21-1 COST-VOLUME-PROFIT ANALYSIS CHAPTER 21 21-2 Cost-Volume-Profit Analysis l You must understand...

21-1

COST-VOLUME-PROFITANALYSIS

CHAPTER 21CHAPTER 21

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Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis You must understand the relationships

between costs, volume and “profit”i.e., costs, volume and revenues

The concept is also known as“Break-Even Analysis”

Focuses on short-run decision makingi.e, time frame during which a company can’t change effects of certain past decisions

Long-run decision making is covered in Chapter 26

You must understand the relationshipsbetween costs, volume and “profit”

i.e., costs, volume and revenues The concept is also known as

“Break-Even Analysis” Focuses on short-run decision making

i.e, time frame during which a company can’t change effects of certain past decisions

Long-run decision making is covered in Chapter 26

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Cost-Volume-Profit AnalysisCost-Volume-Profit AnalysisAssumptionsAssumptions

Throughout the relevant range (range of activity where cost behavior assumptions are valid) Unit sales price remains constant Unit variable cost remains constant Total fixed cost remains constant

All costs may be classified as eitherfixed or variable

Throughout the relevant range (range of activity where cost behavior assumptions are valid) Unit sales price remains constant Unit variable cost remains constant Total fixed cost remains constant

All costs may be classified as eitherfixed or variable

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Cost Behavior PatternsCost Behavior Patterns Cost behavior means

how a cost will react to changes in the level of business

activity.

Variable CostsVariable Costsreact differently.

Fixed CostsFixed Costs and

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Cost Behavior PatternsCost Behavior PatternsFixed CostsFixed Costs

Total fixed costs remain constantconstant over wide ranges of activity/volume.

Per unit fixed costs decreasedecrease as volume level increases.

Example: basic monthly telephone charge Total cost is unchanged regardless

of number of local calls. Cost per local call decreases as

number of local calls increases.

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TotalTotal Fixed Cost Example Fixed Cost Example Your monthly basic telephone bill is probably

unchanged as you make more local calls.

Number of Local Calls

Mo

nth

ly B

asic

T

elep

ho

ne

Bill

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PerPer UnitUnit Fixed Cost Example Fixed Cost Example

Number of Local Calls

Mo

nth

ly B

asic

Tel

eph

on

e B

ill p

er L

oca

l Cal

l

The average cost per local call decreasesas more local calls are made.

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Total variable costs increase andand decrease in proportion to increases and decreases in volume.

Per unit variable costs remain constantconstant over wide ranges of volume.

Example: long distance telephone chargesTotal cost will increase as a

function of minutes talked.Cost per minute remains unchanged.

Cost Behavior PatternsCost Behavior PatternsVariable CostsVariable Costs

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TotalTotal Variable Cost Example Variable Cost Example Your total long distance telephone billis based on how many minutes you talk.

Minutes Talked

To

tal L

on

g D

ista

nce

Tel

eph

on

e B

ill

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PerPer UnitUnit Variable Cost Example Variable Cost Example

Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

The cost per long distance minute talked is constant. For example, 10 cents per minute.

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Summary of Variable and Fixed Cost Behavior

Cost In Total Per Unit

Total variable cost changes Variable cost per unit remainsVariable as activity level changes. the same over wide ranges

of activity.

Total fixed cost remains Fixed cost per unit goesFixed the same even when the down as activity level goes up.

activity level changes.

Cost Behavior PatternsCost Behavior Patterns

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Cost Behavior QuestionCost Behavior Question

Fixed costs are usually characterized by:

a. Unit costs that remain constant.

b. Total costs that increase as activity decreases.

c. Total costs that increase as activity increases.

d. Total costs that remain constant.






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a.

b.

c.

d.

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Variable costs are usually characterized by:

a. Unit costs that decrease as activity increases.









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a.

b.

c.

d.

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Contains fixed portion incurred even when facility is unused and a variable portion which increases with usage.

Example: monthly electric utility charge Fixed service fee

Variable charge perkilowatt hour used

Cost Behavior PatternsCost Behavior PatternsMixed CostsMixed Costs

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$

Total Cost


Activity/Volume Level

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Activity/Volume Level

Total Cost

$

Fixed Portion

Variable Portion


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Definition: Constant fixed cost over a range of activity with an increase at a certain level to a new, higher fixed cost.

