© The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Chapter 22 Cost-Volume-Profit Analysis

© The McGraw-Hill Companies, Inc., 2007McGraw-Hill/Irwin

Chapter 22

Cost-Volume-Profit Analysis


Conceptual Learning Objectives

C1: Describe different types of cost behavior in relation to production and sales volume

C2: Identify assumptions in cost-volume profit analysis and explain their impact

C3: Describe several applications of cost-volume-profit analysis


A1: Compare the scatter diagram, high-low, and regression methods of estimating costs

A2: Compute contribution margin and describe what it reveals about a company’s cost structure

A3: Analyze changes in sales using the degree of operating leverage

Analytical Learning Objectives


P1: Determine cost estimates using three different methods

P2: Compute the break-even point for a single product company

P3: Graph costs and sales for a single product company

P4: Compute break-even point for a multiproduct company

Procedural Learning Objectives


CVP analysis is used to answer questions such as: What sales volume is needed to earn a

target income? What is the change in income if selling

prices decline and sales volume increases?

How much does income increase if we install a new machine to reduce labor costs?

What is the income effect if we change the sales mix of our products or services?

CVP analysis is used to answer questions such as: What sales volume is needed to earn a

target income? What is the change in income if selling

prices decline and sales volume increases?

How much does income increase if we install a new machine to reduce labor costs?

What is the income effect if we change the sales mix of our products or services?

Questions Addressed byCost-Volume-Profit Analysis

C2


Number of Local Calls

Mo

nth

ly B

asic

T

elep

ho

ne

Bill

Total fixed costs remain unchangedwhen activity changes.

Your monthly basictelephone bill probablydoes not change when

you make more local calls.

Total Fixed CostC1


Number of Local Calls

Mo

nth

ly B

asic

Tel

eph

on

e B

ill p

er L

oca

l Cal

l

Fixed costs per unit declineas activity increases.

Your average cost perlocal call decreases as

more local calls are made.1- Economic of scale2- Learning curve

Fixed Cost Per UnitC1


Minutes Talked

To

tal L

on

g D

ista

nce

Tel

eph

on

e B

illTotal variable costs change

when activity changes.

Your total long distancetelephone bill is basedon how many minutes

you talk.

Total Variable CostC1


Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

Variable costs per unit do not changeas activity increases.

The cost per long distanceminute talked is constant.

For example, 7cents per minute.

Variable Cost Per UnitC1


Summary of Variable and Fixed Cost Behavior

Cost In Total Per Unit

Variable Changes as activity level

changes.Remains the same over wide

ranges of activity.

FixedRemains the same even

when activity level changes.Dereases as activity level

increases.

Cost Behavior SummaryC1


Mixed costs contain a fixed portion that is incurred even when the

facility is unused, and a variable portion that increases with usage.

Example: monthly electric utility charge Fixed service fee Variable charge per

kilowatt hour used

Mixed CostsC1


Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

Total mixed cost

Fixed Monthly

Utility Charge

Mixed CostsC1


Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.

Step-Wise CostsC1


Activity

Co

st

Total cost increases to a new higher cost for the

next higher range of activity.

Step-Wise CostsC1


Costs that increase when activity increases, but in a nonlinear manner.

Activity

To

tal

Co

st

Curvilinear CostsC1


A scatter diagram of past cost behavior may be helpful in analyzing mixed costs.

Scatter DiagramP1


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

P1

Scatter Diagram


Draw a line through the plotted data points so that about equal numbers of points fall above and below the line.

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

***

**

**

*

*


P1

Scatter Diagram


Vertical distance

is the change in cost.

Horizontal distance is the change in activity.

Unit Variable Cost = Slope = Δin costΔin units

0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*


P1

Scatter Diagram


The following relationships between units produced and costs are observed:

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

Units Cost

High activity level 67,500 29,000$ Low activity level 17,500 20,500 Change 50,000 8,500$

The High-Low MethodP1


Unit variable cost = = = $0.17/ unitΔin costΔin units

$8,500$50,000

Units Cost


Exh. 22-6

P1

The High-Low Method


Units Cost


Unit variable cost = = = $0.17/unit

Fixed cost = Total cost – Total variable

Δin costΔin units

$8,500$50,000

Exh. 22-6

P1

The High-Low Method


Units Cost


Unit variable cost = = = $0.17 /unit

Fixed cost = Total cost – Total variable cost

Fixed cost = $29,000 – ($0.17 per unit × $67,500)

Fixed cost = $29,000 – $11,475 = $17,525

Δin costΔin units

$8,500$50,000

Exh. 22-6

P1

The High-Low Method


The objective of the cost analysis remains the

same: determination of total fixed cost and the

variable unit cost.

Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators.

Least-Squares RegressionP1


Let’s extend our

knowledge of

cost behavior to

break-even analysis.

Break-Even AnalysisP2


The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company earns neither a profit nor incurs a loss.

