs 20,250Net income $12,150

Yes, the fare decrease should be implemented because net income increases to $12,150.

*$120 – (.10 X $120)**400 + 100

EXERCISE 6-5

(a) HALL COMPANYCVP Income Statement

For the Year Ended December 31, 2014

Total Per Unit

Sales (60,000 X $26)........................................Variable costs (60,000 X $12).........................Contribution margin (60,000 X $14)...............Fixed costs......................................................Net income......................................................

$1,560,000 720,000 840,000 500,000$ 340,000

$26 12$14



(b) HALL COMPANYCVP Income Statement

For the Year Ended December 31, 2014

Total Per Unit

Sales [(60,000 X 105%) X $24.50*].................Variable costs (63,000 X $9.00**)...................Contribution margin (63,000 X $15.50)..........Fixed costs ($500,000 + $150,000).................Net income......................................................

$1,543,500 567,000 976,500 650,000$ 326,500

$24.50 9.00$15.50

*$26.00 – ($3 X 50%) = $24.50.**$12.00 – ($12 X 25%) = $9.00.

EXERCISE 6-6

Sales MixPercentage

ContributionMargin Per Unit

Weighted-AverageContribution Margin

LawnmowersWeed-trimmersChainsaws

20%50%30%

$30$20$40

$ 6 10 12$28

Total break-even sales in units = $4,200,000 ÷ $28 = 150,000 units

Sales MixPercentage

TotalBreak-even Sales

in Units

Sales UnitsNeeded

Per ProductLawnmowersWeed-trimmersChainsawsTotal units

20%50%30%

XXX

150,000150,000150,000

===

30,000 units 75,000 units 45,000 units150,000 units


EXERCISE 6-7

(a)

Sales MixPercentage

ContributionMargin Ratio

Weighted-AverageContributionMargin Ratio

Oil changesBrake repair

70%30%

20%60%

.14

.18

.32

Total break-even sales in dollars = $16,000,000 ÷ .32 = $50,000,000

Sales MixPercentage

TotalBreak-even Sales

in Dollars

Sales DollarsNeeded

Per ProductOil changesBrake repairTotal sales

70%30%

XX

$50,000,000$50,000,000

==

$35,000,000 15,000,000$50,000,000

(b)

Sales to achieve target net income = ($80,000 + $60,000) ÷ .32 = $437,500

Sales MixPercentage

TotalSales Needed

Sales DollarsNeeded Per Product

Per StoreOil changesBrake repairTotal sales

70%30%

XX

$437,500$437,500

==

$306,250 131,250$437,500

EXERCISE 6-8

(a)

Sales MixPercentage



Mail pouches and small boxesNon-standard boxes

80%

20%

20%

70%

.16

.14

.30

Total break-even sales in dollars = $12,000,000 ÷ .30 = $40,000,000 6-20 Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only)


Sales MixPercentage

Total Break-even Salesin Dollars

Sales DollarsNeeded

Per ProductMail pouches and small boxesNon-standard boxesTotal sales

80%

20%

X

X

$40,000,000

$40,000,000

=

=

$32,000,000

8,000,000$40,000,000

(b)

Sales MixPercentage



Mail pouches and small boxesNon-standard boxes

40%

60%

20%

70%

.08

.42

.50

Total break-even sales in dollars = $12,000,000 ÷ .50 = $24,000,000

Sales MixPercentage

Total Break-even Salesin Dollars

Sales DollarsPer Product

Mail pouches and small boxesNon-standardized boxesTotal sales

40%

60%

X

X

$24,000,000

$24,000,000

=

=

$ 9,600,000

14,400,000$24,000,000

EXERCISE 6-9

(a) Weighted-average unitcontribution margin = ($40 X .30) + ($20 X .60) + ($60 X .10) = $30

Break-even point in units = $630,000 ÷ $30 = 21,000

(b) Shoes (21,000 X .30) = 6,300 pairs of shoesGloves (21,000 X .60) = 12,600 pairs of glovesRange-finders (21,000 X .10) = 2,100 range-finders



(c) Shoes: 6,300 X $40 = $252,000Gloves: 12,600 X $20 = 252,000Range-finders: 2,100 X $60 = 126,000Total contribution margin 630,000Fixed costs 630,000Net income $ 0

EXERCISE 6-10

(a) Sales mix percentageiPad division: $600,000 ÷ ($600,000 + $400,000) = .60iPod division: $400,000 ÷ ($600,000 + $400,000) = .40

Contribution margin ratio:iPad division: $180,000 ÷ $600,000 = .30iPod division: $140,000 ÷ $400,000 = .35

(b) Weighted-average contribution = $320,000 = .32 ORmargin ratio $1,000,000

Weighted-average contributionmargin ratio = (.60 X .30) + (.40 X .35) = .32

(c) Break-even point in dollars = $120,000 ÷ .32 = $375,000

(d) Sales dollars needed at break-even point for each divisioniPad division: $375,000 X .60 = $225,000iPod division: $375,000 X .40 = $150,000

EXERCISE 6-11

(a) Product

A B C

Contribution margin per unit (a)Machine hours required (b)Contribution margin per unit of limited resource (a) ÷ (b)

$ 5 2$2.50

$ 2 1$ 2

$ 3 2$1.50

(b) Product A should be manufactured because it results in the highest contribution margin per machine hour.



(c) 1. ProductA B C

Machine hours (a) (1,500 ÷ 3)Contribution margin per unit of limited resource (b)Total contribution margin [(a) X (b)]

500

$ 2.50$1,250

500

$ 2$1,000

500

$1.50$ 750

The total contribution margin = ($1,250 + $1,000 + $750) = $3,000.

2. Product A

Machine hours (a)Contribution margin per unit of limited resource (b)Total contribution margin [(a) X (b)]

1,500$ 2.50$3,750

EXERCISE 6-12

(a) Product D: $30 ÷ $10 = 3.0 hours per unitProduct E: $80 ÷ $10 = 8.0 hours per unitProduct F: $35 ÷ $10 = 3.5 hours per unit

(b) Product D E F

Selling price $200 $ 300 $250Variable costs 125 160 180Contribution margin 75 140 70Direct labor hours per unit ÷ 3.0 ÷ 8.0 ÷ 3.5Contribution margin per

direct labor hour $ 25 $17.50 $ 20

(c) Product D should be produced because it generates the highest contri-bution margin per direct labor hour.

Product D Total direct labor hours available 2,000Contribution margin per direct labor hour X $25

Total contribution margin $50,000


EXERCISE 6-13

(a) ProductBasic Deluxe

Selling price per unitVariable costs per unit

$40 20

$ 52 22

Contribution margin per unit (a) $20 $ 30Machine hours required (b) .5 .8Contribution margin per

machine hour (a) ÷ (b) $40 $37.50

(b) The Basic product should be manufactured because it results in the higher contribution margin per machine hour.

(c) 1. Basic Deluxe Total Machine hours allocated 500 500 1,000X Contribution margin per machine hour $40 $37.50

Contribution margin $20,000 $18,750 $38,750

2. Basic Deluxe Total Machine hours allocated 1,000 –0– 1,000X Contribution margin per machine hour $40 $37.50

Contribution margin $40,000 –0– $40,000

EXERCISE 6-14

(a)Contribution

Margin ÷Net

Income =Degree of Operating

LeverageArmstrongContador

$260,000$450,000

÷÷

$100,000$100,000

==

2.604.50

Interpretation: Contador has a higher degree of operating leverage. Its earnings would increase (decrease) by a greater amount than Armstrong if each experienced an equal increase (decrease) in sales.



(b)Armstrong Company Contador Company

SalesVariable costsContribution marginFixed costsNet income

$550,000** 264,000** 286,000** 160,000**$126,000**

$550,000*** 55,000*** 495,000*** 350,000***$145,000***

*$500,000 X 1.1 **$240,000 X 1.1***$ 50,000 X 1.1

(c) Each company experienced a $50,000 increase in sales. However, be-cause of Contador’s higher operating leverage, it experienced a $45,000 ($145,000 – $100,000) increase in net income while Armstrong experienced only a $26,000 ($126,000 – $100,000) increase. This is what we would have expected, since Contador’s degree of operating leverage exceeds that of Armstrong.