Example: A supervisor’s salary is $30,000 for a process that produces 10,000 units. When volume increased beyond 10,000 units, a second process was added with a second supervisor, increasing total salaries to $60,000.

Cost Behavior PatternsCost Behavior PatternsStep CostsStep Costs

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Sal

arie

s in

T

ho

usa

nd

s o

f D

oll

ars

0 10 20 Activity in Thousands

0

30

60

Cost Behavior PatternsCost Behavior PatternsStep CostsStep Costs

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Cost Behavior PatternsCost Behavior PatternsCurvilinear CostsCurvilinear Costs

Costs that increase when activity increases, but in a non-linear manner

Activity

To

tal

Co

st

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Definition: Range of activity where the cost behavior assumptions are valid Total fixed costs remain constant. Per unit variable costs remain unchanged.

The cost behavior assumptions discussed earlier allow us to use linear relationships.

How does this differ from what you learned in your economics course?

Definition: Range of activity where the cost behavior assumptions are valid Total fixed costs remain constant. Per unit variable costs remain unchanged.

The cost behavior assumptions discussed earlier allow us to use linear relationships.

How does this differ from what you learned in your economics course?

Cost Behavior PatternsCost Behavior PatternsRelevant RangeRelevant Range

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Economics (Economies of Scale) Extremely wide range assumed e.g., 0 to

Accounting Relatively narrow range assumed e.g., 40,000 units to 100,000 units

Economics (Economies of Scale) Extremely wide range assumed e.g., 0 to

Accounting Relatively narrow range assumed e.g., 40,000 units to 100,000 units

8

Cost Behavior PatternsCost Behavior PatternsRelevant RangeRelevant Range

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The Linearity AssumptionThe Linearity Assumptionand the Relevant Rangeand the Relevant Range

Activity

To

tal

Co

st

Economist’sCurvilinear Total Cost Function

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Activity

To

tal

Co

st

Economist’sCurvilinear Total Cost Function

Accountant’s Straight-Line Approximation (constant

unit variable cost)


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A straight line closely approximates a curvilinear variable cost line within the

relevant range.

RelevantRange

Accountant’s Straight-Line Approximation (constant

unit variable cost)

To

tal

Co

st

Activity


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Example: Office space is available at a rental

rate of $30,000 per year in increments of 1,000 square feet. As the business grows

more space is rented, increasing the total

cost.

Fixed Costs and Relevant RangeFixed Costs and Relevant Range

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Total cost doesn’t change for a wide range of activity,

and then jumps to a new higher cost for

the next higher range of activity.

0 1,000 2,000 3,000 Rented Area (Square Feet)

Ren

t C

ost

in

T

ho

usa

nd

s o

f D

oll

ars

0

30

60

90

Relevant

Range

Relevant

Range

Relevant

Range

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How does this type of fixed cost differ from a step cost?


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How does this type of fixed cost differ from a step cost?

Step costs can be adjusted more quickly

and . . .

The width of the activity steps is much

wider for the fixed cost.


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Methods for Analyzing CostsMethods for Analyzing Costs

We will separate a mixed cost into

its fixed and variable

components.

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Two methods will be used:

Scatter Diagram

High-low method

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Plot the data points on a graph (total cost vs. activity).

0 1 2 3 4

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

****

**

**

*

*

Activity, 1,000’s of Units Produced

Scatter DiagramScatter DiagramA scatter diagram of past cost behavior

is helpful in analyzing mixed costs.

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Scatter DiagramScatter DiagramDraw a line through the plotted data points so that about an equal numbers of points fall above and below the line.

0 1 2 3 4

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

****

**

**

*

*


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Scatter DiagramScatter Diagram

Estimated fixed cost = $10,000

0 1 2 3 4

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

****

**

**

*

*


Where line intercepts with cost axis is total fixed cost.

Review regression analysis calculations from your statistics class and bring your scientific

calculator to the next test.

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Now, the

High-low method

(You are responsible for knowing how to

use it.)

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.

Analyzing Mixed CostsAnalyzing Mixed CostsHigh-Low MethodHigh-Low Method

Objective: To separate total cost into fixed and variable portions.

Step 1 - Calculate variable cost per unit.V.C./unit = in cost ÷ in units

Objective: To separate total cost into fixed and variable portions.

