Ch04

CHAPTER 4COST-VOLUME-PROFIT ANALYSIS: A MANAGERIAL PLANNING TOOL

DISCUSSION QUESTIONS

1. CVP analysis allows managers to focus on selling prices, volume, costs, profits, and sales mix. Many different “what-if” questions can be asked to assess the effect of changes in key variables on profits.

2. The units sold approach defines sales vol-ume in terms of units of product and gives answers in these same terms. The unit con-tribution margin is needed to solve for the break-even units. The sales revenue ap-proach defines sales volume in terms of rev-enues and provides answers in these same terms. The overall contribution margin ratio can be used to solve for the break-even sales dollars.

3. Break-even point is the level of sales activity where total revenues equal total costs, or where zero profits are earned.

4. At the break-even point, all fixed costs are covered. Above the break-even point, only variable costs need to be covered. Thus, contribution margin per unit is profit per unit, provided that the unit selling price is greater than the unit variable cost (which it must be for break even to be achieved).

5. Variable cost ratio = Variable costs/Sales

Contribution margin ratio = Contribution margin/Sales

Contribution margin ratio = 1 – Variable cost ratio

6. No. The increase in contribution is $9,000 (0.3 × $30,000), and the increase in advertis-ing is $10,000. If the contribution margin ratio is 0.40, then the increased contribution mar-gin is $12,000 (0.4 × $30,000). This is $2,000 above the increased advertising expense, so the increased advertising would be a good decision.

7. Sales mix is the relative proportion sold of each product. For example, a sales mix of 3:2 means that three units of one product are sold for every two of the second product.

8. Packages of products, based on the ex-pected sales mix, are defined as a single product. Selling price and cost information for this package can then be used to carry out CVP analysis.

9. This statement is wrong; break-even analy-sis can be easily adjusted to focus on tar-geted profit.

10. The basic break-even equation is adjusted for targeted profit by adding the desired tar-geted profit to the total fixed costs in the nu-merator. The denominator remains the con-tribution margin per unit.

11. A change in sales mix will change the contri-bution margin of the package (defined by the sales mix), and thus will change the units needed to break even.

12. Margin of safety is the sales activity in excess of that needed to break even. The higher the margin of safety, the lower the risk.

13. Operating leverage is the use of fixed costs to extract higher percentage changes in prof-its as sales activity changes. It is achieved by increasing fixed costs while lowering variable costs. Therefore, increased leverage implies increased risk, and vice versa.

14. Sensitivity analysis is a “what-if” technique that examines the impact of changes in un-derlying assumptions on an answer. A com-pany can input data on selling prices, vari-able costs, fixed costs, and sales mix and set up formulas to calculate break-even points and expected profits. Then, the data can be varied as desired to see what impact changes have on the expected profit.

15. A declining margin of safety means that sales are moving closer to the break-even point. Profit is going down, and the possibility of loss is greater. Managers should analyze the reasons for the decreasing margin of safety and look for ways to increase revenue and/or decrease costs.

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4-24-2

MULTIPLE-CHOICE EXERCISES

4–1 d

4–2 c

4–3 a

4–4 d

4–5 e

4–6 b

4–7 b

4–8 d

4–9 d Break-even units = = 3,000

4–10 d Variable cost ratio = = 0.80, or 80%

Contribution margin ratio = = 0.20, or 20%

4–11 e

4–12 a Units to be sold = = 6,200

4-4-11

CORNERSTONE EXERCISES

Cornerstone Exercise 4–13

1. Variable cost per unit = Direct materials + Direct labor

+ Variable factory overhead + Variable selling expense

= $30 + $5 + $12 + $2

= $49

2. Total fixed expense = $14,000 + $15,400 = $29,400

3. Head-First CompanyContribution Margin Income Statement

For the Coming Year

Total Per Unit

Sales ($70 × 5,000 helmets).................................. $350,000 $70Total variable expense ($49 × 5,000)................... 245,000 49 Total contribution margin..................................... $105,000 $21Total fixed expense............................................... 29,400 Operating income ................................................. $ 75,600