EXERCISE 6-15

(a)Contribution

Margin÷ Net Income =

Degree ofOperating Leverage

Manual systemComputerized system

$300,000

$900,000

÷

÷

$250,000

$250,000

=

=

1.20

3.60

(b) The computerized system would produce profits that are 3.0 times (3.60 ÷ 1.20) as much as the manual system. With a $150,000 increase in sales, net income would increase $30,000 ($280,000 – $250,000) under the manual system and $90,000 ($340,000 – $250,000) under the computerized system.



ManualSystem

Computerized System

SalesVariable costsContribution marginFixed costsNet income

$1,650,000 1,320,000* 330,000 50,000$ 280,000

$1,650,000 660,000**

990,000 650,000$ 340,000

*($1,200,000 ÷ $1,500,000) X $1,650,000**($600,000 ÷ $1,500,000) X $1,650,000

(c)(Actual Sales – Break-even Sales) ÷ Actual Sales = Margin of Safety Ratio

Manual system

Computerized

system

($1,500,000

($1,500,000

–

–

$250,000*)

$1,083,333**)

÷

÷

$1,500,000

$1,500,000

=

=

.83

.28

*$ 50,000 ÷ ($300,000 ÷ $1,500,000)**$650,000 ÷ ($900,000 ÷ $1,500,000)

The manual system could weather the greater decline in sales before reaching the break-even point. Under the manual system sales could drop 83% before suffering a loss, while sales under the computerized system could only decline by 28% before suffering a loss.

EXERCISE 6-16

(a)Contribution

Margin÷

NetIncome =

Degree of OperatingLeverage

Traditional YamsAuto-Yams

$ 80,000$240,000

÷÷

$50,000$50,000

==

1.604.80

Auto-Yams, which relies more heavily on fixed costs, has the higher degree of operating leverage, 4.8 versus 1.60. That means for every dollar of increase (decrease) in sales, Auto-Yams will generate 3 (4.80 ÷ 1.60) times more (less) in contribution margin and net income.



(b)

% Changein Sales X

Degree ofOperatingLeverage =

% Change inNet Income

15% decrease: Traditional Yams Auto-Yams

(15%)(15%)

XX

1.604.80

==

(24.0%)(72.0%)

10% increase: Traditional Yams Auto-Yams

10%10%

XX

1.604.80

==

16.0%48.0%

(c) There are several possible answers that could be given. For example, if the candied Yams business is fairly stable, Auto-Yams might be the choice, because they will generate the higher contribution margin and net income. If, however, sales swing widely from year to year, Traditional Yams might be chosen because they will provide the more stable contribution margin and net income. Finally, if the investment banker is a risk taker, she might choose Auto-Yams in spite of year to year sales swings.

EXERCISE 6-17

(a) Unit Cost

Direct materials $ 7.50 Direct labor 2.45 Variable manufacturing overhead 5.80

Manufacturing cost per unit $15.75



(b) FELDE COMPANYIncome Statement

For the Year Ended December 31, 2014Variable Costing

Sales (80,000 lures X $25) $2,000,000 Variable cost of goods sold (80,000 lures X $15.75) $1,260,000Variable selling and administrative expenses (80,000 lures X $3.90) 312,000 1,572,000Contribution margin 428,000 Fixed manufacturing overhead 225,000Fixed selling and administrative expenses 240,100 465,100Net Income (loss) $ (37,100)

(c) Unit Cost

Direct materials $ 7.50 Direct labor 2.45 Variable manufacturing overhead 5.80 Fixed manufacturing overhead ($225,000 ÷ 90,000) 2.50

Manufacturing cost per unit $18.25

(d)FELDE COMPANYIncome Statement

For the Year Ended December 31, 2014Absorption Costing

Sales (80,000 lures X $25) $2,000,000 Cost of goods sold (80,000 lures X $18.25) 1,460,000Gross profit 540,000 Variable selling and administrative expenses (80,000 lures X $3.90) $312,000Fixed selling and administrative expenses 240,100 552,100Net Income $ (12,100 )


*EXERCISE 6-18

(a)Direct materials used $ 79,000Direct labor incurred 30,000Variable manufacturing overhead 21,500Variable manufacturing costs $130,500

Variable manufacturing cost per unit = $130,500 ÷ 9,000 = $14.50 per unit

Finished goods inventory cost = (9,000 – 8,200 units) X $14.50= $11,600

(b) Absorption costing would show a higher net income because a portion of the fixed costs are deferred to future periods. The following computa-tion indicates that finished goods inventory will be $4,000 higher under absorption costing which will cause its net income to be $4,000 higher.

Direct materials used $ 79,000Direct labor incurred 30,000Variable manufacturing overhead 21,500Fixed manufacturing overhead 45,000Total manufacturing costs $175,500

Total manufacturing costs per unit = $175,500 ÷ 9,000 = $19.50 per unit

Finished goods inventory cost = (9,000 – 8,200 units) X $19.50 = $15,600

Inventory (absorption costing) $15,600Inventory (variable costing) 11,600

$ 4,000

*EXERCISE 6-19

(a) Utility Expense

Months ina year X Kilowatt

hours X Hourly Charge = Variable

Utilities

12 X 500 X $0.40 = $2,400

Months ina year X Monthly

Fee = FixedUtilities

12 X $1,500 = $18,000


*EXERCISE 6-19 (Continued)

Variable CostingLabor:

Crate builders $38,000 Material:

Wood 54,000 Variable Overhead:

Utilities 2,400 Nails 350

Total manufacturing costs $94,750

(b)

Absorption CostingLabor:

Crate builders $ 38,000 Material:

Wood 54,000 Variable overhead:

Utilities 2,400 Nails 350

Fixed overhead:Utilities 18,000 Rent 21,400

Total manufacturing costs $134,150

(c) The entire difference in costs between the two methods is due to the fact that fixed overhead is included as part of manufacturing costs only under the absorption costing method. This difference amounts to $39,400 ($18,000 + $21,400).


SOLUTIONS TO PROBLEMS

PROBLEM 6-1A

(a) Sales were $2,000,000 and variable expenses were $1,100,000, which means contribution margin was $900,000 and CM ratio was .45. Fixed ex-penses were $1,035,000. Therefore, the break-even point in dollars is:

$1,035,000 = $2,300,000.45

(b) 1. The effect of this alternative is to increase the selling price per unit to $31.25 ($25 X 125%). Total sales become $2,500,000 (80,000 X $31.25). Thus, contribution margin ratio changes to 56% [($2,500,000 – $1,100,000) ÷ $2,500,000]. The new break-even point is:

$1,035,000 = $1,848,214 (rounded).56

2. The effects of this alternative are: (1) fixed costs decrease by $160,000, (2) variable costs increase by $100,000 ($2,000,000 X 5%), (3) total fixed costs become $875,000 ($1,035,000 – $160,000), and the contribution margin ratio becomes .40 [($2,000,000 – $1,100,000 – $100,000) ÷ $2,000,000]. The new break-even point is:

$875,000 = $2,187,500.40

3. The effects of this alternative are: (1) variable and fixed cost of goods sold become $734,000 each, (2) total variable costs become $884,000 ($734,000 + $92,000 + $58,000), (3) total fixed costs are $1,251,000 ($734,000 + $425,000 + $92,000) and the contribution margin ratio becomes .558 [($2,000,000 – $884,000) ÷ $2,000,000]. The new break-even point is:

$1,251,000 = $2,241,935 (rounded).558

Alternative 1 is the recommended course of action using break-even analysis because it has the lowest break-even point.