Step 1 - Calculate variable cost per unit.V.C./unit = in cost ÷ in units

Step 2 - Calculate total variable cost at either high or low volume level and subtract it from totaltotal cost at the same volume level to determine total fixedfixed cost at any level.

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WiseCo recorded the following production activity and maintenance costs for two months:

The High-Low MethodThe High-Low Method

Units Cost

High activity level 9,000 9,700$Low activity level 5,000 6,100 Change 4,000 3,600$

Using these two levels of activity, compute: the variable cost per unit the total fixed cost

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Units Cost


Unit variable cost = = = $.90in costin units

$3,600$4,000

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Units Cost


Unit variable cost = = = $.90

Fixed cost = Total cost – Total variable cost

in costin units

$3,600$4,000

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Units Cost



Fixed cost = Total cost – Total variable costFixed cost = $9,700 – ($.90 per unit × 9,000 units)Fixed cost = $9,700 – $8,100 = $1,600

in costin units

$3,600$4,000

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Choosing the low activity level will

give the same result.


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Fixed cost = Total cost – Total variable costFixed cost = $6,100 – ($.90 per unit × 5,000 units)Fixed cost = $6,100 – $4,500 = $1,600


Units Cost


in costin units

$3,600$4,000

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Now that we understand cost behavior, let’s

turn our attention to

cost-volume-profit analysis.

Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis

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Objective

Determine the effects that changes in selling prices, costs, and/or volume will

have on profits in the short run.

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Cost-Volume-Profit ChartCost-Volume-Profit Chart

Income

Loss

Sales

Total costs

Units of Activity

Co

sts

and

Rev

enu

ein

Do

llar

s

Break-even Point

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At any point on the cost-volume-profitchart the following relationships are valid:

At any point on the cost-volume-profitchart the following relationships are valid:

Profit EquationsProfit Equations

Variable costs + Fixed costs

Net income = Revenue – Total costs

Contribution Margin = Revenue – Variable costs

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.

Relevant sales volume range

The Cost-Volume-Profit Chart 240

220 -

200 -

180 -

160 -

140 -

120 -

100 -

80 -

60 -

40 -

20 -

01 2 3 4 5 6 7 8 9 10 11 12

- - - - - - - - - - -

Units (000)

Do

llar

s ($

000)

Variable costsVariable costsFixed costs

Total costs

Total costs

Sales

SalesBreak-even point

Net income

Fixed costsNet lo

ss

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Let’s look at the OK Company example.

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Contribution margin is amount by which revenue exceeds variable costs of producing the revenue.

Contribution margin is amount by which revenue exceeds variable costs of producing the revenue.

Cost-Volume-Profit AnalysisCost-Volume-Profit AnalysisTotal Unit

Sales Revenue (2,000 units) 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

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Contribution margin goes to cover fixed costs and ...Contribution margin goes to cover fixed costs and ...

Total Unit




Less: Fixed costs 30,000

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Total Unit





Net income 10,000$


Contribution margin goes to cover fixed costs and …

after covering fixed costs, any remainingcontribution margin contributes to net income.

Contribution margin goes to cover fixed costs and …

after covering fixed costs, any remainingcontribution margin contributes to net income.

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Net income 10,000$

How much contribution margin does OKneed to cover its fixed costs (i.e., break even)?


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Answer $30,000


Answer $30,000

Total Unit





Net income 10,000$

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Net income 10,000$

How many units must OK sell tocover its fixed costs (break even)?


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$30,000 ÷ $20 per unit = 1,500 units


$30,000 ÷ $20 per unit = 1,500 units






Net income 10,000$

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Contribution margin 30,000 20$


Net income $ 0P R

OOF


$30,000 ÷ $20 per unit = 1,500 units


$30,000 ÷ $20 per unit = 1,500 units

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Contribution margin per unit is sales price per unit less variable cost per unit. Conceptually, it represents the amount of each sales dollar which “contributes” to

fixed costs and profit (net income).

Break-even units = Fixed costs

Contribution margin per unit

We have just seen one of the basic cost-volume-profit relationships, the

break-even break-even computation in units.


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Break-even (BE) Computation

BEunits = Fixed costs

Contribution margin per unit

Finding the Break-Even PointFinding the Break-Even Point

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The contribution margin rate is computed eithereither by dividing contribution margin per unit by selling price per unit oror by dividing total contribution margin by

total revenues.

