CHAPTER 4 COST-VOLUME-PROFIT ANALYSIS: A … 3e sm04.pdf · COST-VOLUME-PROFIT ANALYSIS: A...

Copyright © 2018 by Nelson Education Ltd. 4-1

CHAPTER 4 COST-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 volume in terms of units of product and gives answers in these same terms. The unit contribution margin is needed to solve for the break-even units. The sales revenue approach defines sales volume in terms of revenues 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 advertising is $10,000. If the contribution margin ratio is 0.40, then the increased contribution 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 expected 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 analysis can be easily adjusted to focus on target profit.

10. The basic break-even equation is adjusted for target profit by adding the desired target profit to the total fixed costs in the numerator. The denominator remains the contribution margin per unit.

11. A change in sales mix will change the contribution 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 profits 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 underlying assumptions on an answer. A company can input data on selling prices, variable 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.

4-2 Copyright © 2018 by Nelson Education Ltd.

CORNERSTONE EXERCISES

Cornerstone Exercise 4–1

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

+ Variable factory overhead + Variable selling expense

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

= $49

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

3. Head-First Company

Contribution Margin Income Statement For the Coming Year

Total Per Unit

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


1. Break-even units = Total fixed cost

(Price Unit variable cost)-

= $29,400

($70 $49)-

= 1,400 helmets


Contribution Margin Income Statement At Break-Even

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



1. Variable cost ratio = Variable cost per unit

Price

= $70

$49

= 0.70, or 70%

2. Contribution margin ratio = (Price Variable cost per unit)

Price

-

= ($70 $49)

$70

-

= 0.30, or 30%


Contribution Margin Income Statement For the Coming Year

Percent of Sales

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


1. Break-even sales dollars = Total fixed cost

Contribution margin ratio

= 0.30

$29,400

= $98,000


Cornerstone Exercise 4–4 (Continued)

2. Head-First Company Contribution Margin Income Statement

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


1. Break-even units = (Total fixed cost + Target income)


= ($29,400 + $81,900)

($70 $49)-

= 5,300 helmets


Contribution Margin Income Statement At 5,300 Helmets Sold

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


1. Sales for target income = (Total fixed cost + Target income)


= ($29,400 + $81,900)

0.30

= $371,000




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

3. A contribution margin income statement helps managers make better decisions in that it focuses their attention on those areas that are easiest to control. Variable costs are usually more easily controlled than fixed costs.


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 Unit Variable Contribution Sales Contribution Product Price Cost Margin Mix Margin

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



2. Break-even packages = Fixed cost

Package contribution margin

= $182

$54,600

= 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


Contribution Margin Income Statement At Break-Even

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


1. Contribution margin ratio = ($570,000 $388,000)

$570,000

-

= 0.3193

Break-even sales dollars = Total fixed cost


= 0.3193

$54,600

= $170,999




At Break-Even Sales Dollars

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


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 = Total contribution margin

Operating income

= $75,600

*$105,000 = 1.4

* 5,000 × ($70 - $49)


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


EXERCISES

Exercise 4–12

1. Direct materials .......................................................................... $ 5.85 Direct labour ............................................................................... 2.10 Variable overhead ...................................................................... 3.15 Variable selling and administrative expense ........................... 2.40 Unit variable cost ....................................................................... $13.50

Unit contribution margin = Price – Unit variable cost

= $24.00 – $13.50

= $10.50

2. Contribution margin ratio = $24

$10.50 = 0.4375, or 43.75%

Variable cost ratio = $24

$13.50 = 0.5625, or 56.25%

3. Break-even units ($78,000 + $56,925) / ($24 - $13.50) = 12,850

4. Sales ($24 × 12,850) ................................................................... $308,400 Variable costs ($13.50 × 12,850) ............................................... 173,475 Total contribution margin .................................................... 134,925 Less: Fixed expenses ($78,000 + $ 56,925) .............................. 134,925 Operating income ................................................................. $ 0

Exercise 4–13

1. Unit variable cost = $19.00 × 0.60 = $11.40

Unit contribution margin = $19.00 – $11.40 = $7.60

2. Break-even units = $7.60

$874,000 = 115,000


Exercise 4–13 (Continued)

3. Break-even sales revenue = $19.00 × 115,000 = $2,185,000

OR

Break-even sales revenue = 0.40

$874,000 = $2,185,000

4. Sales ........................................................................................... $2,185,000 Less: Variable costs (0.6 x $2,185,000) .................................... 1,311,000 Contribution margin .................................................................. 874,000 Less: Fixed costs ....................................................................... 874,000 Operating income ...................................................................... $ 0 5. Break-even operations always result in a profit of zero.