1. Break-even units =

=

= 1,400 helmets


At Break-Even Total

Sales ($70 × 1,400 helmets)....................................................... $98,000Total variable expense ($49 × 1,400)......................................... 68,600 Total contribution margin.......................................................... $29,400Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 0

4-4-22


1. Variable cost ratio =

=

= 0.70, or 70%

2. Contribution margin ratio =

=

=

= 0.30, or 30%


For the Coming YearPercentof Sales

Sales ($70 × 5,000 helmets).................................. $350,000 100%Total variable expense ($49 × 5,000)................... 245,000 70 Total contribution margin..................................... $105,000 30Total fixed expense............................................... 29,400 Operating income ................................................. $ 75,600


1. Break-even sales dollars =

=

= $98,000

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Cornerstone Exercise 4–16 (Concluded)


At Break-Even Total

Sales............................................................................................ $98,000Total variable expense ($98,000 × 0.70).................................... 68,600 Total contribution margin.......................................................... $29,400Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 0



=

= 5,300 helmets


At 5,300 Helmets Sold Total

Sales ($70 × 5,300 helmets)....................................................... $371,000Total variable expense ($49 × 5,300)......................................... 259,700 Total contribution margin.......................................................... $111,300Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 81,900


1. Sales for target income =

=

= $371,000

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At 5,300 Helmets Sold Total

Sales............................................................................................ $371,000Total variable expense ($371,000 × 0.70).................................. 259,700 Total contribution margin.......................................................... $111,300Total fixed expense.................................................................... 29,400 Operating income....................................................................... $ 81,900


1. Any package with 5 bicycle helmets for every 1 motorcycle helmet is fine. For example, 5:1, or 10:2, or 30:6. Throughout the rest of this exercise, we will use 5:1.

Unit Unit Package UnitVariable Contribution Sales Contribution

Product Price Cost Margin Mix Margin

Bicycle helmet $ 70 $ 49 $21 5 $105Motorcycle helmet 220 143 77 1 77 Package total $182

2. Break-even packages =

=

= 300 packages

Break-even bicycle helmets = Number of packages × Sales mix amount

= 300 × 5

= 1,500

Break-even motorcycle helmets = Number of packages × Sales mix amount

= 300 × 1

= 300

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At Break-Even Total

Sales [($70 × 1,500) + ($220 × 300)]........................................... $171,000Total variable expense [($49 × 1,500) + ($143 × 300)].............. 116,400 Total contribution margin.......................................................... $ 54,600Total fixed expense.................................................................... 54,600 Operating income....................................................................... $ 0



= 0.3193

Break-even sales dollars =

=

= $170,999


At Break-Even Sales Dollars

Total Sales............................................................................................ $170,999Total variable expense ($170,999 × 0.6807).............................. 116,399 Total contribution margin.......................................................... $ 54,600Total fixed expense.................................................................... 54,600 Operating income....................................................................... $ 0

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1. Margin of safety in units = Budgeted units – Break-even units

= 5,000 – 1,400

= 3,600

2. Margin of safety in sales revenue = Budgeted sales – Break-even sales

= $350,000 – $98,000

= $252,000


Degree of operating leverage =

=

= 1.4


1. Percent change in operating income = DOL × % Change in sales

= 1.4 × 15%

= 21%

2. Expected operating income = Original income + (% Change × Original income)

= $75,600 + (0.21 × $75,600)

= $91,476

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EXERCISES

Exercise 4–24

1. Direct materials........................................................................... $3.90Direct labor.................................................................................. 1.40Variable overhead....................................................................... 2.10Variable selling and administrative expense........................... 1 .60 Unit variable cost........................................................................ $9 .00

Unit contribution margin = Price – Unit variable cost

= $16 – $9

= $7

2. Contribution margin ratio = = 0.4375, or 43.75%

Variable cost ratio = = 0.5625, or 56.25%

3. Break-even units = = 12,850

4. Sales ($16 × 12,850).................................................................... $205,600Variable cost ($9 × 12,850)......................................................... 115,650