The break-even formula may also be expressed in sales dollars.

Break-even dollars = Fixed costs

Contribution margin ratio rate

Conceptually, the contribution margin rate represents the percentage of each sales dollar which

“contributes” to fixed costs and profit (net income).


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The break-even formula may also be expressed in sales dollars:

BE$ = Fixed costs

Contribution margin rate


OK’s CMR

CMR = contribution margin as a percentage of sales.

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Total Unit Percent

Sales Revenue (1,500 units) 75,000$ 50$ 100%

Less: Variable costs 45,000 30 60%

Contribution margin 30,000 20$ 40%

OK’s CMR is 40%or $20/$50.

OK’s contribution margin per unit is $20.

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Tulip Co. sells its plant cartons at $5.00 per unit. If fixed costs are $200,000 and variable

costs are $3.00 per unit, how many units must be sold to break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units



a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Cost-Volume-Profit AnalysisCost-Volume-Profit AnalysisQuestionQuestion

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a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units



a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units


= $200,000$5.00 – $3.00

= 100,000 units

Fixed costsUnit contribution

a.

b.

c.

d.

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Use the CMR formula to determine the amount of sales revenue Tulip Co. needs to

break even. Fixed costs ($200,000), unit sales price ($5), and per unit variable cost

($3) are unchanged.

a. $200,000

b. $300,000

c. $400,000

d. $500,000



($3) are unchanged.

a. $200,000

b. $300,000

c. $400,000

d. $500,000


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($3) are unchanged.

a. $200,000

b. $300,000

c. $400,000

d. $500,000



($3) are unchanged.

a. $200,000

b. $300,000

c. $400,000

d. $500,000


CMR = ($5.00 – $3.00) ÷ $5.00 = .40

BE$ = $200,000 ÷ .40 = $500,000

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Product 1 Product 2Amount % Amount % Total %

Sales 20,000$ 100% 80,000$ 100% 100,000$ 100%

Less: Variable costs 15,000 75% 40,000 50% 55,000 55%4000Contribution margin 5,000$ 25% 40,000$ 50% 45,000$ 45%


Income 18,000$

Calculating Break-Even forCalculating Break-Even fora Multiproduct Company a Multiproduct Company

Forget it! You

are not

responsible

for this

concept.

Forget it! You

are not

responsible

for this

concept.

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Break-even formulas may be adjusted to show the sales volume needed to earn

any amount of income.

Cost-Volume-Profit AnalysisCost-Volume-Profit AnalysisDesired IncomeDesired Income

Add desired income to fixed costs in thenumerator. No other changes are needed.

Add desired income to fixed costs in thenumerator. No other changes are needed.

BE$ = Fixed costs + Desired income

Contribution margin rate

BEunits = Fixed costs + Desired incomeContribution margin per unit

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costs are $3.00 per unit, how many units must be sold to earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units



a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units


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a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units



a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

Fixed costs + Desired income Unit contribution

$200,000 + $40,000 $5.00 – $3.00

= 120,000 units


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Excess of current sales over thebreak-even volume of sales. (i.e., the amount by which sales may decline before reaching break-even sales.)

Excess of current sales over thebreak-even volume of sales. (i.e., the amount by which sales may decline before reaching break-even sales.)

Margin of safety = Current sales – Break-even sales

Margin of SafetyMargin of Safety

Let’s calculate the marginof safety for OK Company.

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Margin of SafetyMargin of SafetyCurrent sales 100,000$ Breakeven sales 75,000 - Margin of safety 25,000$

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The margin of safety may also be expressed as a percentage of current sales.

The margin of safety may also be expressed as a percentage of current sales.

Margin of SafetyMargin of Safety

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Margin of SafetyMargin of SafetyMargin of safety Current sales - Break-even sales percentage Current sales

=

$100,000 - $75,000 $100,000

=

= 25%

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THE ENDTHE END

21-1 COST-VOLUME-PROFIT ANALYSIS CHAPTER 21 21-2 Cost-Volume-Profit Analysis l You must understand...

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Transcript of 21-1 COST-VOLUME-PROFIT ANALYSIS CHAPTER 21 21-2 Cost-Volume-Profit Analysis l You must understand...