Cost-Volume-Profit Analysis

11-1

Cost-Volume-Profit

11

Prepared by

Coby Harmon

University of California, Santa Barbara

Westmont College

WILEY

Kimmel ● Weygandt ● Kieso

Survey of Accounting, First Edition

11-2

CHAPTER OUTLINE

Explain variable, fixed, and mixed costs and the relevant range.1

LEARNING OBJECTIVES

Apply the high-low method to determine the components of mixed

costs.2

Prepare a CVP income statement to determine contribution margin.3

Compute the break-even point using three approaches.4

Determine the sales required to earn target net income and determine

margin of safety.5

11-3

Cost Behavior Analysis is the study of how specific costs

respond to changes in the level of business activity.

 Some costs change; others remain the same.

 Helps management plan operations and decide between

alternative courses of action.

 Applies to all types of businesses and entities.

 Starting point is measuring key business activities.

LO 1

LEARNING

OBJECTIVE

Explain variable, fixed, and mixed costs

and the relevant range.1

11-4

Cost Behavior Analysis is the study of how specific costs

respond to changes in the level of business activity.

 Activity levels may be expressed in terms of:

► Sales dollars (in a retail company)

► Miles driven (in a trucking company)

► Room occupancy (in a hotel)

► Dance classes taught (by a dance studio)

 Many companies use more than one measurement base.

Cost Behavior Analysis

LO 1

11-5

Cost Behavior Analysis is the study of how specific costs

respond to changes in the level of business activity.

 Changes in the level or volume of activity should be

correlated with changes in costs.

 Activity level selected is called activity or volume index.

 Activity index:

► Identifies the activity that causes changes in the

behavior of costs.

► Allows costs to be classified as variable, fixed, or mixed.

Cost Behavior Analysis

LO 1 11-6

 Costs that vary in total directly and proportionately with

changes in the activity level.

► Example: If the activity level increases 10 percent, total

variable costs increase 10 percent.

► Example: If the activity level decreases by 25 percent,

total variable costs decrease by 25 percent.

 Variable costs remain the same per unit at every level of

activity.

VARIABLE COSTS

LO 1

11-7

Illustration: Damon Company manufactures tablet computers that

contain a $10 camera. The activity index is the number of

tablets produced. As Damon

manufactures each tablet, the total cost

of the cameras used increases by $10.

As part (a) of ILLUSTRATION 11-1

shows, total cost of the cameras will be

$20,000 if Damon produces 2,000

tablets, and $100,000 when it produces

10,000 tablets. We also can see that a

variable cost remains the same per unit

as the level of activity changes.

ILLUSTRATION 11-1 Behavior of total and

unit variable costs LO 1

VARIABLE COSTS

11-8

Illustration: Damon Company manufactures tablet computers that

contain a $10 camera. The activity index is the number of

tablets produced. As Damon

manufactures each tablet, the total cost

of the cameras used increases by $10.

As part (b) of ILLUSTRATION 11-1

shows, the unit cost of $10 for the

camera is the same whether Damon

produces 2,000 or 10,000 tablets.

LO 1

VARIABLE COSTS

ILLUSTRATION 11-1 Behavior of total and

unit variable costs

11-9

ILLUSTRATION 11-1

Behavior of total and unit variable costs

LO 1

VARIABLE COSTS

11-10

 Costs that remain the same in total regardless of

changes in the activity level within a relevant range.

 Fixed cost per unit cost varies inversely with activity:

As volume increases, unit cost declines, and vice versa

 Examples:

► Property taxes

► Insurance

► Rent

► Depreciation on buildings and equipment

FIXED COSTS

LO 1

11-11

Illustration: Damon Company leases its productive facilities at a cost

of $10,000 per month. Total fixed costs of the

facilities will remain constant at every

level of activity, as part (a) of

ILLUSTRATION 11-2 shows.

LO 1

FIXED COSTS

ILLUSTRATION 11-2

Behavior of total and unit

fixed costs 11-12

Illustration: Damon Company leases its productive facilities at a cost

of $10,000 per month. Total fixed costs of the

facilities will remain constant at every

level of activity. But, on a per unit basis,

the cost of rent will decline as activity

increases, as part (b) of ILLUSTRATION

11-2 shows. At 2,000 units, the unit cost

per tablet computer is $5 ($10,000 ÷

2,000). When Damon produces 10,000

tablets, the unit cost of the rent is only $1

per tablet ($10,000 ÷ 10,000).