Total contribution margin..................................................... $ 89,950Less: Fixed expenses ($52,000 + $37,950)............................... 89,950

Operating income.................................................................. $ 0

Exercise 4–25

1. Unit variable cost = $7.60 × 0.60 = $4.56

Unit contribution margin = $7.60 – $4.56 = $3.04


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Exercise 4–25 (Concluded)

3. Break-even sales revenue = $7.60 × 115,000 = $874,000

OR

Break-even sales revenue = = $874,000

4. Sales............................................................................................ $874,000Less: Variable costs................................................................... 524,400 Contribution margin................................................................... $349,600Less: Fixed costs........................................................................ 349,600 Operating income....................................................................... $ 0

Exercise 4–26


= = 0.20, or 20%

2. Variable cost ratio = = 0.80, or 80%

OR

Variable cost ratio = 1 – Contribution margin ratio = 1.00 – 0.20 = 0.80

3. Break-even revenue =

= = $34,500

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Exercise 4–27

1. Sales ($14 × 27,000).................................................................... $378,000Variable cost ($9.50 × 27,000).................................................... 256,500

Total contribution margin..................................................... $121,500Less: Fixed expenses................................................................. 126,000 Operating income....................................................................... $ (4,500 )


3. Units to earn target income = = 30,200

Exercise 4–28


=

= 187,500

2. Unit variable cost includes all variable costs on a unit basis:

Direct materials..................................................................... $0.27Direct labor............................................................................ 0.58Variable overhead................................................................. 0.63Variable selling...................................................................... 0 .17 Unit variable cost.................................................................. $1 .65

Unit variable manufacturing cost includes the variable costs of production on a unit basis:

Direct materials..................................................................... $0.27Direct labor............................................................................ 0.58Variable overhead................................................................. 0 .63 Unit variable manufacturing cost........................................ $1 .48

Unit variable cost is used in CVP because it includes all variable costs, not just manufacturing costs.

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3. Units to earn $12,600 =

= 203,250

4. Sales revenue to earn $12,600 = 203,250 × $2.45 = $497,962.50

Exercise 4–29


2. Expected sales in units.............................................................. 380,000Break-even units......................................................................... (208,000)Margin of safety (in units).......................................................... 172,000

3. Expected sales revenue ($6.28 × 380,000)................................ $2,386,400Break-even sales revenue*........................................................ 1,306,240 Margin of safety (in dollars)....................................................... $1,080,160

*Break-even revenue = Price × Break-even units = $6.28 × 208,000 units

Exercise 4–30

A B C D Sales $15,000 $15,600* $16,250* $10,600Total variable costs 5,000 11,700 9,750 5,300 *

Total contribution margin $10,000 $ 3,900 $ 6,500* $ 5,300*Total fixed costs 9,500 * 4,000 6,136 * 4,452

Operating income (loss) $ 500 $ (100 )* $ 364 $ 848

Units sold 3,000* 1,300 125 1,000Price per unit $5.00 $12* $130 $10.60*Variable cost per unit $1.67* $9 $78* $5.30*Contribution margin per unit $3.33* $3 $52* $5.30*Contribution margin ratio 67%* 25%* 40% 50%*Break even in units 2,853* 1,333* 118* 840*

*Designates calculated amount.

(Note: Calculated break-even units that include a fractional amount have been rounded to the nearest whole unit.)

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Exercise 4–31

1. Variable cost ratio = = 0.45, or 45%

Contribution margin ratio = = 0.55, or 55%

2. Because all fixed costs are covered by break even, any revenue above break even contributes directly to operating income.

Sales Contribution margin ratio = Increased operating income

$30,000 × 0.55 = $16,500

Therefore, operating income will be $16,500 higher.