Exercise 4–14

1. Contribution margin ratio ($481,250/$875,000) = 55%

2. Variable cost ratio ($393,250/$4875,000) = 45%

3. Break-even sales revenue ($327,000/.55) = $594,546 (rounded up).


Exercise 4–15

1. Contribution Margin Income Statement Starfirst Company

Contribution Margin Income Statement Sales $1,575,000 Variable costs 1,222,500 Contribution margin 352,500 Fixed costs 183,300 Operating income $ 169,200

2. Break-even point in units

Contribution margin per unit: $42 - $32.60 = $9.40 Break-even point in units: $183,300/$9.40 = 19,500 units

3. Units needed to generate $200,000 in operating income

Fixed costs + Target profit = $183,300 + $200,000 = $383,300 Units required = $383,300/$9.40 = 40,777 units (rounded)

Exercise 4–16

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

Direct materials ..................................................................... $0.27 Direct labour ......................................................................... 0.58 Variable overhead ................................................................. 0.63 Variable selling ..................................................................... 0.17 Unit variable cost .................................................................. $1.65

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

Direct materials ..................................................................... $0.27 Direct labour ......................................................................... 0.58 Variable 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.



2. Break-even units = ($131,650 + $18,350)

($2.45 $1.65) -

= $0.80

$150,000

= 187,500

3. Units to earn $12,600 = ($131,650 + $18,350 + $12,600)

($2.45 $1.65)-

= 203,250

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

or

$131,650 + $18,350 + $12,600 = $162,600 ÷ .3265* = $498,009

*contribution margin ratio = ($2.45 – $1.65) ÷ $2.45 = 0.3265 (rounded)

Exercise 4–17

1. Contribution margin = Sales – variable costs = $11.75 - $6.58 = $5.17 Break-even in units = Fixed costs/ CM per unit = $1,500,437/$5.17 = 290,220 *

2. Margin of safety = Sales volume – Break-even sales = 570,000 – 290,220

= 279,780 units

3. Contribution margin ratio = CM/Sales = $5.17/$11.75 = 44% Break-even sales in dollars = Fixed costs / Contribution margin ratio

= $1,500,437/.44 = $3,410,084 Sales dollars = $11.75 x 570,000 = $6,697,500 Margin of safety = Sales dollars – Break-even dollars = $6,697,500 - $3,410,084 = $3,287,416

*Rounded


Exercise 4–18

A B C D Sales $15,000 $15,600* $16,250* $10,600 Total 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 1,000 Price 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.)

Exercise 4–19

1. Variable cost ratio: Variable cost/Sales revenue = $303,885/$675,300 = 45%

Contribution margin ratio = CM/Sales = $371,415/$675,300 = 55% 2. If sales increase by $50,000, operating income increases by

$50,000 x CM ratio = $50,000 x 0.55 = $27,500 3. Sales revenue needed to break even: Fixed costs/CM ratio = $247,610/0.55 = $450,200 Revenue $450,200 Variable expenses 202,590 Contribution margin 247,610 Fixed expenses 247,610 Operating income 0 4. Expected margin of safety = Sales revenue – Break-even sales revenue

= $675,300 – $450,200 = $225,100 5. Margin of safety if sales are $500,000 = $500,000 – $450,200 = $49,800


Exercise 4–20

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

2. Variable Sales Total Product Price – Cost = CM × Mix = CM

DVDs $12 $4 $8 2 $16 Equipment sets 15 6 9 1 9 Total $25

Break-even packages = $25

$70,000 = 2,800

Break-even DVDs = 2 × 2,800 = 5,600

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


Exercise 4–21

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 $16 Equipment sets 15 6 9 1 9 Yoga mats 18 13 5 4 20 Total $45