Computing Break-Even PointP2


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

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

Total Unit

Sales Revenue (2,000 units) 200,000$ 100$

Less: Variable costs 140,000 70

Contribution margin 60,000$ 30$

Less: Fixed costs 24,000

Net income 36,000$

Computing Break-Even PointP2


Total Unit





Net income 36,000$

How much contribution margin must this company have to cover its fixed costs (break even)?

Answer: $24,000

P2

Computing Break-Even Point


How many units must this company sell to cover its fixed costs (break even)?

Total Unit





Net income 36,000$

Answer: $24,000 ÷ $30 per unit = 800 units

P2



We have just seen one of the basic CVP relationships – the break-even computation.

Break-even point in units = Fixed costs

Contribution margin per unit


Unit sales price less unit variable cost($30 in previous example)

Exh. 22-8

P2


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

Break-even point in dollars = Fixed costs

Contribution margin ratio

Unit contribution margin Unit sales price

Exh. 22-9

P2



ABC Co. sells product XYZ 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

ABC Co. sells product XYZ 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

P2



ABC Co. sells product XYZ 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


break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Unit contribution = $5.00 - $3.00 = $2.00

Fixed costsUnit contribution =

$200,000$2.00 per unit

= 100,000 units

P2



Use the contribution margin ratio formula to determine the amount of sales revenue ABC must

have to break even. All information remains unchanged: fixed costs are $200,000; unit sales

price is $5.00; and unit variable cost is $3.00.

a. $200,000

b. $300,000

c. $400,000

d. $500,000




a. $200,000

b. $300,000

c. $400,000

d. $500,000

P2






a. $200,000

b. $300,000

c. $400,000

d. $500,000




a. $200,000

b. $300,000

c. $400,000

d. $500,000


Contribution margin ratio = $2.00 ÷ $5.00 = .40

Break-even revenue = $200,000 ÷ .4 = $500,000

P2



Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s Total fixed costsTotal costs

Draw the total cost line with a slopeequal to the unit variable cost.

Plot total fixed costs on the vertical axis.

Preparing a CVP ChartP3


Sales

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s Starting at the origin, draw the sales line with a slope equal to the unit sales price.

Preparing a CVP Chart

Break-even Point

Total costsTotal fixed costs

P3


A limited range of activity called the relevant range, where CVP relationships are linear. Unit selling price remains constant. Unit variable costs remain constant. Total fixed costs remain constant.

Production = sales (no inventory changes).

Assumptions of CVP AnalysisC2


Income (pretax) = Sales – Variable costs – Fixed costs


Computing Income from Expected Sales Exh.

22-12

C3


Rydell expects to sell 1,500 units at $100 each next month. Fixed costs are $24,000

per month and the unit variable cost is $70. What amount of income should

Rydell expect?


= [1,500 units × $100] – [1,500 units × $70] – $24,000

= $21,000


= [1,500 units × $100] – [1,500 units × $70] – $24,000

= $21,000

Computing Income from Expected Sales

Exh. 22-13

C3


Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income.

Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income.

Unit sales = Fixed costs + Target incomeContribution margin per unit

Dollar sales = Fixed costs + Target income


Computing Sales for a Target Income

C3


ABC Co. sells product XYZ 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 earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

ABC Co. sells product XYZ 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 earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units

C3 Computing Sales for a Target Income



earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units


earn income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units = 120,000 units


Fixed costs + Target income Unit contribution

$200,000 + $40,000 $2.00 per unit

C3 Computing Sales for a Target Income


Target net income is income after income tax. But we can use target income before tax in our calculations.

Target net income is income after income tax. But we can use target income before tax in our calculations.

Dollar sales =

Fixed Target income costs before tax


+

Computing Sales (Dollars) for aTarget Net Income

Exh. 22-14

C3


To convert target net income to before-tax income, use the following formula:

Before-tax income = Target net income

1 - tax rate

C3 Computing Sales (Dollars) for aTarget Net Income


Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the

unit variable cost is $70, and the tax rate is 25 percent.

What is Rydell’s before-tax income andincome tax expense?



Before-tax income = Target net income

1 - tax rate

Before-tax income = = $24,000$18,000

1 - .25

Income tax = .25 × $24,000 = $6,000

Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the

unit variable cost is $70, and the tax rate is 25 percent.

What is Rydell’s before-tax income andincome tax expense?



Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.

What monthly sales revenue will Rydellneed to earn the target net income?



Dollar sales =

Fixed Target net income costs before tax


+

Dollar sales = = $160,000

$24,000 + $24,00030%

Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.

What monthly sales revenue will Rydellneed to earn the target net income?



The formula for computing dollar sales may be used to compute unit sales by substituting contribution per unit in the denominator.

The formula for computing dollar sales may be used to compute unit sales by substituting contribution per unit in the denominator.

Contribution margin per unitUnit sales =

Fixed Target net income taxes before taxes

+ +

Unit sales = = 1,600 units$24,000 + $24,000

$30 per unit

Formula for Computing Sales (Units) for a Target Net Income

Exh. 22-16

C3


Margin of safety is the amount by which sales can drop before the company

incurs a loss.

Margin of safety may be expressed as a percentage of expected sales.