LO 1

FIXED COSTS

ILLUSTRATION 11-2

Behavior of total and unit

fixed costs

11-13

ILLUSTRATION 11-2

Behavior of total and unit fixed costs

LO 1

FIXED COSTS

11-14

Variable costs are costs that:

a. Vary in total directly and proportionately with changes

in the activity level.

b. Remain the same per unit at every activity level.

c. Neither of the above.

d. Both (a) and (b) above.

Question

LO 1

FIXED COSTS

11-15 LO 1 11-16

 Throughout the range of possible levels of activity, a

straight-line relationship usually does not exist for either

variable costs or fixed costs.

 Relationship between variable costs and changes in

activity level is often curvilinear.

RELEVANT RANGE

 For fixed costs, the relationship

is also nonlinear – some fixed

costs will not change over the

entire range of activities, while

other fixed costs may change.

LO 1

11-17

ILLUSTRATION 11-3 Nonlinear behavior of variable and fixed costs

LO 1

RELEVANT RANGE

11-18

Range of activity over which a company expects to

operate during a year. ILLUSTRATION 11-4 Linear behavior within

relevant range

LO 1

RELEVANT RANGE

11-19

The relevant range is:

a. The range of activity in which variable costs will be

curvilinear.

b. The range of activity in which fixed costs will be

curvilinear.

c. The range over which the company expects to operate

during a year.

d. Usually from zero to 100% of operating capacity.

Question

LO 1

RELEVANT RANGE

11-20

 Costs that have both a variable element and a fixed

element.

 Change in total but not proportionately with changes

in activity level.

MIXED COSTS

ILLUSTRATION 11-5 Behavior of a mixed cost

LO 1

11-21

Helena Company, reports the following total costs at two

levels of production.

Classify each cost as variable, fixed, or mixed.

Variable

Fixed

Mixed

LO 1

DO IT! 1 Types of Costs

11-22

HIGH-LOW METHOD

 High-Low Method uses the total costs incurred at the

high and the low levels of activity to classify mixed costs

into fixed and variable components.

 The difference in costs between the high and low levels

represents variable costs, since only variable-cost

element can change as activity levels change.

LO 2

LEARNING

OBJECTIVE

Apply the high-low method to determine the

components of mixed costs.2

11-23

STEP 1: Determine variable cost per unit using the following

formula:

HIGH-LOW METHOD

ILLUSTRATION 11-6 Formula for variable cost per unit using high-low method

LO 2 11-24

Illustration: Metro Transit Company has the

following maintenance costs and mileage data for

its fleet of buses over a 6-month period.

Change in Costs (63,000 - 30,000) $33,000

High minus Low (50,000 - 20,000) 30,000 =

$1.10 cost per

unit

HIGH-LOW METHOD

ILLUSTRATION 11-7 Assumed maintenance

costs and mileage data

LO 2

11-25

STEP 2: Determine the fixed cost by subtracting the total variable

cost at either the high or the low activity level from the total cost at

that activity level.

HIGH-LOW METHOD

ILLUSTRATION 11-8 High-low method computation of fixed costs

LO 2 11-26

Maintenance costs are therefore $8,000 per month of fixed costs

plus $1.10 per mile of variable costs. This is represented by the

following formula:

Maintenance costs = $8,000 + ($1.10 x Miles driven)

Example: At 45,000 miles, estimated maintenance costs would

be:

Fixed $ 8,000

Variable ($1.10 x 45,000) 49,500

$57,500

HIGH-LOW METHOD

LO 2

11-27

ILLUSTRATION 11-9 Scatter plot for Metro

Transit Company

HIGH-LOW METHOD

LO 2 11-28

Mixed costs consist of a:

a. Variable cost element and a fixed cost element.

b. Fixed cost element and a controllable cost element.

c. Relevant cost element and a controllable cost

element.

d. Variable cost element and a relevant cost element.

Question

HIGH-LOW METHOD

LO 2

11-29 LO 2 11-30

Byrnes Company accumulates the following data concerning a

mixed cost, using units produced as the activity level.

(a) Compute the variable- and fixed-cost elements using the high-

low method.

(b) Estimate the total cost if the company produces 8,000 units.