$118,350 = 2,630

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

3. Switzer Company

Income Statement For the Coming Year

Sales ........................................................................................... $555,000 Less: Total variable costs ......................................................... 330,000 Contribution margin ............................................................. 225,000 Less: Total fixed costs .............................................................. 118,350 Operating income ................................................................. $106,650

Contribution margin ratio = $555,000

$225,000 = 0.405, or 40.5%

Break-even revenue = 0.405

$118,350 = $292,222

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


Exercise 4–22

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 $180 $ 105 $75 3 $225 Large basic 300 225 75 5 375 Carved 525 412 113 1 113 Total $713


$669,750 = 940 (rounded up)

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

3. Sonora Company

Income Statement For the Coming Year

Sales ........................................................................................... $25,650,000 Less: Total variable costs ......................................................... 18,520,000 Contribution margin ............................................................. 7,130,000 Less: Total fixed costs .............................................................. 669,750 Operating income ................................................................. $ 6,460,250

Contribution margin ratio = $7,130,000

$25,650,000 = 0.2780, or 27.80%


$669,750 = $2,409,173

4. Margin of safety = $25,650,000 – $2,409,173 = $23,240,827


Exercise 4–23

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Units Sold

Rev

enu

e an

d C

ost

($)

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

X

X



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

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Units Sold

Rev

enu

e an

d C

ost

($)

Break-even point = 3,750 units

X

X



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

0

10,000

20,000

30,000

40,000

50,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Units Sold

Re

ven

ue

and

Co

st (

$)


X

X



2. c. Selling price increases to $12:

0

10,000

20,000

30,000

40,000

50,000

60,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Units Sold

Re

ven

ue

and

Co

st (

$)


X

X



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

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Units Sold

Rev

enu

e a

nd

Co

st (

$)


Exercise 4–24

1. Unit contribution margin: $75 - $24.75 = $50.25 per unit

Break-even units: Fixed costs

Contribution margin =

$984,025

$50.25 = 19,583 units

2. Sell 30,000 units above break-even

Operating income increases by the contribution margin. Contribution margin for 30,000 units = 30,000 x $50.25= $1,507,500

3. Contribution margin ratio = Contribution margin

Sales =

$50.25

$75 = 67%

Break-even in dollars = Fixed costs

CM ratio =

$984,025

.67 = $1,468,694 *

Revenues up by $500,000 to $2,300,000, then CM at new level = $2,300,000 x .67 = $1,541,000 New operating income = CM – fixed costs = $1,541,000 - $984,025 = $556,975 *rounded up

X

X


Exercise 4–25

1. Break-even sales dollars = *0.58

$1,833,300 = $3,160,862

*Contribution margin ratio = $4,500,000

$2,610,000 = 0.58, or 58%

2. Margin of safety = $4,500,000 – $3,160,862 = $1,339,138

3. Degree of operating leverage = Contribution margin

Operating income

= $776,700

$2,610,000

= 3.36

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

New operating income = $776,700 + (0.67 × $776,700) = $1,297,089

Exercise 4–26

1. Variable Sales Package Product Price – Cost = CM × Mix = CM

Vases $100 $75 $25 2 $ 50 Figurines 175 105 70 1 70 Total $120


$75,000 = 625

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 Package Product Price – Cost = CM × Mix = CM

Vases $100 $75 $25 3 $ 75 Figurines 175 105 70 2 140 Total $215


$88,150 = 410

Break-even vases = 3 × 410 = 1,230

Break-even figurines = 2 × 410 = 820

3. It is better to use contribution margin ratio in determining break-even for a multi-product company because it makes the calculations easier when dealing with sales mix.

Exercise 4–27

1. a. Variable cost per unit = $6,720,000

350,000 = $19.20

b. Contribution margin per unit = 350,000

$1,680,000 = $4.80

c. Contribution margin ratio = $24.00

$4.80 = 0.20, or 20%

d. Break-even units = $4.80

$1,512,000 = 315,000

e. Break-even sales dollars = 0.20

$1,512,000 = $7,560,000

OR

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



2. Units for target income = ($1,512,000 + $300,000)

$4.80 = 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 = $1,680,000

$168,000 = 10.0

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


PROBLEMS

Problem 4–28

1. Break-even point in units = Fixed costs/Contribution margin per unit

= $3,213,924/$21 = 153,044 units

2. Units to sell to earn $2,700,000 = (Fixed costs + Target profit)/CM per unit

= ($3,213,924 + $2,700,000)/$21 = 281,616*

3. Contribution margin ratio = CM/Sales = $21/$60 = 35% Sales increase by $300,000; Additional operating income = Increased sales * CM ratio = $300,000 x .35 = $105,000