PROBLEM 6-2A

(a) (1)Current Year

Sales

Variable costsDirect materialsDirect laborManufacturing overhead ($350,000 X .70)Selling expenses ($250,000 X .40)Administrative expenses ($270,000 X .20)

Total variable costsContribution margin

$1,500,000

511,000290,000245,000100,000

54,000 1,200,000$ 300,000

Current Year Projected YearSales

Variable costsDirect materialsDirect laborManufacturing overheadSelling expensesAdministrative expenses


$1,500,000

511,000290,000245,000100,000

54,000 1,200,000$ 300,000

X 1.1

X 1.1X 1.1X 1.1X 1.1X 1.1X 1.1X 1.1

$1,650,000

562,100319,000269,500110,000

59,400 1,320,000$ 330,000

(2)Fixed Costs Current Year Projected year

Manufacturing overhead ($350,000 X .30)Selling expenses ($250,000 X .60)Administrative expenses ($270,000 X .80)

Total fixed costs

$105,000150,000

216,000$471,000

$105,000150,000

216,000$471,000


PROBLEM 6-2A (Continued)

(b) Unit selling price = $1,500,000 ÷ 100,000 = $15Unit variable cost = $1,200,000 ÷ 100,000 = $12Unit contribution margin = $15 – $12 = $3Contribution margin ratio = $3 ÷ $15 = .20

Break-even point in units = Fixed costs ÷ Unit contribution margin157,000 units = $471,000 ÷ $3.00

Break-even point in dollars = Fixed costs ÷ Contribution margin ratio$2,355,000 = $471,000 ÷ .20

(c) Sales dollarsrequired for = (Fixed costs + Target net income) ÷ Contribution margin ratiotarget net income

$3,355,000 = ($471,000 + $200,000) ÷ .20

(d) Margin of safetyratio

= (Expected sales – Break-even sales) ÷ Expected sales

29.8% = ($3,355,000 – $2,355,000) ÷ $3,355,000

(e) (1)Current Year

Sales

Variable costsDirect materialsDirect labor ($290,000 – $104,000)Manufacturing overhead ($350,000 X .30)Selling expenses ($250,000 X .90)Administrative expenses ($270,000 X .20)


$1,500,000

511,000186,000105,000225,000

54,000 1,081,000$ 419,000



Fixed costManufacturing overhead ($350,000 X .70)Selling expenses ($250,000 X .10)Administrative expenses ($270,000 X .80)

Total fixed costs

$245,00025,000

216,000$486,000

(2) Contribution margin ratio = $419,000 ÷ $1,500,000 = .28 (rounded)

(3) Break-even point in dollars = $486,000 ÷ .28 = $1,735,714 (rounded)

The break-even point in dollars declined from $2,355,000 to $1,735,714. 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 to compensate 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) which would increase the break-even point.


PROBLEM 6-3A

(a) ProductEconomy Standard Deluxe

Selling price $30 $50 $100Less: Variable costs 14 15 46 Contribution margin per unit $16 $35 $ 54

Ignoring the machine time constraint, the Deluxe product should be produced because it has the highest contribution margin per unit.

(b) ProductEconomy Standard Deluxe

Contribution margin per unit (a) $16 $ 35 $ 54Machine hours required (b) .5 .8 1.6 Contribution margin per limited resource (a)/(b) $32 $43.75 $33.75

(c) If additional machine hours become available, the additional time should be used to produce the Standard product since it has the highest contri-bution margin per machine hour.


PROBLEM 6-4A

(a)

Sales MixPercentage X

ContributionMargin Ratio =


AppetizersMain entreesDessertsBeverages

15%50%10%25%

XXXX

50%25%50%80%

====

.075

.125

.050

.200

.450

Total sales required to achieve target net income = ( $1,053,000 + $117,000 ) ÷ .45 = $2,600,000


Total SalesNeeded =

Sales fromEach Product


15%50%10%25%

XXXX

$2,600,000$2,600,000$2,600,000$2,600,000

====

$ 390,000 1,300,000 260,000 650,000$2,600,000

(b)

Sales MixPercentag

eX




25%25%10%40%

XXXX

50%10%50%80%

=

=

=

=

.125

.025

.050

.320

.520

Total sales required to achieve target net income = ( $1,638,000* + $117,000) ÷ .52 = $ 3,375,000

*$1,053,000 + $585,000 6-36 Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only)


Thus, sales would have to increase by $775,000 ($3,375,000 – $2,600,000) to achieve the target net income. This increase in sales is driven by the increase in fixed costs. The sales of each product line would be:


Total SalesNeeded =



25%25%10%40%

XXXX

$3,375,000$3,375,000$3,375,000$3,375,000

====

$ 843,750 843,750 337,500 1,350,000$3,375,000

(c)





15%50%10%25%

XXXX

50%10%50%80%

====

.075

.050

.050

.200

.375

The weighted-average contribution margin ratio computed in part (a) was 45%. With the contribution margin ratio on entrees falling to 10%, that average will now be 37.5% as shown previously. Applying this to the new fixed costs of $1,638,000 and target net income of $117,000 we get:

Total sales required to achieve target net income = ($1,638,000 + $117,000) ÷ .375 = $ 4,680,000


Total SalesNeeded =



15%50%10%25%

X

X

X

X

$4,680,000$4,680,000$4,680,000$4,680,000

====

$ 702,000 2,340,000 468,000 1,170,000$4,680,000

Relative to parts (a) and (b), the total required sales for (c) would increase. It appears that the least risky approach would be for Phil to switch to the new sales mix, but not to incur the additional fixed costs of expanding operations. If the switch in sales mix appears to be successful, then it may


be appropriate for him to incur the additional fixed costs necessary for expansion of operations.


PROBLEM 6-5A

(a) To determine the break-even point in dollars we must first calculate the contribution margin ratio for each company.

ContributionMargin ÷ Sales =

Contribution MarginRatio

Viejo CompanyNuevo Company

$220,000$320,000

÷÷

$500,000$500,000

==

.44

.64

FixedCosts ÷


Break-even Pointin Dollars

Viejo CompanyNuevo Company

$180,000$280,000

÷÷

.44

.64==

$409,091$437,500

(Actual Sales – Break-even Sales) ÷ Actual Sales =Margin of Safety

RatioViejo CompanyNuevo Company ($500,000

($500,000

––

$409,091)$437,500)

÷÷

$500,000$500,000

=

=

.182

.125

(b)Contribution

Margin ÷Net


LeverageViejo CompanyNuevo Company

$220,000$320,000

÷÷

$40,000$40,000

==

5.58.0

Because Nuevo Company relies more heavily on fixed costs, it has a higher degree of operating leverage. This means that its net income will be more sensitive to changes in sales. For a given change in sales, the change in net income will be 1.45 (8.0 ÷ 5.5) times higher for Nuevo Company than for Viejo Company.

(c)Viejo Company Nuevo

CompanySales $600,000* $600,000Variable costs 336,000** 216,000***Contribution margin 264,000 384,000Fixed costs 180,000 280,000Net income $ 84,000 $104,000

*$500,000 X 1.2**$280,000 X 1.2

***$180,000 X 1.2 Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only) 6-39


(d)Viejo Company Nuevo

CompanySales $400,000* $400,000Variable costs 224,000** 144,000***Contribution margin 176,000 256,000Fixed costs 180,000 280,000Net income (Loss) ($ 4,000) ($ 24,000)

*$500,000 X .80**$280,000 X .80

***$180,000 X .80

(e) In part (b) the degree of operating leverage of Nuevo Company was higher than that of Viejo Company, telling us that the net income of Nuevo Company was more sensitive to changes in sales than that of Viejo Company. In part (c) we see that a 20% increase in sales increased the net income of Nuevo Company by $64,000 ($104,000 – $40,000), while the net income of Viejo Company increased by only $44,000 ($84,000 – $40,000). However, in part (d) we see that a 20% decrease in sales resulted in a $64,000 ($40,000 + $24,000) decline in net income for Nuevo Company, while Viejo Company’s net income only declined by $44,000 ($40,000 + $4,000). The increased risk caused by higher operating leverage is also seen in part (a). Nuevo Company has a higher break-even point, and a lower margin of safety ratio than Viejo Company. Thus, while operating leverage can be very beneficial for a company that expects its sales to increase, it can also significantly increase a company’s risk.


PROBLEM 6-6A

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

Sales.......................................................... $75,000Variable costs ($31,500 + $13,500).......... 45,000 Contribution margin................................. 30,000Less: Fixed costs ($8,610 + $10,260)..... 18,870 Operating income..................................... $11,130

Contribution margin ratio = $30,000 ÷ $75,000 = 40%

Break-even point = $18,870 ÷ 40% = $47,175

(b) If a hired workforce replaces sales agents, commissions will be reduced to 8% of sales, or $6,000; but fixed costs will increase by $7,500.