3. Break-even sales revenue = = $114,545 (rounded to the nearest

dollar)

Sales............................................................................................ $114,545Less: Variable cost ($114,545 × 0.45)........................................ 51,545

Contribution margin.............................................................. $ 63,000Less: Fixed cost.......................................................................... 63,000

Operating income.................................................................. $ 0

4. Expected sales............................................................................ $315,000Break-even sales........................................................................ 114,545

Margin of safety..................................................................... $200,455

5. Sales revenue............................................................................. $280,000Break-even sales........................................................................ 114,545

Margin of safety..................................................................... $165,455

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Exercise 4–32

1. Sales mix is 2:1 (twice as many DVDs are sold as equipment sets).

2. Variable Sales TotalProduct Price – Cost = CM × Mix = CM

DVDs $12 $4 $8 2 $16Equipment sets 15 6 9 1 9

Total $25

Break-even packages = = 2,800

Break-even DVDs = 2 × 2,800 = 5,600

Break-even equipment sets = 1 × 2,800 = 2,800

Exercise 4–33

1. Sales mix is 2:1:4 (twice as many DVDs will be sold as equipment sets, and four times as many yoga mats will be sold as equipment sets).


DVDs $12 $ 4 $8 2 $16Equipment sets 15 6 9 1 9Yoga mats 18 13 5 4 20

Total $45


Break-even DVDs = 2 × 2,630 = 5,260

Break-even equipment sets = 1 × 2,630 = 2,630

Break-even yoga mats = 4 × 2,630 = 10,520

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3. Switzer CompanyIncome Statement

For the Coming Year

Sales............................................................................................ $555,000Less: Total variable costs.......................................................... 330,000

Contribution margin.............................................................. $225,000Less: Total fixed costs............................................................... 118,350

Operating income.................................................................. $106,650

Contribution margin ratio = = 0.405, or 40.5%

Break-even revenue = = $292,222

4. Margin of safety = $555,000 – $292,222 = $262,778

Exercise 4–34

1. Sales mix is 3:5:1 (three times as many small basics will be sold as carved models, and five times as many large basics will be sold as carved models).


Small basic $120 $ 70 $50 3 $150Large basic 200 150 50 5 250Carved model 350 275 75 1 75

Total $475

Break-even packages = = 940

Break-even small basic models = 3 × 940 = 2,820

Break-even large basic models = 5 × 940 = 4,700

Break-even carved models = 1 × 940 = 940

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3. Sonora CompanyIncome Statement

For the Coming Year

Sales............................................................................................ $17,100,000Less: Total variable costs.......................................................... 12,350,000

Contribution margin.............................................................. $ 4,750,000Less: Total fixed costs............................................................... 446,500

Operating income.................................................................. $ 4,303,500

Contribution margin ratio = = 0.2778, or 27.78%

Break-even revenue = = $1,607,271

4. Margin of safety = $17,100,000 – $1,607,271 = $15,492,729

Exercise 4–35

Break-even point = 2,500 units; + line is total revenue, and x line is total cost.

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X

X

Exercise 4–35 (Continued)

2. a. Fixed costs increase by $5,000:

Break-even point = 3,750 units

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X

X


2. b. Unit variable cost increases to $7:


4-4-1717

X

X


2. c. Selling price increases to $12:


4-4-1818

X

X


2. d. Both fixed costs and unit variable cost increase:


Exercise 4–36

1. Unit contribution margin = = $27

Break-even units = = 20,000 units

2. Operating income = 30,000 × $27 = $810,000

3. Contribution margin ratio = = 0.45, or 45%

Break-even sales revenue = = $1,200,000

Profit = ($200,000 × 0.45) – $54,000 = $36,000

4-4-1919

X

X

Exercise 4–37

1. Break-even sales dollars = = $1,580,431

*Contribution margin ratio = = 0.58, or 58%

2. Margin of safety = $2,250,000 – $1,580,431 = $669,569

3. Degree of operating leverage =

=

= 3.36

4. Percent change in operating income = 3.36 × 0.20 = 0.67

New operating income = $388,350 + (0.67 × $388,350) = $648,545

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Exercise 4–38

1. Variable Sales PackageProduct Price – Cost = CM × Mix = CM

Vases $40 $30 $10 2 $20Figurines 70 42 28 1 28

Total $48


Break-even vases = 2 × 625 = 1,250

Break-even figurines = 1 × 625 = 625

2. The new sales mix is 3 vases to 2 figurines.

Variable Sales PackageProduct Price – Cost = CM × Mix = CM

Vases $40 $30 $10 3 $30Figurines 70 42 28 2 56

Total $86


Break-even vases = 3 × 410 = 1,230

Break-even figurines = 2 × 410 = 820

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Exercise 4–39

1. a. Variable cost per unit = = $19.20

b. Contribution margin per unit = = $4.80

c. Contribution margin ratio = = 0.20, or 20%

d. Break-even units = = 315,000

e. Break-even sales dollars = = $7,560,000

OR

Break-even sales dollars = 315,000 × $24 = $7,560,000

2. Units for target income = = 377,500

3. Additional operating income = $50,000 × 0.20 = $10,000

4. Margin of safety in units = 350,000 – 315,000 = 35,000 units

Margin of safety in sales dollars = $8,400,000 – $7,560,000 = $840,000

5. Degree of operating leverage = = 10.0

6. New operating income = $168,000 + [(10 × 0.10) ($168,000)] = $336,000

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PROBLEMS

Problem 4–40


=

=

= 89,600 units

2. Units for target profit =

=

= 169,600 units

3. Contribution margin ratio = = 0.40

With additional sales of $50,000, the additional profit would be 0.40 × $50,000 = $20,000.

4. Current units = $2,480,000

= 124,000 units$20

Margin of safety in units = 124,000 – 89,600 = 34,400 units

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Problem 4–41


=

= 19,200 units


= 16,500 units

3. The reduction in fixed costs reduces the break-even point because less contri-bution margin is needed to cover the new, lower fixed costs. Operating income goes up, and the margin of safety also goes up.

Problem 4–42

1. Unit contribution margin = = $15

Break-even point = = 66,667 units

Contribution margin ratio = = 0.3

Break-even sales = = $3,333,333

OR

= $50 × 66,667 = $3,333,350 (rounded)

Note: Difference in break-even sales due to rounding.

2. Increased contribution margin ($1,000,000 × 0.3).................... $300,000Less: Increased advertising expense....................................... 100,000

Increased profit..................................................................... $200,000

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Problem 4–42 (Concluded)

3. $315,000 × 0.3 = $94,500

4. Margin of safety = $6,400,000 – $3,333,333 = $3,066,667

Or

= $6,400,000 – $3,333,350 = $3,066,650 (rounded)

Note: Difference in margin of safety due to rounding in break-even sales.

5. = 2.09 (operating leverage)

20% × 2.09 = 41.8% (profit increase)

Problem 4–43

1. Sales mix:

Squares: = 10,000 units

Circles: = 50,000 units

Variable Contribution Sales TotalProduct Price – Cost* = Margin × Mix = CM

Squares $30 $10 $20 1 $ 20Circles 50 10 40 5 200

Package $220

* = $10

= $10

Break-even packages = = 7,400 packages

Break-even squares = 7,400 × 1 = 7,400

Break-even circles = 7,400 × 5 = 37,000

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2. New mix:Variable Contribution Sales Total

Product Price – Cost* = Margin × Mix = CM

Squares $30 $10 $20 3 $ 60Circles 50 10 40 5 200

Package $260

Break-even packages = = 6,262 packages

Break-even squares = 6,262 × 3 = 18,786

Break-even circles = 6,262 × 5 = 31,310

3. Increase in contribution margin for squares (25,000 × $20).. . $ 500,000Decrease in contribution margin for circles (5,000 × $40)...... (200,000 )

Increase in total contribution margin.................................. $ 300,000Less: Additional fixed expenses............................................... 245,000

Increase in income................................................................ $ 55,000

Gosnell would gain $55,000 by increasing advertising for the squares. This is a good strategy.

