Cost Behavior and Cost-Volume-Profit Analysis

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Cost Cost Behavior Behavior and Cost-and Cost-Volume-Volume-

Profit Profit AnalysisAnalysis

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Classify costs by their behavior as variable costs, fixed costs, or

mixed costs.

Objective 1Objective 1Objective 1Objective 1

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Jason Inc. produces stereo sound systems under the brand name of J-Sound. The parts for the J-Sound stereos are purchased from outside

suppliers for $10 per unit (a variable cost) and assembled in Jason Inc.’s

Waterloo plant.

Jason Inc.’s Waterloo Plant 4-1

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Total Variable Cost GraphT

otal

Dir

ect

Mat

eria

ls C

ost $300,000

$250,000$200,000$150,000$100,000 $50,000

10 20 300Total Units (Model JS-12)

Produced (thousands)

Variable Cost Graphs (Cont’d) 4-1

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Unit Variable Cost Graph

$20

$15

$10

$5

0

Dir

ect

Mat

eria

ls

Cos

t p

er U

nit

10 20 30Total Units (Model JS-

12) Produced (thousands)

Variable Cost Graphs

(Concluded)

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Tot

al C

osts

$300,000$250,000$200,000$150,000$100,000 $50,000

10 20 300

$20$15$10

$5

0

Cos

t per

Uni

t

10 20 30

Number ofUnits of Model JS-12 Produced

Units Produced (000)

Units Produced (000)

Direct Materials Cost

per UnitTotal Direct

Materials Cost

5,000 units $10 $ 50,00010,000 10 l00,00015,000 10 150,00020,000 10 200,00025,000 10 250,00030,000 10 300,000

Unit Cost Compared to Total Cost 4-1

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The production supervisor for Minton Inc.’s Los Angeles plant

is Jane Sovissi. She is paid $75,000 per year. The plant

produces from 50,000 to 300,000 bottles of La Fleur Perfume.

Minton Inc.’s Los Angeles Plant 4-1

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Number ofBottles of Perfume

ProducedTotal Salary

for Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375

250,000 75,000 0.300300,000 75,000 0.250

Salary per Bottle of Perfume Produced

Fixed Versus Variable Cost of Jane Sovissi’s Salary

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Tot

al C

osts

$150,000$125,000$100,000$75,000$50,000

$25,000

100 200 3000Bottles Produced (000)

Number ofBottles of Perfume

Produced

Un

it C

ost

$1.50$1.25$1.00

$.75$.50

$.25

100 200 3000Units Produced (000)

Total Salary for Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375

Salary per Bottle of Perfume Produced

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Simpson Inc. manufactures sails using rented equipment.

The rental charges are $15,000 per year, plus $1 for each machine hour used over

10,000 hours.

Simpson Inc. Example 4-1

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Tot

al C

osts

0Total Machine Hours (000)

$45,000$40,000 $35,000$30,000$25,000$20,000$15,000$10,000 $5,000

10 20 30 40

Mixed costs are usually separated into

their fixed and variable components

for management analysis.

Mixed Cost Graph for Simpson Inc.’s Equipment Rental Charges

4-1

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The high-low method is a simple cost estimate

technique that may be used for separating mixed costs into their fixed and

variable components.

High-Low Method 4-1

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Example Exercise 4-1

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The manufacturing cost of Alex Industries for the first three months of the year are provided below:

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Total Cost ProductionJanuary $80,000 1,000 unitsFebruary $125,000 2,500March $100,000 1,800

Using the high-low method, determine the (a) variable cost per unit, and (b) the total fixed cost.

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For Practice: PE4-1A, PE4-1B

Follow My Example 4-1

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b. $50,000 = $125,000 – ($30 x 2,500) or $80,000 – ($30 x 1,000)

a. $30 per unit =$125,000 – $80,000

(2,500 – 1,000)

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Total Variable

Costs

Total Units Produced

Unit Variable

Costs


Tot

al C

osts

Per

Uni

t Cos

t

Total costs increase and

decrease proportionately

with activity level.

Summary of Cost Behavior Concepts

Unit costs remain the same per unit

regardless of activity.

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Tot

al C

osts


Per

Uni

t Cos

t

Unit costs remain the same

regardless of activity.

Total costs increase and

decrease with activity

level.

Summary of Cost Behavior Concepts

Total Fixed Costs

Unit Fixed Costs

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Compute the contribution margin, the contribution margin ratio,

and the unit contribution margin, and explain how they may be

useful to managers.


4-2

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Cost-Volume-Profit Relationships

Cost-volume-profit analysis is the systematic examination of the

relationships among selling prices, sales and production volume, costs, expenses, and profits.

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The contribution margin is the excess of sales revenues over

variable costs. It contributes first toward covering fixed costs, then

contributes to profit.