Sales.......................................................... $75,000Variable costs ($31,500 + $6,000)............ 37,500 Contribution margin................................. 37,500Less: Fixed costs ($18,870* + $7,500).... 26,370 Operating income..................................... $11,130

*($8,610 + $10,260)


Break-even point = $26,370 ÷ 50% = $52,740

(c) Operating leverage = contribution margin ÷ operating income

(1) Current situation: from part (a)$30,000 ÷ $11,130 = 2.70

(2) Proposed situation: from part (b)$37,500 ÷ $11,130 = 3.37



The calculations indicate that at a sales level of $75 million, a percentage change in sales and contribution margin will result in 2.70 times that percentage change in operating income if Bonita continues to use sales agents. If they choose to employ their own, the change in operating income will be 3.37 times the percentage change in sales.

The higher contribution margin per dollar of sales and higher fixed costs from Bonita 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.

(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 8% commission along with additional fixed costs of $7.5 million. None of the other costs is relevant, because they will not change between alternatives.

Let the sales volume = S18% X S = (8% X S) + $7,500,000 .18S = .08S + $7,500,000 .10S = $7,500,000 S = $75,000,000


*PROBLEM 6-7A

(a) GARDNER COMPANYIncome Statement


Sales (2,500 tons X $2,000)..........................

Variable cost of goods soldInventory, January 1..............................Variable cost of goods manufactured [4,000 tons X ($2,000 X .15)]..............Variable cost of goods available for sale................................................Inventory, December 31 [1,500 tons X ($2,000 X .15)] ............Variable cost of goods sold..................Variable selling expenses [2,500 tons X ($2,000 X .10)].............

Contribution margin......................................Fixed manufacturing overhead....................Fixed administrative expenses....................Net income.....................................................

$ –0–

1,200,000

1,200,000

450,000 750,000

500,000

2,000,000 500,000

$5,000,000

1,250,000 3,750,000

2,500,000$1,250,000


*PROBLEM 6-7A (Continued)

GARDNER COMPANYIncome Statement


Sales (4,000 tons X $2,000)............................Variable cost of goods sold

Inventory, January 1...............................Variable cost of goods manufactured [2,500 tons X ($2,000 X .15)]...............Variable cost of goods available for sale..................................................Inventory, December 31..........................Variable cost of goods sold...................Variable selling expenses [4,000 tons X ($2,000 X .10)]...............

Contribution margin.......................................Fixed manufacturing overhead.....................Fixed administrative expenses......................Net income......................................................

$ 450,000

750,000

1,200,000 –0– 1,200,000

800,000

2,000,000 500,000

$8,000,000

2,000,000 6,000,000

2,500,000$3,500,000

(b) GARDNER COMPANYIncome Statement


Sales (2,500 tons X $2,000).......................Cost of goods sold

Inventory, January 1..........................Cost of goods manufactured............Cost of goods available for sale.......Inventory, December 31....................Cost of goods sold............................

Gross profit................................................Variable selling expenses [2,500 tons X ($2,000 X .10)].................Fixed administrative expenses................Net income.................................................

$ –0– 3,200,000 3,200,000 1,200,000

500,000 500,000

(1)

(2)

$5,000,000

2,000,000 3,000,000

1,000,000$2,000,000


(1) 4,000 X [($2,000 X .15) + ($2,000,000 ÷ 4,000)](2) 1,500 X [($2,000 X .15) + ($2,000,000 ÷ 4,000)]



GARDNER COMPANYIncome Statement


Sales (4,000 tons X $2,000)...................Cost of goods sold

Inventory, January 1......................Cost of goods manufactured.........Cost of goods available for sale....Inventory, December 31.................Cost of goods sold.........................

Gross profit............................................Variable selling expenses [4,000 tons X ($2,000 X .10)]..............Fixed administrative expenses.............Net income..............................................

$1,200,000 2,750,000 3,950,000 –0–

800,000 500,000

(1)

$8,000,000

3,950,000 4,050,000

1,300,000$2,750,000

(1) 2,500 X [($2,000 X .15) + ($2,000,000 ÷ 2,500)]

(c) The variable costing and the absorption costing net income can be reconciled as follows:

2013 2014

Variable costing net incomeFixed manufacturing overhead expensed with variable costingLess: Fixed manufacturing overhead expensed with absorption costingDifferenceAbsorption costing net income

$2,000,000

(1,250,000 )(1)

$1,250,000

750,000$2,000,000

$2,000,000

(2,750,000 )(2)

$3,500,000

(750,000 $2,750,000

)

(1)In 2013, with absorption costing $1,250,000 of the fixed manufacturing overhead is expensed as part of cost of goods sold, and $750,000

is included in the ending inventory.


(2)In 2014, with absorption costing $2,750,000 of fixed manufacturing overhead is expensed as part of cost of goods sold. This includes the fixed manufacturing overhead for 2014 of $2,000,000 plus $750,000 of fixed manufacturing overhead from 2013 that was included in the beginning inventory for 2014.



(d) Income parallels sales under variable costing as seen in the increase in net income in 2014 when 1,500 additional units were sold. In contrast, under absorption costing, income parallels production as seen in the higher net income in 2013 when production exceeded sales by 1,500 tons.


*PROBLEM 6-8A

(a)

DILITHIUM BATTERIES DIVISIONIncome Statement


_______________________________________________________________ 60,000 90,000

Produced Produced Sales (60,000 units X $30) $1,800,000 $1,800,000Cost of goods sold (60,000 units X $21) 1,260,000 (60,000 X $18) 1,080,000Gross profit 540,000 720,000Variable selling and administrative expenses (60,000 units x $2) 120,000 120,000Fixed selling and administrative expenses 50,000 50,000Net income $ 370,000 $ 550,000

(b)

DILITHIUM BATTERIES DIVISIONIncome Statement


_______________________________________________________________ 60,000 90,000 Produced Produced

Sales (60,000 units X $30) $1,800,000 $1,800,000Variable cost of goods sold (60,000 units X $12) 720,000 720,000Variable selling and administrative expenses (60,000 units X $2) 120,000 120,000Contribution margin 960,000 960,000Fixed manufacturing overhead 540,000 540,000Fixed selling and administrative expenses 50,000 50,000Net income $ 370,000 $ 370,000



(c) If the company produces 90,000 units, but only sells 60,000 units, then 30,000 units will remain in ending inventory. Under absorption costing these 30,000 units will each include $6 of fixed manufacturing overhead—a total of $180,000. However, under variable costing, fixed manufacturing overhead is expensed when incurred. This accounts for the $180,000 difference ($550,000 – $370,000) in net income. This is summarized as:

Net income under absorption costing $550,000Less: Fixed manufacturing overhead included in ending inventory (30,000 units X $6) 180,000Net income under variable costing $370,000

(d) Variable costing has a number of advantages over absorption costing for decision making and evaluation purposes. (1) The use of variable costing is consistent with cost-volume-profit and incremental analysis. (2) Net income computed under variable costing is unaffected by changes in production levels. Note that, under variable costing the company’s net income is $370,000 no matter what the level of production is. (3) Net income computed under variable costing is closely tied to changes in sales levels (not production levels), and therefore provides a more realistic assessment of the company’s success or failure during a period. (4) The presentation of fixed and variable cost components on the face of the variable costing income statement makes it easier to identify these costs and understand their effect on the business. Under absorption costing, the allocation of fixed costs to inventory makes it difficult to evaluate the impact of fixed costs on the company’s results.


PROBLEM 6-1B

(a) Sales were $2,400,000 and variable expenses were $1,536,000, which means contribution margin was $864,000 and CM ratio was .36. Fixed expenses were $936,000. Therefore, the break-even point in dollars is:

$936,000= $2,600,000

.36

(b) 1. The effect of this alternative is to increase the selling price per unit to $15 ($12 X 125%). Total sales become $3,000,000 (200,000 X $15). Thus, contribution margin changes to 48.8% [($3,000,000 – $1,536,000) ÷ $3,000,000]. The new break-even point is:

$936,000= $1,918,033 (rounded)

.488

2. The effects of this alternative are: (1) fixed costs decrease by $120,000, (2) variable costs increase by $144,000 ($2,400,000 X 6%), (3) total fixed costs become $816,000 ($936,000 – $120,000), and the contribution margin becomes .30 [($2,400,000 – $1,536,000 – $144,000) ÷ $2,400,000]. The new break-even point is:

$816,000= $2,720,000

.30

3. The effects of this alternative are: (1) variable and fixed cost of goods sold become $594,400 and $891,600, (2) total variable costs become $1,060,400 ($594,400 + $356,000 + $110,000), (3) total fixed costs are $1,411,600 ($891,600 + $325,000 + $195,000) and the contribution margin becomes .5582 [($2,400,000 – $1,060,400) ÷ $2,400,000]. The new break-even point is:

$1,411,600= $2,529,749 (rounded)

.558

Alternative 1 is the recommended course of action using break-even analysis because it has the lowest break-even point.