Problem 4–44


Margin of safety in units = 830,000 – 650,000 = 180,000

2. Sales revenue ($0.36 × 830,000)................................................ $298,800Total variable cost ($0.27 × 830,000)......................................... 224,100

Total contribution margin..................................................... $ 74,700Total fixed expense.................................................................... 58,500

Operating income.................................................................. $ 16,200

3. Units for target profit =

= 1,050,000

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4. Operating income = Sales – (Variable cost ratio × Sales) – Fixed cost

0.20 Sales = Sales – (0.75 × Sales) – $58,500

0.20 Sales = 0.25 Sales – $58,500

$58,500 = (0.25 Sales – 0.20 Sales)

$58,500 = 0.05 Sales

Sales = $1,170,000

Problem 4–45

1. Contribution margin ratio = = 0.54, or 54%

2. Revenue = = $277,778

3. $560,400 × 110% = $616,440

$257,784 × 110% = 283,562

$332,878

Contribution Margin Ratio = = 0.54

The contribution margin ratio remains at 0.54.

4. Additional variable expense: $560,400 × 0.03 = $16,812

New contribution margin = $302,616 – $16,812 = $285,804

New contribution margin ratio = = 0.51

Break-even point = = $294,118

The effect is to increase the break-even point.

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5. Present contribution margin...................................................... $302,616Projected contribution margin*................................................. 326,604 Increase in contribution margin/profit...................................... $ 23,988

*($560,400 + $80,000) × 0.51 = $326,604

Operating leverage will decrease because the increase in variable costs (the sales commission) causes a decrease in the contribution margin.

Doerhing should pay the commission because profit would increase by $23,988.

Problem 4–46

1. Revenue =

=

= $450,000

2. Of total sales revenue, 60 percent is produced by floor lamps and 40 percent by desk lamps.

= 12,000 units

= 12,000 units

Thus, the sales mix is 1:1.

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Variable Contribution Sales TotalProduct Price – Cost = Margin × Mix = CM

Floor lamps $30 $20.00 $10.00 1 $10.00Desk lamps 20 13.33 6.67 1 6.67 Package $16.67

Number of packages =

=

= 8,998 packages

Floor lamps: 1 × 8,998 = 8,998

Desk lamps: 1 × 8,998 = 8,998

3. Operating leverage =

=

= 4.0

Percentage change in profits = 4.0 × 40% = 160%

Problem 4–47

1. Door Handles Trim Kits

CM $12 – $9 = $3 $8 – $5 = $3CM ratio $3/$12 = 0.25 $3/$8 = 0.375

2. Contribution margin:

($3 × 20,000) + ($3 × 40,000) $180,000

Less: Fixed costs 146,000

Operating income $ 34,000

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3. Sales mix (from Requirement 2): 1 door handle to 2 trim kits

Price – V = CM × Sales Mix = Total CM

Door handle $12 $9 $3 1 $3.00Trim kit 8 5 3 2 6.00

Package $9.00


Door handles = 1 × 16,222 = 16,222Trim kits = 2 × 16,222 = 32,444

4. Revenue (70,000 × $8)................................................................ $560,000Variable cost (70,000 × $5)......................................................... 350,000

Contribution margin.............................................................. $210,000Fixed cost.................................................................................... 111,000


Yes, operating income is $65,000 higher than when both door handles and trim kits are sold.

Problem 4–48


* = $14

Break-even in dollars = 21,429 × $42** = $900,018

OR

= = $900,000

The difference is due to rounding.