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Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000

Contribution Margin Income Statement

4-24

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Contribution Margin Ratio 4-2

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100% 60%

Contribution Margin Ratio = 40%


Contribution Margin Ratio =Sales – Variable Costs

Sales$1,000,000 – $600,000

$1,000,000 Contribution Margin Ratio =

40% 30%10%

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Unit Contribution Margin

The unit contribution margin is also useful for analyzing the

profit potential of proposed projects. The unit contribution margin is the sales price less

the variable cost per unit.

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Using Contribution Margin per Unit as a Shortcut

Sales ($20) $1,000,000Variable costs ($12) 600,000Contribution margin ($8) $ 400,000 Fixed costs 300,000Income from operations $ 100,000

50,000 units

65,000 units

The increase in income from operations of $120,000 could have been determined quickly by multiplying the increase in unit sales (15,000) by

the contribution margin per unit ($8).

$1,300,000 780,000$ 520,000 300,000

$220,000

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100% 60%

40% 30%

10%

$20 12$ 8


Unit contribution margin analyses can provide useful information for managers.

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100% 60%

40% 30%

10%

1. Total contribution margin in dollars.

$20 12$ 8


2. Contribution margin ratio (percentage).

The contribution margin can be expressed three ways:

3. Unit contribution margin (dollars per unit).

Review 4-2

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4-2

Molly Company sells 20,000 units at $12 per unit. Variable costs are $9 per unit, and fixed costs are $25,000. Determine the (a) contrib-ution margin ratio, (b) unit contribution margin, and (c) income from operations.

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4-2

a. 25% = ($12 – $9)/$12 or ($240,000 – $180,000)/$240,000b. $3 per unit = $12 – $9

c. Sales $240,000 (20,000 x $12)Variable costs 180,000 (20,000 x $9)Contribution margin $ 60,000 [20,000 x $12 –$9)]Fixed costs 25,000Income from operations $ 35,000

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Using the unit contribution margin, determine the break-even point and the volume necessary to

achieve a target profit.


4-3

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Break-Even Point

The break-even point is the level of operations at

which a business’s revenues and expired costs

are exactly equal.

4-3

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Barker Corporation’s fixed costs are estimated to be $90,000. The unit contribution margin is calculated as follows:

Unit selling price $25Unit variable cost 15Unit contribution margin $10

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The break-even point is calculated using the following equation:

Break-Even Sales (units) =Fixed Costs


Break-Even Sales (units) =$90,000

$10

Break-Even Sales (units) = 9,000 units

4-3

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Proof of the Preceding Computation

Sales ($25 x 9,000) $225,000Variable costs ($15 x 9,000) 135,000Contribution margin $ 90,000Fixed costs 90,000Income from operations $ 0

Income from operations is zero when 9,000 units are sold—hence, break-

even is 9,000 units.

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Effect of Changes in Fixed Costs

Fixed Fixed CostsCosts

Fixed Fixed CostsCostsIf

Break-Break-EvenEven

Break-Break-EvenEvenThen

Fixed Fixed CostsCosts

Fixed Fixed CostsCostsIf Then Break-Break-

EvenEven


4-3

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Bishop Co. is evaluating a proposal to budget an additional $100,000 for advertising. Fixed costs before the additional advertising are estimated

at $600,000, and the unit contribution margin is $20.

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Without additional advertising:

4-3

Break-Even in Sales (units) =Fixed Costs


Break-Even in Sales (units) =$600,000

$20=

30,000 units

With additional advertising:


$20=

35,000 units

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Effect of Changes in Unit Variable Costs

Unit Unit Variable Variable

CostCost


CostCostIf Break-Break-

EvenEven


Then


CostsCosts


CostsCosts

If Then Break-Break-EvenEven


4-3

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Park Co. is evaluating a proposal to pay an additional 2% commission on sales to its salespeople (a variable cost) as an incentive to increase sales. Fixed costs are estimated at $840,000. The unit contribution margin before the additional 2% commission is determined as follows:


4-3

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Without additional 2% commission:




$105=

8,000 units

With additional 2% commission:


$100=

8,400 units

$250 – [$145 + ($250 x 2%)] = $100

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Effect of Changes in the Unit Selling Price

Unit Unit Selling Selling PricePrice

Unit Unit Selling Selling PricePrice

If



Then

Unit Unit Selling Selling

PricePrice

Unit Unit Selling Selling

PricePriceIf Then



4-3

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Graham Co. is evaluating a proposal to increase the unit selling price of a product from $50 to $60. The following data have been gathered:

Unit selling price $50 $60Unit variable cost 30 30Unit contribution margin $20 $30

Current Proposed

Total fixed costs $600,000 $600,000

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Without price increase:




$20=

30,000 units

With price increase:


$30=

20,000 units

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Summary of Effects of Changes on Break-Even Point

Effect of ChangeDirection of on Break-Even

Change Sales (Units)Type of Change

Fixed cost Increase IncreaseDecrease Decrease

Variable cost per unit Increase IncreaseDecreaseDecrease

Unit sales price Increase DecreaseIncreaseDecrease

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4-3

Nicholas Enterprises sells a product for $60 per unit. The variable cost is $35 per unit, while fixed costs are $80,000. Determine the (a) break-even point in sales units, and (b) break-even point if the selling price were increased to $67 per unit.