PROBLEM 6-2B

(a) (1)Current Year

Sales

Variable costsDirect materialsDirect laborManufacturing overhead ($240,000 X .20)Selling expenses ($200,000 X .30)Administrative expenses ($250,000 X .30)


$1,000,000

327,000190,000

48,00060,000

75,000 700,000$ 300,000

Current Year Projected YearSales

Variable costsDirect materialsDirect laborManufacturing overheadSelling expensesAdministrative expenses


$1,000,000

327,000190,000

48,00060,000

75,000 700,000$ 300,000

X 1.2

X 1.2X 1.2X 1.2X 1.2X 1.2X 1.2X 1.2

$1,200,000

392,400228,000

57,60072,000

90,000 840,000$ 360,000

(2)Fixed Costs Current Year Projected year

Manufacturing overhead ($240,000 X .80)Selling expenses ($200,000 X .70)Administrative expenses ($250,000 X .70)

Total fixed costs

$192,000140,000

175,000$507,000

$192,000140,000

175,000$507,000


PROBLEM 6-2B (Continued)

(b) Unit selling price = $1,000,000 ÷ 40,000 = $25.00Unit variable cost = $700,000 ÷ 40,000 = $17.50Unit contribution margin = $25.00 – $17.50 = $7.50Contribution margin ratio = $7.50 ÷ $25 = .30

Break-even point in units = Fixed costs ÷ Unit contribution margin67,600 units = $507,000 ÷ $7.50

Break-even point in dollars = Fixed costs ÷ Contribution margin ratio$1,690,000 = $507,000 ÷ .30

(c) Sales dollarsrequired for = (Fixed costs + Target net income) ÷ Contribution margin ratiotarget net income

$2,090,000 = ($507,000 + $120,000) ÷ .30

(d) Margin of safetyratio

= (Expected sales – Break-even sales) ÷ Expected sales

19.1% = ($2,090,000 – $1,690,000) ÷ $2,090,000

(e) (1)Current Year

Sales

Variable costsDirect materialsDirect labor ($190,000 – $90,000)Manufacturing overhead ($240,000 X .10)Selling expenses ($200,000 X .80)Administrative expenses ($250,000 X .30)


$1,000,000

327,000100,000

24,000160,000

75,000 686,000$ 314,000

Fixed costManufacturing overhead ($240,000 X .90)Selling expenses ($200,000 X .20)Administrative expenses ($250,000 X .70)

Total fixed costs

$ 216,00040,000

175,000$ 431,000



(2) Contribution margin ratio = $314,000 ÷ $1,000,000 = .314

(3) Break-even point in dollars = $431,000 ÷ .314 = $1,372,611 (rounded)

The break-even point in dollars declined from $1,690,000 to $1,372,611. This means that overall the company’s risk has declined because it doesn’t have to generate so much in sales. The two changes actually had opposing effects on the break-even point. By changing to a more commission-based approach to compensate 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 labor cost, both of which would increase the break-even point.


PROBLEM 6-3B

(a) ProductEconomy Standard Deluxe

Selling price $270 $450 $650Less: Variable costs 144 260 430 Contribution margin per unit $126 $190 $220

Ignoring the machine time constraint, the Deluxe product should be produced because it has the highest contribution margin per unit.

(b) ProductEconomy Standard Deluxe

Contribution margin per unit (a) $126 $ 190 $ 220Machine hours required (b) .6 .8 1.1 Contribution margin per limited resource (a)/(b) $210 $237.50 $ 200

(c) If additional machine hours become available, the additional time should be used to produce the Standard product since it has the highest contri-bution margin per machine hour.


PROBLEM 6-4B

(a)





15%60%10%15%

XXXX

60%25%40%80%

====

.09

.15

.04

.12

.40

Total sales required to achieve target net income = ( $352,000 + $176,000 ) ÷ .40 = $1,320,000

Sales MixPercentage X Total Sales =



15%60%10%15%

XXXX

$1,320,000$1,320,000$1,320,000$1,320,000

====

$ 198,000 792,000 132,000 198,000$1,320,000

(b)





25%40%10%25%

X

X

X

X

60%10%50%80%

====

.15

.04

.05

.20

.44

Total sales required to achieve target net income = ( $528,000* + $176,000) ÷ .44 = $1,600,000

*$352,000 X 1.5



Thus, sales would have to increase by $280,000 ($1,600,000 – $1,320,000) to achieve the target net income. This increase in sales is driven by the increase in fixed costs. The sales of each product line would be:


Total SalesNeeded =

Sales DollarsPer Product


25%40%10%25%

XXXX

$1,600,000$1,600,000$1,600,000$1,600,000

====

$ 400,000 640,000 160,000 400,000$1,600,000

(c)





15%60%10%15%

XXXX

60%10%50%80%

====

.09

.06

.05

.12

.32

The weighted-average contribution margin ratio computed in part (a) was 40%. With the contribution margin ratio on entrees falling to 10%, that average will now be 32% as shown above. Applying this to the new fixed costs of $528,000 and target net income of $176,000 we get:

Total sales required to achieve target net income = ($528,000 + $176,000) ÷ .32 = $2,200,000


Total Sales Needed =



15%60%10%15%

X

X

X

X

$2,200,000$2,200,000$2,200,000$2,200,000

====

$ 330,000 1,320,000 220,000 330,000$2,200,000



Relative to parts (a) and (b), the total required sales for (c) would increase. It appears that the least risky approach would be for Michael to switch to the new sales mix, but not to incur the additional fixed costs of expanding operations. If the switch in sales mix appears to be successful, then it may be appropriate for him to incur the additional fixed costs necessary for expansion of operations.


PROBLEM 6-5B

(a) To determine the break-even point in dollars we must first calculate the contribution margin ratio for each company.

ContributionMargin ÷ Sales =


Lyte CompanyDarke Company

$400,000$800,000

÷÷

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

==

.40

.80

FixedCosts ÷



Lyte CompanyDarke Company

$200,000$600,000

÷÷

.40

.80==

$500,000$750,000

(Actual Sales – Break-even Sales) ÷ Actual Sales =

Margin of Safety

Ratio

Lyte Company

Darke Company

($1,000,000

($1,000,000

–

–

$500,000)

$750,000)

÷

÷

$1,000,000

$1,000,000

=

=

.50

.25

(b)Contribution

Margin ÷Net


LeverageLyte CompanyDarke Company

$400,000$800,000

÷÷

$200,000$200,000

=

=

2.004.00

Because Darke Company relies more heavily on fixed costs, it has a higher degree of operating leverage. This means that its net income will be more sensitive to changes in sales. For a given change in sales, the change in net income will be 2.0 (4.00 ÷ 2.00) times higher for Darke Company than for Lyte Company.



(c)Lyte Company Darke

CompanySales $1,300,000* $1,300,000Variable costs 780,000** 260,000***Contribution margin 520,000 1,040,000Fixed costs 200,000 600,000Net income $ 320,000 $ 440,000

*$1,000,000 X 1.3 **$600,000 X 1.3***$200,000 X 1.3

(d)Lyte Company Darke

CompanySales $700,000* $700,000Variable costs 420,000** 140,000***Contribution margin 280,000 560,000Fixed costs 200,000 600,000Net income $ 80,000 ($ 40,000)

*$1,000,000 X .70 **$600,000 X .70***$200,000 X .70

(e) In part (b) the degree of operating leverage of Darke Company was higher than that of Lyte Company, telling us that the net income of Darke Company was more sensitive to changes in sales than that of Lyte Company. In part (c) we see that a 30% increase in sales increased the net income of Darke Company by $240,000 ($440,000 – $200,000), while the net income of Lyte Company increased by only $120,000 ($320,000 – $200,000). However, in part (d) we see that a 30% decrease in sales resulted in a $240,000 ($40,000 + $200,000) decline in net income for Darke Company, while Lyte Company’s net income only declined by $120,000 ($200,000 – $80,000). The increased risk caused by higher operating leverage is also seen in part (a). Darke Company has a higher break-even point, and a lower margin of safety ratio than Lyte Company. Thus, while operating leverage can be very beneficial for a company that expects its sales to increase, it can also significantly increase a company’s risk.