4. Margin of safety = Sales – Break-even sales Sales in units = $13,800,000/$60 = 230,000 units Break-even sales in units = Fixed costs/CM per unit = $3,213,924/$21 = 153,044 units Margin of safety = 230,000 units – 153,044 units = 76,956 units

*rounded up


Problem 4–29

1. Break-even units = Fixed cost


= $96,000

($10 $5)-

= 19,200 units

2. Break-even units = ($96,000 $13,500)

($10 $5)

--

= 16,500 units

3. The reduction in fixed costs reduces the break-even point because less

contribution margin is needed to cover the new, lower fixed costs. Operating income goes up, and the margin of safety also goes up.

Problem 4–30

1. Unit contribution margin = 384,000

$5,760,000 = $15

Break-even point = $15

$3,000,000 = 200,000 units

Contribution margin ratio = $50

$15 = 0.3

Break-even sales = 0.3

$3,000,000 = $10,000,000

OR

= $50 × 200,000 = $10,000,000

2. Increased contribution margin ($3,000,000 × 0.3) ................... $900,000 Less: Increased advertising expense ...................................... 300,000 Increased profit ..................................................................... $600,000


Problem 4–30 (Continued)

3. $945,000 × 0.3 = $283,500

4. We can simply focus on increased sales revenue to determine profitability

because any increase in profit will automatically add the gross margin of those sales to profit. The fixed costs do not change.

5. Margin of safety = $19,200,000 – $10,000,000 = $9,200,000

6. $2,760,000

$5,760,000 = 2.09 (operating leverage)

20% × 2.09 = 41.8% (profit increase)

Problem 4–31

1. Sales mix:

Squares: $30

$300,000 = 10,000 units

Circles: $50

$2,500,000 = 50,000 units

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

Squares $30 $10 $20 1 $ 20 Circles 50 10 40 5 200 Package $220

*10,000

$100,000 = $10

50,000

$500,000 = $10


$1,628,000 = 7,400 packages

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

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



2. New mix: Variable Contribution Sales Total Product Price – Cost = Margin × Mix = CM

Squares $30 $10 $20 3 $ 60 Circles 50 10 40 5 200 Package $260


$1,628,000 = 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) ... $ 500,000 Decrease in contribution margin for circles (5,000 × $40) ...... (200,000) Increase in total contribution margin ................................. 300,000 Less: Additional fixed expenses .............................................. 245,000 Increase in income ............................................................... $ 55,000

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

Problem 4–32

1. Break-even point in units = Fixed costs / Unit contribution margin per unit

Contribution margin per unit = $0.90 - $0.63 = $0.27 Break-even = $210,600 / $0.27 = 780,000 bottles

Margin of safety = Sales volume – Break-even volume 830,000 bottles – 780,000 bottles = 50,000 bottles

2. Revenue $747,000 ($0.90 x 830,000) Variable costs 522,900 ($0.63 x 830,000) Contribution margin 224,100 Fixed costs 210,600 Operating income $ 13,500



3. Units to generate $40,500 in profit = (Fixed costs + Target profit)/CM

($210,600 + $40,500)/$0.27 = 930,000 bottles

4. Sales dollars to earn operating income of 20% of sales (Fixed costs + 0.2 × Sales)/Contribution margin% = Sales CM% = ($0.90 – $0.63)/$0.90 = 30% (210,600 + 0.2X)/CM% = X 702,000 + 0.6667X = X 0.3333X = 702,000 X = $2,106,211

Problem 4–33

1. Contribution margin ratio = $560,400

$302,616 = 0.54, or 54%

2. Break-even revenue = 0.54

$150,000 = $277,778

3. $560,400 × 110% = $616,440

$257,784 × 110% = 283,562

$332,878

Contribution margin ratio = $616,440

$332,878 = 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 = $560,400

$285,804 = 0.51


$150,000 = $294,118

The effect is to increase the break-even revenue.