57For Practice: PE4-3A, PE4-3B


a. 3,200 units = $80,000/($60 – $35)

b. 2,500 units = $80,000/($67 – $35)

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Target Profit

The sales volume required to earn a target profit is determined by modifying the break-even equation.

Sales (units) =Fixed Costs + Target ProfitUnit Contribution Margin

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Fixed costs are estimated at $200,000, and the desired profit is $100,000. Unit contribution margin is $30.


Sales (units) =Fixed Costs + Target ProfitUnit Contribution Margin$30

Sales (units) = 10,000 units

Units Required for Target Profit 4-3

$200,000 $100,000

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Sales (10,000 units x $75) $750,000Variable costs (10,000 x $45) 450,000Contribution margin (10,000

x $30) $300,000Fixed costs 200,000Income from operations $100,000

Proof that sales of 10,000 units will Proof that sales of 10,000 units will provide a profit of $100,000.provide a profit of $100,000.

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4-3

The Forest Company sells a product for $140 per unit. The variable cost is $60 per unit, and fixed costs are $240,000. Determine the (a) break-even point in sales units, and (b) break-even point in sales units if the company desires a target profit of $50,000.



a. 3,000 units = $240,000/($140 – $60)

b. 3,625 units = ($240,000 + $50,000)/($140 – $60)

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Using a cost-volume-profit chart and a profit-volume chart,

determine the break-even point and the volume necessary to

achieve a target profit.


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Cost-Volume-Profit (Break-Even) Chart

A cost-volume-profit chart, sometimes called a

break-even chart, may assist management in

understanding relationships among costs, sales, and operating profit or loss.

4-4

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Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

The cost-volume-profit chart in Exhibit 5 (Slides 65-73) is based on the following data:

4-4

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Sale

s an

d C

osts

(in

th

ousa

nds)

0Units of Sales (in thousands)

$500$450$400$350$300$250$200$150$100$ 50

Cost-Volume-Profit Chart

Volume is shown on the horizontal axis.Volume is shown on the horizontal axis.

Dollar amounts

are indicated along the vertical

axis.

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1 2 3 4 5 6 7 8 9 10

4-4

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Cost-Volume-Profit Chart (Continued)

Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

1 2 3 4 5 6 7 8 9 10

A sales line is plotted by determining one value ($500,000 in sales divided by the $50 selling price equals 10,000 units).

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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

1 2 3 4 5 6 7 8 9 10

Now, beginning at zero on the left corner of the graph, connect a straight line to the dot.


4-4

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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

Fixed cost of $100,00 is a horizontal line.

1 2 3 4 5 6 7 8 9 10


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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

Similar to the sales line, a point is determined on the cost line (10,000 @ $30 = $300,000 + $100,000 = $400,000)

1 2 3 4 5 6 7 8 9 10


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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

Beginning with the total fixed cost at the vertical axis ($100,000), draw a line to the red dot. This is the total cost

line.

1 2 3 4 5 6 7 8 9 10


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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

Horizontal and vertical lines are drawn at the intersection point of the sales and cost lines, which is the break-even point.

1 2 3 4 5 6 7 8 9 10


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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

Break-even is sales of 5,000 units or $250,000.

1 2 3 4 5 6 7 8 9 10


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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

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Profit area

Loss area

Cost-Volume-Profit Chart (Concluded)

4-4

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Revised Cost-Volume-Profit Chart

Using the data from Slide 64, assume that a proposal to reduced fixed cost by

$20,000 is to be evaluated. A cost-volume-profit chart can be created to

assist in this evaluation.

4-4

Click this button to go to Slide 64. Return to this slide by typing “74” and striking “Enter.”

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Sale

s an

d C

osts

(in

th

ousa

nds)


$500$450$400$350$300$250$200$150$100$ 50

1 2 3 4 5 6 7 8 9 10

$80,000

If fixed costs can be reduced to $80,000, the new break-even point is sales of $200,000 or 4,000 units.

Revised Cost-Volume-Profit Chart

4-4

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Profit-Volume Chart

Another graphic approach to cost-volume-profit analysis, the profit-volume chart, plots

only the difference between total sales and total costs (or profits). Again, the data from

Slide 64 (shown below) will be used.