PROBLEM 6-6B

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

Sales.................................................................... $120,000Variable costs ($58,500 + $19,500)................... 78,000 Contribution margin........................................... 42,000Less: Fixed costs ($11,000 + $10,000)............. 21,000 Operating income............................................... $ 21,000


Break-even point = $21,000 ÷ 35% = $60,000

(b) If a hired workforce replaces sales agents, commissions will be reduced to 10% of sales, or $12,000; but fixed costs will increase by $12,000.

Sales.................................................................... $120,000Variable costs ($58,500 + $12,000)................... 70,500 Contribution margin........................................... 49,500Less: Fixed costs ($21,000* + $12,000)........... 33,000 Operating income............................................... $ 16,500

*($11,000 + $10,000)

Contribution margin ratio = $49,500 ÷ $120,000 = 41.25%

Break-even point = $33,000 ÷ 41.25% = $80,000

(c) Operating leverage = contribution margin ÷ operating income

(1) Current situation: from part (a)$42,000 ÷ $21,000 = 2.00

(2) Proposed situation: from part (b)$49,500 ÷ $16,500 = 3.00



The calculations indicate that at a sales level of $120 million, a percentage change in sales and contribution margin will result in 2.00 times that percentage change in operating income if Peaches continues to use sales agents. If they choose to employ their own, the change in operating income will be 3.00 times the percentage change in sales.

The higher contribution margin per dollar of sales and higher fixed costs from Peaches 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.

(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 (16.25% of sales) is exactly equal to the cost of paying employees 10% commission along with additional fixed costs of $12.0 million. None of the other costs is relevant, because they will not change between alternatives.

Let the sales volume = S16.25% X S = (10% X S) + $12,000 .1625S = .10S + $12,000 .0625S = $12,000 S = $192,000


*PROBLEM 6-7B

(a) FAB COMPANYIncome Statement


Sales (400,000 yards X $2.50).......................

Variable cost of goods soldInventory, January 1..............................Variable cost of goods manufactured [500,000 yards X $2.50 X 30%]...........Variable cost of goods available for sale.................................................Inventory, December 31 [100,000 yards X $2.50 X 30%]..........Variable cost of goods sold..................Variable selling expenses [400,000 yards X $2.50 X 10%]..........

Contribution margin......................................Fixed manufacturing overhead.....................Fixed administrative expenses.....................Net income.....................................................

$ –0–

375,000

375,000

75,000 300,000

100,000

400,000 100,000

$1,000,000

400,000 600,000

500,000 $ 100,000


*PROBLEM 6-7B (Continued)

FAB COMPANYIncome Statement


Sales (500,000 yards X $2.50).....................

Variable cost of goods soldInventory, January 1............................Variable cost of goods manufactured [400,000 yards X $2.50 X 30%]........Variable cost of goods available for sale..............................................Inventory, December 31......................Variable cost of goods sold................Variable selling expenses [500,000 yards X ($2.50 X 10%)].....

Contribution margin....................................Fixed manufacturing overhead..................Fixed administrative expenses..................Net income...................................................

$ 75,000

300,000

375,000 –0–

375,000

125,000

400,000 100,000

$1,250,000

500,000 750,000

500,000$ 250,000

(b) FAB COMPANYIncome Statement


Sales (400,000 yards X $2.50)...................Cost of goods sold

Inventory, January 1..........................Cost of goods manufactured............Cost of goods available for saleInventory, December 31.....................Cost of goods sold.............................

Gross profit................................................Variable selling expenses [400,000 yards X ($2.50 X .10)]..............Fixed administrative expenses.................Net income.................................................

$ –0– 775,000 775,000 155,000

100,000 100,000

(1)

(2)

$1,000,000

620,000 380,000

200,000$


180,000

(1) 500,000 X [($2.50 X 30%) + ($400,000 ÷ 500,000)](2) 100,000 X [($2.50 X 30%) + ($400,000 ÷ 500,000)]



FAB COMPANYIncome Statement


Sales (500,000 yards X $2.50)...............Cost of goods sold

Inventory, January 1......................Cost of goods manufactured.........Cost of goods available for sale...Inventory, December 31.................Cost of goods sold.........................

Gross profit............................................Variable selling expenses [500,000 yards X ($2.50 X .10)]..........Fixed administrative expenses.............Net income..............................................

$ 155,000 700,000 855,000 –0–

125,000 100,000

(1)

$1,250,000

855,000 395,000

225,000$

170,000

(1) 400,000 X [($2.50 X 30%) + ($400,000 ÷ 400,000)]

(c) The variable costing and the absorption costing income from opera-tions can be reconciled as follows:

2013 2014

Variable costing net incomeFixed manufacturing overhead expensed with variable costingLess: Fixed manufacturing overhead expensed with absorption costingDifferenceAbsorption costing income

$400,000

(320,000 )(1)

$100,000

80,000$180,000

$400,000

(480,000 )(2)

$250,000

(80,000 $170,000

)

(1)In 2013, with absorption costing $320,000 of the fixed manufacturing overhead is expensed as part of cost of goods sold, and $80,000

is included in the ending inventory.


(2)In 2014, with absorption costing $480,000 of fixed manufacturing overhead is expensed as part of cost of goods sold. This includes the fixed manufacturing overhead for 2014 of $400,000 plus $80,000 of fixed manufacturing overhead from 2013 that was included in the beginning inventory for 2014.



(d) Income parallels sales under variable costing as seen in the increase in net income in 2014 when 100,000 additional units were sold. In contrast, under absorption costing, income parallels production as seen in the higher net income in 2013 when production exceeded sales by 100,000.


*PROBLEM 6-8B

(a)

ELECTRICOIL DIVISIONIncome Statement


200,000 250,000 Produced Produced

Sales (200,000 units X $9) $1,800,000 $1,800,000Cost of goods sold (200,000 units X $5.50) 1,100,000 (200,000 X $5.00) 1,000,000Gross profit 700,000 800,000Variable selling and administrative expenses (200,000 units X $0.40) 80,000 80,000Fixed selling and administrative expenses 15,000 15,000Net income $ 605,000 $ 705,000

(b)

ELECTRICOIL DIVISIONIncome Statement


_______________________________________________________________

200,000 250,000 Produced Produced

Sales (200,000 units X $9) $1,800,000 $1,800,000Variable cost of goods sold (200,000 units X $3) 600,000 600,000Variable selling and administrative expenses (200,000 units X $0.40) 80,000 80,000Contribution margin 1,120,000 1,120,000Fixed manufacturing overhead 500,000 500,000Fixed selling and administrative expenses 15,000 15,000Net income $ 605,000 $ 605,000 Copyright © 2012 John Wiley & Sons, Inc. Weygandt, Managerial Accounting, 6/e, Solutions Manual (For Instructor Use Only) 6-69


(c) If the company produces 250,000 units, but only sells 200,000 units, then 50,000 units will remain in ending inventory. Under absorption costing these 50,000 units will each include $2.00 of fixed manufacturing cost—a total of $100,000. However, under variable costing, fixed manu-facturing cost is expensed when incurred. This accounts for the $100,000 difference ($705,000 – $605,000) in net income. This is summarized as:

Net income under absorption costing $705,000Less: Fixed manufacturing cost included in ending inventory 100,000Net income under variable costing $605,000

(d) Variable costing has a number of advantages over absorption costing for decision making and evaluation purposes. (1) The use of variable costing is consistent with cost-volume-profit and incremental analysis: (2) Net income computed under variable costing is unaffected by changes in production levels. Note that, under variable costing the company’s net income is $605,000 no matter what the level of production is. (3) Net income computed under variable costing is closely tied to changes in sales levels (not production levels), and therefore provides a more realistic assessment of the company’s success or failure during a period. (4) The presentation of fixed and variable cost components on the face of the variable costing income statement makes it easier to identify these costs and understand their effect on the business. Under absorption costing, the allocation of fixed costs makes it difficult to evaluate the impact of fixed costs on the company’s results.