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

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

Operating leverage will decrease from 1.98 ($302,616/$152,616) to 1.85 ($326,604/$176,604) because the increase in the contribution margin of $23,988 is exactly equal to the increase in the operating income, which results in a decrease in the operating leverage.

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

Problem 4–34

1. Revenue = Fixed cost

(1 Variable rate)-

= (1/3)

$150,000

= $450,000

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

by desk lamps.

$30

$360,000 = 12,000 units

$20

$240,000 = 12,000 units

Thus, the sales mix is 1:1.



Variable Contribution Sales Total Product Price – Cost = Margin × Mix = CM

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

Number of packages = Fixed cost

(Package contribution margin)

= $16.67

$150,000

= 8,998 packages

Floor lamps: 1 × 8,998 = 8,998

Desk lamps: 1 × 8,998 = 8,998

3. Operating leverage = Contribution margin

Operating income

= $50,000

$200,000

= 4.0

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

4. The theory behind the operating leverage concept is that a company will increase its profits in direct relationship to the relationship between its fixed costs and its variable costs. The more fixed costs a company has the more impact an increase in revenues will have on profit because its fixed costs have been covered.


Problem 4–35

1. Door Handles Trim Kits

CM $12 – $9 = $3 $8 – $5 = $3 CM 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

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 Trim kit 8 5 3 2 6 Package $9

Break-even packages = $146,000

$9 = 16,222

Door handles = 1 × 16,222 = 16,222 Trim kits = 2 × 16,222 = 32,444 4. Revenue (70,000 × $8) ............................................................... $560,000 Variable cost (70,000 × $5) ........................................................ 350,000 Contribution margin ............................................................. 210,000 Fixed costs ................................................................................. 111,000 Operating income ................................................................. $ 99,000

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


Problem 4–36

1. Break-even in units = Fixed costs

Contribution margin per unit

Contribution margin per unit = $604,800

36,000 = $16.80

Break-even in units= $504,000

$16.80 = 30,000 units

Break-even in dollars = Fixed costs

CM%

CM = $604,800

$1,512,000 = 40%

Break-even in dollars = $504,000

.4 = $1,260,000

Proof: $1,260,000

$42 = 30,000 units

2. Margin of safety = Actual units – Break-even units =

36,000 – 30,000 = 6,000 units 3. Fixed costs go up by $250,000 to $754,000; Variable costs are lowered to 45%

of sales.

Revenue $1,512,000 Variable costs (45%) 680,400 Contribution margin 831,600 Fixed costs 754,000 Operating income $ 77,600

Break-even in units = Fixed costs

CM/unit

CM per unit = $831,600

36,000 = $23.10

Break-even in units = $754,000

$23.10 = 32,641 units *

Break-even in dollars = $754,000

.55 = $1,370,909 *rounded up


Problem 4–37

Steven Kissick, Lawyer Contribution Income Statement

Revenue $180,000 Variable costs Direct 66,000 Indirect 17,500 Contribution margin 96,500 Fixed costs Direct 88,000 Indirect 110,000 Operating income/(Loss) (101,500) Income tax (27.5%) 0 Net loss $(101,500)

1. Break-even revenue = Fixed costs


Contribution margin ratio = Contribution margin

Revenue

$96,500

$180,000 = 53.61%

($88,000 + $110,000)

0.5361 = $369,334 *rounded

2. To generate $150,000 after tax income, the pre-tax income

must be = $150,000

(1 - Tax rate)

Pre-tax income is = $206,897

Target revenue = (Fixed cost + Target profit)

CM%

($198,000 + $206,897)

0.5361 = $755,264 *rounded up

3. At $350 per hour, it would appear that this target is not reasonable. Based

on a 40-hour week and 50 working weeks of the year, there are 2,000 hours in a normal work year. Kissick would have to bill 2,158 hours per year to achieve his objective. If he raised his rate to $380, his goal would be realized.