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000

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Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000 Operating profit $100,000

The maximum operating loss is equal to the fixed costs of $100,000. Assuming that the

maximum unit sales within the relevant range is 10,000 units, the maximum operating profit is

$100,000, computed as follows:

4-4

Maximum profit

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Units of Sales (in thousands)

1 2 3 4 5 6 7 8 9 10

Profit Line

Operating Operating lossloss

Operating Operating profitprofit

$100,000$75,000$50,000$25,000

$ 0$(25,000)$(50,000)$(75,000)

$(100,000)

Op

erat

ing

Pro

fit

(Los

s)

Maximum loss is $100,000, the fixed costs.

Profit-Volume Chart

Break-Even Point

4-4

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Assumptions of Cost-Volume-Profit Analysis

The primary assumptions are:

1. Total sales and total costs can be represented by a straight line.

2. Within the relevant range of operating activity, the efficiency of operations does not change.

3. Costs can be accurately divided into fixed and variable components.

4. The sales mix is constant.5. There is no change in the inventory quantities

during the period.

4-4

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Compute the break-even point for a business selling more than one

product, the operating leverage, and the margin of safety, and explain how

managers use these concepts.


4-5

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Sales Mix Considerations

The sales volume necessary to break even or to earn a target profit for a business selling two or more products depends upon the sales

mix. The sales mix is the relative distribution of sales among the

various products sold by a business.

4-5

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Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows:

Unit Unit Unit SalesSelling Variable Contribution Mix

Product Price Cost Margin %

A $ 90 $70 $20 20%B 140 95 45 80%

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For Cascade Company, the overall enterprise product is called E.

Unit selling price of E: ($90 x 0.8) + ($140 x 0.2) = $100

Unit variable cost of E: ($70 x 0.8) + ($ 95 x 0.2) = $ 75

Unit contribution margin of E: ($20 x .08) + ($45 x .02) = $ 25

4-5Cascade Company Example

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4-5Break-Even Point of 8,000 Units of E

Break-Even Sales (units) =Fixed Costs


Break-Even Sales (units) =$200,000

$25

Break-Even Sales (units) = 8,000 units

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Verification of Analysis

Break-even point

4-5

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4-5

Megan Company has fixed cost of $180,000. The unit selling price, variable cost per unit, and contribution margin per unit for the company’s two products are provided below:

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Variable Contribution SalesSelling Cost per Margin per Mix

Product Price Unit Unit %

Q $ 160 $100 $20 75%Z 140 95 45 25%

Determine the break-even point in units of Q and Z.

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4-5

Unit selling price of E: ($160 x .75) + ($100 x .25) = $145

Unit variable cost of E: ($100 x .75) + ($80 x .25) = $95

Unit contribution marginof E: ($60 x .75) + ($20 x .25), or $145 – $95 = $50

Break-even sales (units) = 3,600 units = $180,000/$50

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The relative mix of a business’s variable costs and fixed costs is measured by the operating leverage. It is computed as follows:

4-5Operating Leverage

Operating Leverage =Contribution Margin

Income from Operations

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Both companies have the same contribution margin.

Jones Inc. Wilson Inc.

Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Operating leverage ? ?

4-5Operating Leverage Example

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Contribution Margin


$100,000

$20,000= 5 Jones Inc.:


Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Operating leverage ? ? 5

4-5

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Contribution Margin


$100,000

$50,000= 2 Wilson Inc.:


Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Operating leverage ? ? 25

4-5

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High Versus Low Operating Leverage 4-5

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4-5

The Tucker Company reports the following data.



4.0 = ($750,000 – $500,000)/($750,000 – $500,000 – $187,500) = $250,000/$62,500

Sales $750,000Variable costs $500,000Fixed costs $187,500

Determine Tucker Company’s operating leverage.

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Margin of Safety

The difference between the current sales revenue and the

sales revenue at the break-even point is called the

margin of safety.

4-5

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If sales are $250,000, the unit selling price is $25, and the sales at the break-even point are $200,000, the margin of safety is 20%, computed as follows:

4-5

Margin of Safety =Sales – Sales at Break-Even Point

Sales

Margin of Safety = 20%

Margin of Safety =$250,000 – $200,000

$250,000

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4-5

The Rachel Company has sales of $400,000, and the break-even point in sales dollars is $300,000. Determine the company’s margin of safety.



25% = ($400,000 – $300,000)/$400,000

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Preparing a Variable Costing Income Statement

Number UnitTotal Cost of Units Cost

Manufacturing costs:Variable $375,000 15,000 $25Fixed 150,000 15,000 10 Total $525,000 $35

Selling and administrativeexpenses:

Variable ($5 per unit sold) $ 75,000Fixed 50,000 Total $125,000

4-5

Cost Behavior and Cost-Volume-Profit Analysis

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