BYP 6-1 DECISION-MAKING AT CURRENT DESIGNS

(a)

Rotomolded Kayaks+

Composite Kayaks=

Weighted Average Unit Contribution

Margin(($950 – $570) X .80) (($2,000 – $1,340) X .20) $436

(b) Break-even Sales = $820,000 ÷ $436 = 1,881 units

Break-even Sales Distribution: Rotomolded Kayaks = 1,881 X 80% = 1,505 units

Composite Kayaks = 1,881 X 20%= 376 units

(c) Target Net Income in Units:

Rotomolded Kayaks + Composite Kayaks =

Weighted-Average CM/Unit

($380 X .70) ($660 X .30) $464

Required Sales in Units = ($820,000 + $2,000,000) ÷ $464 = 6,078 units

Break-even Sales Distribution: Rotomolded Kayaks = 6,078 X 70%= 4,255

unitsComposite Kayaks = 6,078 X 30%

= 1,823 units

(d) CVP Income Statement

Rotomolded Composite Sales $2,000,000 $1,000,000Variable Costs 1,200,000 * 670,000 **Contribution Margin 800,000 330,000Fixed Costs 660,000 160,000 Net Income $ 140,000 $ 170,000

*($570 ÷ $950) X $2,000,000 **($1,340 ÷ $2,000) X $1,000,000


BYP 6-1 (Continued)

(e) Degree of Operating Leverage

Rotomolded Kayaks = $800,000 ÷ $140,000 = 5.71Composite Kayaks = $330,000 ÷ $170,000 = 1.94

At a sales mix of 2/3 to 1/3, the degree of operating leverage is nearly three times as high for the rotomolded kayaks as it is for the composite kayaks. This means that the company’s net income will respond more quickly to a change in the sales of rotomolded kayaks than to composite kayaks. For example, an increase in sales of the rotomolded kayaks will increase the company’s net income at a faster rate than an increase in the sales of the composite kayaks. This result will differ depending on what sales mix assumption is made.


BYP 6-2 DECISION-MAKING ACROSS THE ORGANIZATION

(a)Sales (10,000 seats X $500)

$5,000,000Variable costs (10,000 seats X $200) 2,000,000Contribution margin 3,000,000Fixed costs 2,000,000Net income $1,000,000

(b) Contribution margin ratio = $3,000,000 ÷ $5,000,000 = .60

Break-even point in dollars = $2,000,000 ÷ .60 = $3,333,333

Margin of safety ratio = ($5,000,000 – $3,333,333) ÷ $5,000,000 = .333

Degree of operating leverage = $3,000,000 ÷ $1,000,000 = 3.0

(c)Sales (10,000 seats X $500)

$5,000,000Variable costs (10,000 seats X $ 100) 1,000,000Contribution margin 4,000,000Fixed costs 3,000,000Net income $1,000,000

(d) Contribution margin ratio = $4,000,000 ÷ $5,000,000 = .80

Break-even point in dollars = $3,000,000 ÷ .80 = $3,750,000

Margin of safety ratio = ($5,000,000 – $3,750,000) ÷ $5,000,000 = .25

Degree of operating leverage = $4,000,000 ÷ $1,000,000 = 4.00

(e) By automating its manufacturing process the company will replace some of its variable costs with fixed costs. This shift toward more fixed costs will increase its break-even point from $3,333,333 to $3,750,000 and reduce its margin of safety from 33.3% to 25%. This means that under the old system sales could fall by 33.3% percent before the company would operate at a loss, whereas under the automated system they could only fall by 25%. Both of these findings suggest that the company would be riskier with the automated system. However, the company’s degree of operating leverage would increase from 3.0 to 4.00. This means that with a change in sales, the change in net income would be 1.33 (4 ÷ 3)


times higher under the automated system. This would be good if the company expects sales to increase, but would be bad if the company’s sales fall.


BYP 6-3 MANAGERIAL ANALYSIS

(a) The contribution margin ratios under each approach are:

Current approach $500,000/$2,000,000 = .25Automated approach $1,000,000/$2,000,000 = .50

This means that for every dollar of sales, net income goes up by 25 cents under the current approach, but by $.50 under the automated approach.

(b) The break-even points in sales dollars under each approach are:

Current approach $380,000/.25 = $1,520,000Automated approach $800,000/.50 = $1,600,000

This shows that, under the automated approach, the company’s sales would have to be 5.26% higher just to break-even.

(c) At the current level of sales, the margin of safety ratio under each approach is:

Current approach ($2,000,000 – $1,520,000)/$2,000,000 = .24Automated approach ($2,000,000 – $1,600,000)/$2,000,000 = .20

The company has a low margin of safety under either approach. Under the current approach sales could drop 24% before the company would be operating at a loss. Under the automated approach the company’s sales could drop by 20% before it would be operating at a loss.

(d) The degree of operating leverage under each approach at the current level of sales is:

Current approach $500,000/$120,000 = 4.17Automated approach $1,000,000/$200,000 = 5.00

This means that for a 10% drop in sales net income would drop by 41.7 percent for the current approach, but 50% for the automated


approach. Recall, however, that at the current level of sales the company makes considerably more money using the automated approach.


BYP 6-3 (Continued)

(e) In order to solve for the sales level where net income would be equal under either approach, set the two CVP equations equal to each other and solve for sales:

Sales – ((1 – .75) X Sales) – $380,000 = Sales – ((1 – .5) X Sales) – $800,000(.25 X Sales) – $380,000 = (.5 X Sales) – $800,000(.25 X Sales) = $420,000

Sales = $1,680,000

When sales are equal to $1,680,000 the company would make the same amount of income under either approach.

Current approach $1,680,000 – [(1 – .25) X $1,680,000] – $380,000 = $40,000Automated approach $1,680,000 – [(1 – .5) X $1,680,000] – $800,000 = $40,000

(f) Based upon this numeric analysis it would appear that the decision to purchase the automated system would be a good decision. The current level of sales far exceeds the break-even point, and, unless sales were to fall all the way to $1,680,000, the company would be better off under the automated system. However, there are many difficult issues that should also be considered. Not-the-least of these is the decision to lay-off 15 employees, many of whom have likely been with the company for a long time. Also, the company should carefully evaluate whether the automated system will be able to attain the same level of quality as the skilled employees. Perhaps the automated system would be more appropriate for some of the painting work, while skilled labor would be more appropriate for other painting work.


BYP 6-4 REAL-WORLD FOCUS

(a)($ in millions)

ConsumerProducts

PetProducts

Soup andInfant-Feeding

Products Sales Variable costs Contribution margin

Contribution margin÷ Sales

Contribution margin ratio

Division sales÷ Total sales

Sales mix percentage

$1,031.8 610.0$ 421.8

$ 421.8 1,031.8 40.9%

$1,031.8 2,171.1 47.5%

$ 837.3 350.0$ 487.3

$ 487.3 837.3 58.2%

$ 837.3 2,171.1 38.6%

$ 302.0 100.0$ 202.0

$ 202.0 302.0 66.9%

$ 302.0 2,171.1 13.9%

(b)




Consumer productsPet productsSoup and infant-feeding products

47.5%38.6%

13.9%

40.9%58.2%

66.9%

.194 .225

.093 .512

Break-even point in dollars = $860,300,000 ÷ .512 = $1,680,273,438

Sales MixPercentage X Total Sales =

Sales fromEach Product*

Consumer productsPet productsSoup and infant- feeding productsTotal sales

47.5%38.6%

13.9%

XX X

$1,680,273,438$1,680,273,438

$1,680,273,438

==

=

$ 798,129,883 648,585,547

233,558,008$1,680,273,438

*Sales are rounded



(a) The four primary product lines are FedEx Express (provides express transportation); FedEx Ground (small package ground delivery); FedEx Freight (regional, less-than-truckload freight service); and FedEx Services (Kinkos). The key factors affecting operating results are the volumes of shipments transported through networks; the mix of services purchased by customers; the prices obtained for services; ability to manage cost structure for capital expenditures and operating expenses; and ability to match operating costs to shifting volumes.