Problem 4–38

1. Revenue – Variable costs – Fixed costs = Operating profit At break-even, profit = 0 27,500X = 22,500 + 62,400 27,500X = 84,900 X = $3.09 rounded up

2. Revenue – Variable costs – Fixed costs = Operating income

(Fixed costs + Operating income)

Contribution margin ratio = Revenue

(X + $33,000)

0.35 = $228,000

X

.35 = $228,000 –

$33,000

0.35

X = (228,000 – $94,286) × 0.35 X = $46,800 3. Revenue – Variable cost – Fixed cost = Operating income

$800,000 – (X*$800,000) – $220,000 = 0 (X*$800,000) = $800,000 – $220,000

X = $580,000

$800,000 = 72.5%


Problem 4–39

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 = $5.60

$1.40 = 0.25

2. Break-even in units = ($32,300 + $12,500)

$1.40 = 32,000 boxes

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

OR

= ($32,300 + $12,500)

0.25 = $179,200

3. Sales ($5.60 × 35,000) ................................................................ $196,000 Variable costs ($4.20 × 35,000) ................................................. 147,000 Contribution margin ............................................................. 49,000 Fixed cost ................................................................................... 44,800 Operating income ................................................................. $ 4,200 4. Margin of safety = $196,000 – $179,200 = $16,800

5. Break-even in units = $44,800

($6.20 $4.20)- = 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, because operating income will increase by $14,000 ($18,200 – $4,200).

Problem 4–40

1. Company A: $50,000

$100,000 = 2

Company B: $50,000

$300,000 = 6



2. Company A Company B

X = $50,000

(1 0.8)- X =

$250,000

(1 0.4)-

X = 0.2

$50,000 X = 0.6

$250,000

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

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

3. Company A: 2 × 50% = 100%

Company B: 6 × 50% = 300%

The percentage increase in profits for Company B is much higher than Company A’s increase because Company B has a much higher degree of operating leverage (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 4-41

1. Total sales = $500,000 + $1,080,000 + $2,760,000 + $3,600,000 = $7,940,000

Total variable costs = $300,000 + $630,000 + $1,650,000 + $2,350,000 + $25,000 + $150,000 + $240,000 + $213,000 = $5,558,000

Contribution margin = $7,940,000 - $5,558,000 = $2,382,000

Contribution margin % = $2,382,000 / $7,940,000 = 30%

Total fixed costs = $25,000 + $220,000 + $300,000 + $300,000 + $64,200 + $50,000 + $50,000 + $150,000 + $270,000 = $1,429,200

Revenue needed to break-even = $1,429,200 /.30 = $4,764,000


Problem 4-41 (Continued)

2. Contribution Margin Per Product

Product A Product B Product C Product D Revenue $500 $1,800 $9,200 $36,000

Variable

Product 300 1,050 5,500 23,500

Sell/Admin 25 250 800 2,130

Contribution $175 $ 500 $2,900 $10,370

Package of products: A= 10; B= 6; C= 3; D= 1

Contribution per package: (10 x 175) + (6 x 500) + (3 x 2,900) + (1 x 10,370) = $23,820

Packages required to break-even:

Fixed costs ($1,429,200) divided by contribution per package ($23,820) = 60.

Quantity of each product: A=60 x 10 = 600; B= 60 x 6 = 360; C= 60 x 3 = 180; D= 60 x 1 = 60.

Calculation to check: Revenue = (600 x $500) + (360 x $1,800) + (180 x $9,200) + (60 x $36,000) = $300,000 + $648,000 + $1,656,000 + $2,160,000) = $4,764,000.

3. After-tax profit of $1,625,000 is pre-tax profit of ($1,625,000 divided by (1 - .35)) or $2,500,000.

Fixed costs plus target profit = $1,429,200 + $2,500,000 = $3,929,200.

Target revenues = $3,929,200 divided by contribution margin ratio of .30 or $13,097,333.


Problem 4-41 (Continued)

4. After-tax profit of $1,300,000 is pre-tax profit of $2,000,000.

Target units are calculated by taking the fixed costs plus the target pre-tax profit divided by the contribution margin per package and then calculating the number of each unit in a package.

Fixed costs ($1,429,200) plus target profit ($2,000,000) = $3,429,200

Target packages: $3,429,200 / $23,820 = 144 packages (rounded)

By product: A: 10 x 144 = 1,440; B: 6 x 144 = 864; C: 3 x 144 = 432; D: 1 x 144 = 144.