Computing the Margin of Safety Exh.

22-17

Margin of safety Expected sales - Break-even sales percentage Expected sales

=

C3


Margin of safety Expected sales - Break-even sales percentage Expected sales

=

If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety in dollars and as a

percentage?

Exh. 22-17

C3 Computing the Margin of Safety


If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety in dollars and as a percentage?

Margin of safety = $100,000 - $80,000 = $20,000

Margin of safety Expected sales - Break-even sales percentage Expected sales=

Margin of safety $100,000 - $80,000 percentage $100,000

= = 20%

Exh. 22-17

C3 Computing the Margin of Safety


The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost.

Consider the following example.

The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost.

Consider the following example.

Sensitivity AnalysisC3


Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged.

What is the new break-even point in dollars?

Sensitivity Analysis ExampleC3


Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged.

Revised Break-evenpoint in dollars

Revised fixed costsRevised contribution margin ratio

Revised Break-evenpoint in dollars

$30,00040%

= $75,000=

=

Exh. 22-18

C3

Sensitivity Analysis Example


The CVP formulas may be modified for use when a company sells more than one product. The unit contribution margin is replaced with the

contribution margin for a composite unit. A composite unit is composed of specific

numbers of each product in proportion to the product sales mix.

Sales mix is the ratio of the volumes of the various products.

Computing MultiproductBreak-Even Point

P4


The resulting break-even formulafor composite unit sales is:

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Consider the following example:

Continue

Exh. 22-19

P4 Computing MultiproductBreak-Even Point


Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix.

Haircuts Basic Ultra Budget

Selling Price 10.00$ 16.00$ 8.00$ Variable Cost 6.50 9.00 4.00 Unit Contribution 3.50$ 7.00$ 4.00$ Sales Mix Ratio 4 2 1



Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the

break-even point in composite units and in number of units for each haircut at the given sales mix.

Haircuts Basic Ultra Budget

Selling Price 10.00$ 16.00$ 8.00$ Variable Cost 6.50 9.00 4.00 Unit Contribution 3.50$ 7.00$ 4.00$ Sales Mix Ratio 4 2 1

A 4:2:1 sales mix means that if there are 500 budget cuts, then there will be

1,000 ultra cuts, and 2,000 basic cuts.



HaircutsBasic Ultra Budget

Selling Price $10.00 $16.00 $8.00Variable Cost 6.50 9.00 4.00 Unit Contribution $3.50 $7.00 $4.00Sales Mix Ratio × 4 × 2 × 1

14.00$ 14.00$ 4.00$

Step 1: Compute contribution margin per composite unit.



HaircutsBasic Ultra Budget

Selling Price $10.00 $16.00 $8.00Variable Cost 6.50 9.00 4.00 Unit Contribution $3.50 $7.00 $4.00Sales Mix Ratio × 4 × 2 × 1Weighted Contribution 14.00$ + 14.00$ + 4.00$ = 32.00$

Contribution margin per composite unit

Step 1: Compute contribution margin per composite unit.





=

Step 2: Compute break-even point in composite units.

Exh. 22-19





=

Step 2: Compute break-even point in composite units.


$96,000$32.00 per

composite unit

=


= 3,000 composite units

Exh. 22-19



Sales CompositeProduct Mix Cuts Haircuts

Basic 4 × 3,000 = 12,000Ultra 2 × 3,000 = 6,000

Budget 1 × 3,000 = 3,000

Step 3: Determine the number of each haircut that must be sold to break even.



HaircutsBasic Ultra Budget Combined

Selling Price 10.00$ 16.00$ 8.00$ Variable Cost 6.50 9.00 4.00 Unit Contribution 3.50$ 7.00$ 4.00$ Sales Volume × 12,000 × 6,000 × 3,000 Total Contribution 42,000$ 42,000$ 12,000$ 96,000$

Fixed Costs 96,000 Income $ 0

Step 4: Verify the results.

Multiproduct Break-EvenIncome Statement Exh.

22-20

P4


A measure of the extent to which fixed costs are being used in an organization.

A measure of the extent to which fixed costs are being used in an organization.

A measure of how a percentage change in sales will affect profits.

A measure of how a percentage change in sales will affect profits.

Contribution margin Net income

= Degree of operating leverage

Operating LeverageA3


Rydell Company

Sales (1,200 units) 120,000$ Less: variable expenses 84,000 Contribution margin 36,000 Less: fixed expenses 24,000 Net income 12,000$

$36,000 $12,000

= 3.0

Contribution margin Net income

= Degree of operating leverage

If Rydell increases sales by 10percent, what will the percentage

increase in income be?

Operating LeverageA3


Percent increase in sales 10%

Degree of operating leverage × 3

Percent increase in income 30%

Operating LeverageRydell Company

Sales (1,200 units) 120,000$ Less: variable expenses 84,000 Contribution margin 36,000 Less: fixed expenses 24,000 Net income 12,000$

A3


End of Chapter 22

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© The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Chapter 22 Cost-Volume-Profit Analysis