(b)

FEDEX GROUNDIncome Statement

For the Year Ended May 31, 2008Variable Costing

(In Millions)____________________________________________________________

Revenues....................................................... $ 6,751Variable costs:

Salaries and employee benefits.............. $1,073Purchased transportation....................... 2,691Fuel............................................................ 201Maintenance and repairs......................... 145Intercompany charges............................. 658 4,768Contribution margin................................ 1,983

Fixed costs:Rentals...................................................... 189Depreciation and amortization................ 305Other.......................................................... 753 1,247

Net income..................................................... $ 736

ContributionMargin ÷ Revenues =


$1,983 ÷ $6,751 = 29.4%

Fixed Costs ÷ContributionMargin Ratio =


$1,247 ÷ .294 = $4,241.5 million


BYP 6-5 (Continued)

(c)(i)

2008 2006

FedEx ExpressFedEx GroundFedEx FreightFedEx Services

$24,421 ÷ $38,244 = 63.9% 6,751 ÷ $38,244 = 17.6% 4,934 ÷ $38,244 = 12.9% 2,138 ÷ $38,244 = 5.6%

$21,446 ÷ $32,485 = 66.0% 5,306 ÷ $32,485 = 16.3% 3,645 ÷ $32,485 = 11.2% 2,088 ÷ $32,485 = 6.4%

Total $38,244 $32,485

(ii) 2008 2006FedEx ExpressFedEx GroundFedEx FreightFedEx Services

7.8%10.9%

6.7%(41.7%)*

8.2%13.3%13.3%____

*$(891) ÷ $2,138

(iii) In part (ii) we see that in all divisions the company’s operating margins declined. We also see in part (ii) that in 2006 FedEx Express had the lowest operating margin (8.2%), and FedEx Services had the lowest in 2008 (–41.7%) while FedEx Ground had the highest (13.3% and 10.9%). In part (i) we see that the company shifted its sales mix percentage down in FedEx Express (66.0% to 63.9%) and FedEx Services (6.4% and 5.6%) but increased its sales mix percentage for FedEx Ground (16.3% to 17.6%) and FedEx Freight (11.2% to 12.9%). Thus, during this period two of the company’s divisions became more profitable, and the company successfully shifted its sales mix so that more of its revenue came from its more profitable divisions.



(a) Smart Balance relies very heavily on outsourcing. It keeps it employees and investments in fixed assets to a minimum. As a consequence it has very low fixed costs.

(b) The company keeps new-product development and marketing in house.

(c) The potential advantage of having very low fixed costs is that the company has a lower break-even point. It can be profitable at relatively low volumes of sales and therefore it has less potential for financial failure.

(d) The potential disadvantage of this approach is that its low fixed costs means that the company has low operating leverage. If the company’s sales increase significantly, it would not enjoy the same increase in profitability as a company that was producing its own goods.


BYP 6-7 COMMUNICATION ACTIVITY

MEMO

To: Bjorn Borg—CEO

From: Student

Re: Best use of limited resources

I share your concern, that, since we are operating at full capacity, we need to ensure that our product mix maximizes our profitability. The decision of how to best utilize our limited productive resources is one of the most important decisions we face. We currently make two different anchors, a traditional fishing anchor, and a high-end yacht anchor. The contribution margin per unit produced of the yacht anchor is three times that of the fishing anchor, thus one might logically assume that we should shift our production toward producing the yacht anchor. However, this assumption ignores an element that is critical to the decision. In order to make a proper decision, we would need to know the contribution margin per unit of limited resource that each product produces. While the yacht anchor has a very high contribution margin, it also consumes considerably more productive resources. I propose that a study be done to determine exactly how much of the limited productive resource is consumed by one unit of each of the two anchor types.

In addition, at the same time that this study is being undertaken, I propose that the marketing department undertake a study of the demand for each anchor type. This is important so that we don’t produce anchors that we can’t sell.

Finally, a shift in our product mix would maximize our profitability at our current level of productive capacity. However, we should also consider a more long-term solution to our production constraints. Since we have been operating at, or near full capacity for two years, it would seem appropriate to undertake a study of whether an acquisition of additional plant equipment would be appropriate.


*BYP 6-8 ETHICS CASE

(a) The division’s net income increased by $225,000 ($525,000 – $300,000). This represents a 75% increase over the previous year ($225,000 ÷ $300,000). Thus Brett’s bonus would be 75 X $5,000 = $375,000.

(b) In 2013 the number of units produced and sold were equal. When this occurs variable costing and absorption costing provide the same results. Thus, in 2013, net income under variable costing would have been $300,000. In 2014, units produced exceeded units sold by 5,000 units. However, net income under variable costing is not impacted by the number of units produced. Since the number of units sold did not change from 2013 to 2014, and the selling price, variable cost per unit, and total fixed costs didn’t change, the division’s net income in 2014 would equal its 2013 income of $300,000.

(c) In part (b) it was determined that the division’s net income would have been $300,000 in 2014 under variable costing. Since this is the same as 2013 net income, Brett would not receive a bonus.

(d) If Brett intentionally overproduced inventory in order to increase his bonus, then his actions were unethical. Overproduction of inventory increases the company’s costs related to inventory, such as storage, handling, waste and theft. Based on the information provided wecan’t actually determine Brett’s motives. He may have believed that just-in-time inventory was causing the company to lose sales due to “stock-outs.” If that was the case, there would be options available to the company other than totally giving up on just-in-time practices. In order to eliminate any potential conflicts of interest between Brett and the company, and to ensure that his actions are in the best interest of the company, the company could begin preparing variable costing income statements to supplement its absorption costing statements for the purpose of calculating bonuses. This would eliminate any incentive Brett might have to over-produce, as well as providing useful information for other internal management decision making.


BYP 6-9 ALL ABOUT YOU

(a) Using a common equation for CVP analysis,Sales = Variable Costs + Fixed Costs + Net Income, and substituting the information provided, and knowing that at break-even, net income = $0,

($26 X 300) = Variable Costs + ($4,000 + $1,460) + $0$7,800 = Variable Costs + $5,460 + $0$2,340 = Variable Costs (in total)or $7.80 (variable costs/member/month) = $2,340 ÷ 300

(b) To find the sales required to reach a target net income, contribution margin must be calculated.Contribution Margin = Sales – Variable CostsContribution Margin = $7,800 – $2,340Contribution Margin = $5,460Contribution Margin per Unit = $5,460/300 memberships = $18.20Contribution Margin Ratio = $5,460/$7,800 = 70%

To compute the sales required to reach a target net income of $3,640.Required Sales in Units = (Fixed Costs +

Target Net Income)/Contribution Margin

per Unit

Required Sales in Units = ($5,460 + $3,640)/$18.20Required Sales in Units = 500 memberships

Required Sales in Dollars = 500 memberships X $26= $13,000

Using the contribution margin ratio,Required Sales in Dollars = (Fixed Costs +

Target Net Income)/Contribution Margin Ratio

Required Sales in Dollars = ($5,460 + $3,640)/70%Required Sales in Dollars = $13,000

(c) Answers will vary. Suggested examples include franchise fees, employee wages, utilities, supplies, and maintenance.

(d) Answers will vary.


BYP 6-10 CONSIDERING CORPORATE SOCIAL RESPONSIBILITY

Discussion Guide: If reduction of greenhouse gas emissions is a goal, then one step toward attainment of that goal is to assign a cost to greenhouse-gas emissions. One approach that is currently being used is the buying and selling of carbon-emission rights. As companies buy and sell emission rights, the price of polluting becomes a tangible factor in the formulations that will be used to make future energy-source decisions. This approach has been effective in addressing similar issues, such as the reduction of sulfur emissions. However, as suggested in the “No” response, many believe that, to be effective and fair, an enforceable international agreement on such an approach would be necessary. In the United States, companies currently participate on a voluntary basis; in some other countries, participation is required. Another factor to consider in these decisions is the timing of conversion to new technology. A gradual conversion to new technologies as existing power plants reach the end of their productive lives would be far less costly than a rapid conversion to new technologies that required scrapping existing plants before they are fully depreciated. Decisions about which plants to replace and when to replace them will require careful cost-benefit analyses.


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