Problem 4–42

1. Contribution margin calculated in Problem 4-41 was:

Revenue $7,940,000 Less: Variable costs 5,558,000 Contribution $2,382,000

Revised contribution margin Revenue $7,940,000 Less: Variable costs 6,113,800 Contribution $1,826,200 Contribution margin % 23% Revised contribution margin by product

Product A: $500 – [1.1 ($300 + $25)] = $ 142.50 Product B: $1,800 – [1.1 ($1,050 + $250)] = $ 370 Product C: $9,200 – [1.1 ($5,500 + $800)] = $2,270 Product D: $36,000 – [1.1 ($23,500 + $2,130)] = $7,807 Revised contribution by package Product A: 10 x $142.50 = $ 1,425 Product B: 6 x $370 = $ 2,220 Product C: 3 x $2,270 = $ 6,810 Product D: 1 x $7,807 = $ 7,807 Total revised package contribution $18,262 Revised fixed costs $1,429,200 + $1,000,000 = $2,429,200

Revised break-even in revenues: $2,429,200

.23 = $10,561,739

Revised packages to break even: $2,429,200

$18,262 = 133 packages (rounded)

Per product: A: 133 x 10 = 1,330; B: 133 x 6 =798; C: 133 x 3 =399; D: 133 x 1 = 133.



2. Revised sales revenue = ($500 x 900) + ($1,800 x 400) + ( $9,200 x 500) + ($36,000 x 200) = $12,970,000

Revised contribution

Product A $142.50 x 900 = $128,250

Product B $370 x 400 = $148,000

Product C $2,270 x 500 = $1,135,000

Product D $7,807 x 200 = $1,561,400

Total revised contribution $2,972,650

Revised contribution margin % = $2,972,650 / $12,970,000 = 22.92%

New break even in revenue: $2,429,200 / 22.92% = $10,598,604

Revised sales mix is: A; 9; B: 4; C: 5; D: 2

Revised package contribution: (9 x $142.50) + (4 x $370) + (5 x $2,270) + (2 $7,807) = $29,727 (rounded)

Revised packages to break even: $2,429,200 / $29,727 = 82 packages (rounded)

Revised units to break even: A: 82 x 9 = 738; B: 82 x 4 = 328; C: 82 x 5 = 410; D: 82 x 2 = 164.

3. Using the changes outlined in Requirement 1:

Pre-tax net income is: $2,470,000 / .65 = $3,800,000

Fixed cost plus target income = $2,429,200 + $3,800,000 = $6,229,200

Revenue to meet new target: $6,229,200 / .23 (from 1 above) = $27,083,478

Using changes outlined in Requirement 2:

Fixed costs plus target pre-tax income = $6,229,200

New contribution margin % (from 2 above) = 22.92%

Revenues needed to meet target: $6,229,200 / .2292 = $27,178,010


Problem 4–43

1. Contribution margin ratios:

May of current year = $43,560

$23,910 = 0.549, or 54.9%

May of prior year = $41,700

$23,400 = 0.561, or 56.1%

2. Break-even point in sales dollars (in thousands):

May of current year = 0.549

$20,330 = $37,031

May of prior year = 0.561

$13,800 = $24,599

3. Margin of safety (in thousands):

May of current year = $43,560 – $37,031 = $6,529 May 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 large impact on the break-even point and the margin of safety. Bissonette 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 program 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.


PROFESSIONAL EXAMINATION PROBLEM*

Professional Examination Problem 4–44

1. CM/unit = $4 - $2.40 = $1.60 After-tax net income = [(390,000 × 1.60) - $440,000].6 = ($624,000 – $440,000).6 = $110,400 2. $440,000 / $1.60 = 275,000 boxes 3. Current CM ratio = $1.60 / $4 = 40% New variable costs = $2 × 1.15 + $0.40 = $2.70 Let SP = new selling price (SP - $2.70) / SP = 0.4 SP - $2.70 = 0.4SP SP – 0.4SP = $2.70 0.6SP = $2.70 SP = $4.50 4. CM = $4 - $2.70 = $1.30 CM ratio = $1.30 / $4 = 32.5% Desired operating income = $110,400 / .6 = $184,000 Desired sales volume = ($184,000 + $440,000) / 0.325 = $1,920,000 5. Let X = volume of boxes $1.30X – $440,000 = $4X(0.10) / 0.60 $1.30X – $440,000 = $0.6667X $0.6333X = $440,000 X = $440,000 / $0.6333 = 694,737 boxes

* © CPA Ontario.