** = $42

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2. Margin of safety = $1,218,000 – $900,000 = $318,000

3. Sales............................................................................................ $1,218,000Variable cost (0.45 × $1,218,000)............................................... 548,100

Contribution margin.............................................................. $ 669,900Fixed costs.................................................................................. 550,000


Break-even in units = = 23,810

Break-even in sales dollars = = $1,000,000

* = $23.10

** = 55%

Problem 4–49

1. Variable cost ratio =

= = 0.38, or 38%

Contribution margin ratio =

=

= 0.62, or 62%

2. Break-even sales revenue = = $500,000

3. Margin of safety = Sales – Break-even sales= $930,000 – $500,000 = $430,000

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4. Contribution margin from increased sales = ($7,500)(0.62) = $4,650

Cost of advertising = $5,000

No, the advertising campaign is not a good idea, because the company’s oper-ating income will decrease by $350 ($4,650 – $5,000).

Problem 4–50

1. Income = Revenue – Variable cost – Fixed cost

$0 = 1,500P – $300(1,500) – $120,000

$0 = 1,500P – $450,000 – $120,000

$570,000 = 1,500P

P = $380

2. = 128,000

Unit variable cost = $2.25

Problem 4–51

1. Contribution margin per unit = $5.60 – $4.20*= $1.40

*Variable costs per unit:

$0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20

Contribution margin ratio = = 0.25

2. Break-even in units = = 32,000 boxes

Break-even in sales = 32,000 × $5.60 = $179,200

OR

= = $179,200

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3. Sales ($5.60 × 35,000)................................................................. $196,000Variable cost ($4.20 × 35,000).................................................... 147,000

Contribution margin.............................................................. $ 49,000Fixed cost.................................................................................... 44,800


4. Margin of safety = $196,000 – $179,200 = $16,800

5. Break-even in units = = 22,400 boxes

New operating income = $6.20(31,500) – $4.20(31,500) – $44,800= $195,300 – $132,300 – $44,800 = $18,200

Yes, operating income will increase by $14,000 ($18,200 – $4,200).

Problem 4–52

1. Company A: = 2

Company B: = 6

2. Company A Company B

X = X =

X = X =

X = $250,000 X = $416,667

Company B must sell more than Company A to break even because it must cover $200,000 more in fixed costs (it is more highly leveraged).

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3. Company A: 2 × 50% = 100%

Company B: 6 × 50% = 300%

The percentage increase in profits for Company B is much higher than Com-pany A’s increase because Company B has a higher degree of operating lever-age (i.e., it has a larger amount of fixed costs in proportion to variable costs as compared to Company A). Once fixed costs are covered, additional revenue must cover only variable costs, and 60 percent of Company B’s revenue above break even is profit, whereas only 20 percent of Company A’s revenue above break even is profit.

Problem 4–53

1. Contribution margin ratios:

May of current year = = 0.549, or 54.9%

May of prior year = = 0.561, or 56.1%

2. Break-even point in sales dollars:

May of current year = = $37,031

May of prior year = = $24,599

3. Margin of safety:

May of current year = $43,560 – $37,031 = $6,529May of prior year = $41,700 – $24,599 = $17,101

4. Clearly, the sharp rise in fixed costs from the prior year to the current year has had a strong impact on the break-even point and the margin of safety. Kicker will need to ensure that tight cost control is exercised since the margin of safety is much slimmer. Still, the decision to go with the OEM investment pro-gram could pay large dividends in the future. Note that the margin of safety and break-even point give the company important information on the potential risk of the venture but do not tell it the upside potential.

4-4-3434

CASES

Case 4–54

1. Let X be a package of 3 Grade I cabinets and 7 Grade II cabinets.

0.3X($3,400) + 0.7X($1,600) = $1,600,000

X = 748 packages

Grade I: 0.3 × 748 = 224 unitsGrade II: 0.7 × 748 = 524 units

2. Variable Contribution Sales TotalProduct Price – Cost = Margin × Mix = CM

I $ 3,400 $ 2,686 $714 3 $2,142II 1,600 1,328 272 7 1,904

Package 21,400 17,354 $4,046

Direct fixed costs — I $ 95,000Direct fixed costs — II 95,000Common fixed costs 35,000