CASES

Case 4–45

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 units Grade II: 0.7 × 748 = 524 units

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

I $ 3,400 $ 2,686 $714 3 $2,142 II 1,600 1,328 272 7 1,904 Package 21,400 17,354 $4,046

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

Total fixed costs $225,000

$225,000

$4,046 = 56 packages

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


Case 4–45 (Continued)


I $ 3,400 $ 2,444 $956 3 $2,868 II 1,600 1,208 392 7 2,744 Package 21,400 15,788 $5,612

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

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

Additional contribution margin: 141($956 – $714) + 329($392 – $272) = $73,602 Increase in fixed expenses 44,000 Increase in operating income $29,602

Break-even point for the year: ($225,000 + $75,430)


Grade I: 3 × 54 = 162 Grade II: 7 × 54 = 378

If the new break-even point is the revised break-even point for the current year, therefore total fixed costs must be reduced by the contribution margin 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 = ($225,000 + $44,000 - $118,102)


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




I $3,400 $2,686 $714 1 $714 II 1,600 1,328 272 1 272 Package 5,000 4,014 $986

New 7-month sales revenue $1,000,000 × 130% = $1,300,000

$5,000X = $1,300,000 X = 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 = Fixed cost

(Price Variable cost)-

= $986

$295,000

= 299 packages (or 299 of each cabinet)

The break-even point is computed as follows:

X = ($295,000 - $118,102)

$986

= $986

$176,898

= 179 packages (179 of each)

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


Case 4–46

Per-unit product contribution analysis

T-shirts Sweatshirts Fleece

Jackets

Revenue $6.50 $16.00 $38.50

Materials 1.50 3.00 12.00

Direct labour 2.50 3.00 8.00

Variable selling 0.65 1.60 3.85

Contribution 1.85 8.40 14.65

Product per package 5 3 2

Contribution per package $9.25 $25.20 $29.30

Package revenues = ($6.50 x 5) + ($16.00 x 3) + ($38.50 x 2) = $157.50

Total contribution per package = $9.25 + $25.20 + $29.30 = $63.75

Contribution margin % = $63.75 / $157.50 = 40.48%

Fixed costs: $300,000 + $150,000 + $250,000 = $700,000

Break-even revenues = Fixed costs / contribution margin %

Break-even revenues = $700,000 / .4048 = $1,729,249

Target profit of $140,000 after tax is ($140,000 /.6) = $233,333 pre-tax

Revenue to achieve target = profit fixed costs plus pre-tax target / Contribution margin %

Revenue is ($700,000 + $233,333) / .4048 = $2,305.665

Packages to achieve break-even $700,000 / $63.75 = 10,981 (rounded up)



Units: 54,905 t-shirts (10,981 x 5); 32,943 sweatshirts (10,981 x 3); 21,962 fleece jackets (10,981 x 2)

Packages to achieve target profit: $933,333 / $63.75 = 14,641

Units: 73,205 t-shirts (14,641 x 5); 43,923 sweatshirts (14,641 x 3); 29,282 fleece jackets (14,641 x 2)

Case 4–47

1. Break-even point = Fixed expense

(Price-Variable cost)

First process: $100,000

($30 $10)- = 5,000 cases

Second process: $200,000

($30 $6)- = 8,333 cases

2. Income = X(Price – Variable cost) – Fixed cost X($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. Donna has an ethical obligation to report the correct information to her superior. By altering the sales forecast, Donna would unfairly and unethically influence the decision-making process. Managers certainly have a moral obligation to assess the impact of their decisions on employees, and every effort should be taken to be fair and honest with employees. Donna’s behaviour, however, is not justified by the fact that it would help a number of employees retain their employment. First, Donna has no right to make that decision. Donna certainly 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 alternative 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 Hussan Khalil than any legitimate concerns for the layoff of other employees. Donna should examine her reasoning carefully to assess the real reasons for her behaviour. Perhaps in so doing, the conflict of interest that underlies her decision will become apparent.

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