Total fixed costs $225,000

= 56 packages

Grade I: 3 × 56 = 168Grade II: 7 × 56 = 392

4-4-3535

Case 4–54 (Continued)


I $ 3,400 $ 2,444 $956 3 $2,868II 1,600 1,208 392 7 2,744

Package 21,400 15,788 $5,612

$21,400X = $1,600,000 – $600,000X = 47 packages remaining

Grade I: 3 × 47 = 141Grade II: 7 × 47 = 329

Additional contribution margin:141($956 – $714) + 329($392 – $272) $73,602Increase in fixed expenses 44,000

Increase in income $29,602

Break-even: = 48 packages

Grade I: 3 × 48 = 144Grade II: 7 × 48 = 336

If the new break-even point is interpreted as a revised break-even point for the current year, then total fixed costs must be reduced by the contribution mar-gin already earned (through the first five months) to obtain the units that must be sold for the last seven months. These units would then be added to those sold during the first five months:

Contribution margin earned = $600,000 – (83* × $2,686) – (195* × $1,328) = $118,102

*224 – 141 = 83; 524 – 329 = 195

X = = 27 packages

From the first five months, 28 packages were sold (83/3 or 195/7). Thus, the re-vised break-even point is 55 packages (27 + 28)—in units, 165 of I and 385 of II.

4-4-3636

Case 4–54 (Concluded)


I $3,400 $2,686 $714 1 $714II 1,600 1,328 272 1 272

Package $986

New sales revenue $1,000,000 × 130% = $1,300,000

$5,000X = $1,300,000X = 260 packages

Thus, 260 units of each cabinet will be sold during the rest of the year.

Effect on profits:

Change in contribution margin:$714(260 – 141) – $272(329 – 260) $66,198

Increase in fixed costs:$70,000(7/12) 40,833

Increase in operating income $25,365

X =

=

= 299 packages (or 299 of each cabinet)

The break-even point is computed as follows:

X =

=

= 179 packages (179 of each)

To this, add the units already sold, yielding the revised break-even point:I: 83 + 179 = 262II: 195 + 179 = 374

4-4-3737

Case 4–55

1. Break-even point =

First process: = 5,000 cases

Second process: = 8,333 cases

2. Income = X(Price – Variable cost) – Fixed costX($30 – $10) – $100,000 = X($30 – $6) – $200,000

$20X – $100,000 = $24X – $200,000$100,000 = $4X

X = 25,000 cases

The manual process is more profitable if sales are less than 25,000 cases; the automated process is more profitable at a level greater than 25,000 cases. It is important for the manager to have a sales forecast to help in deciding which process should be chosen.

3. The right to decide which process should be chosen belongs to the divisional manager. Danna has an ethical obligation to report the correct information to her superior. By altering the sales forecast, Danna unfairly and unethically in-fluenced the decision-making process. Managers certainly have a moral obli-gation to assess the impact of their decisions on employees, and every effort should be taken to be fair and honest with employees. Danna’s behavior, how-ever, is not justified by the fact that it helped a number of employees retain their employment. First, Danna had no right to make that decision. Danna cer-tainly has the right to voice her concerns about the impact of automation on the employees’ well-being. In so doing, perhaps the divisional manager would come to the same conclusion even though the automated system appears to be more profitable. Second, the choice to select the manual system may not be the best for the employees anyway. The divisional manager may possess more information, making the selection of the automated system the best al-ternative for all concerned, provided the sales volume justifies its selection. For example, if the automated system is viable, the divisional manager may have plans to retrain and relocate the displaced workers in better jobs within the company. Third, her motivation for altering the forecast seems more driven by her friendship with Jerry Johnson than any legitimate concerns for the layoff of other employees. Danna should examine her reasoning carefully to assess the real reasons for her behavior. Perhaps in so doing, the conflict of interest that underlies her decision will become apparent.

4-4-3838

Ch04

Documents

total contribution margin

unit contribution margin

increased contribution

total variable expense

total fixed costs

sales volume

variable cost ratio

breakeven sales dollars