LO 2

DO IT! 2 High-Low Method

11-31

(a) Compute the variable and fixed cost elements using the high-

low method.

Variable cost: ($14,740 - $11,100) / (9,800 - 7,000) = $1.30 per unit

Fixed cost: $14,740 - $12,740 ($1.30 x 9,800 units) = $2,000

or $11,100 - $9,100 ($1.30 x 7,000) = $2,000

LO 2

DO IT! 2 High-Low Method

11-32

(b) Estimate the total cost if the company produces 8,000 units.

Total cost (8,000 units):

$2,000 + $10,400 ($1.30 x 8,000) = $12,400

LO 2

DO IT! 2 High-Low Method

11-33

Cost-volume-profit (CVP) analysis is the study of the

effects of changes in costs and volume on a company’s

profits.

 Important in profit planning.

 Critical factor in management decisions as

► Setting selling prices,

► Determining product mix, and

► Maximizing use of production facilities.

LO 3

LEARNING

OBJECTIVE

Prepare a CVP income statement to

determine contribution margin. 3

11-34

BASIC COMPONENTS

Cost-Volume-Profit Analysis

ILLUSTRATION 11-10 Components of CVP analysis

LO 3

11-35

Assumptions

1. Behavior of both costs and revenues is linear throughout

the relevant range of the activity index.

2. Costs can be classified accurately as either variable or

fixed.

3. Changes in activity are the only factors that affect costs.

4. All units produced are sold.

5. When more than one type of product is sold, the sales mix

will remain constant.

BASIC COMPONENTS

LO 3 11-36

Which of the following is not involved in CVP analysis?

a. Sales mix.

b. Unit selling prices.

c. Fixed costs per unit.

d. Volume or level of activity.

Question

BASIC COMPONENTS

LO 3

11-37

 A statement for internal use.

 Classifies costs and expenses as fixed or variable.

 Reports contribution margin in the body of the

statement.

► Contribution margin – amount of revenue remaining

after deducting variable costs.

 Reports the same net income as a traditional income

statement.

CVP INCOME STATEMENT

Cost-Volume-Profit Analysis

LO 3 11-38

Illustration: Vargo Video Company produces a high-definition

digital camcorder. Relevant data for the camcorders sold by

this company in June 2017 are as follows.

CVP INCOME STATEMENT

ILLUSTRATION 11-11 Assumed selling and cost data for Vargo Video

LO 3

11-39

Illustration: The CVP income statement for Vargo Video

therefore would be reported as follows.

CVP INCOME STATEMENT

ILLUSTRATION 11-12 CVP income statement, with net income

LO 3 11-40

 Contribution margin is available to cover fixed costs and

to contribute to income.

 Formula for contribution margin per unit and the

computation for Vargo Video are:

Unit Contribution Margin

CVP INCOME STATEMENT

ILLUSTRATION 11-13 Formula for unit contribution margin

LO 3

11-41

Vargo’s CVP income statement assuming a

zero net income.

CVP INCOME STATEMENT

LO 3

Unit Contribution Margin

ILLUSTRATION 11-14 CVP income statement,

with zero net income

11-42

Assume that Vargo sold one more camcorder,

for a total of 1,001 camcorders sold.

CVP INCOME STATEMENT

LO 3

Unit Contribution Margin

ILLUSTRATION 11-15 CVP income statement, with

net income and per unit data

11-43

 Shows the percentage of each sales dollar available

to apply toward fixed costs and profits.

 Formula for contribution margin ratio and the

computation for Vargo Video are:

ILLUSTRATION 11-17 Formula for contribution margin ratio

Contribution Margin Ratio

CVP INCOME STATEMENT

LO 3 11-44

ILLUSTRATION 11-16 CVP income statement, with net income and percent of sales data

CVP INCOME STATEMENT

LO 3

Contribution Margin Ratio

11-45

Assume Vargo Video’s current sales are $500,000 and it wants to

know the effect of a $100,000 (200-unit) increase in sales.

ILLUSTRATION 11-18 Comparative CVP income statements

CVP INCOME STATEMENT

LO 3

Contribution Margin Ratio

11-46

Contribution margin:

a. Is revenue remaining after deducting variable costs.

b. May be expressed as contribution margin per unit.

c. Is selling price less cost of goods sold.

d. Both (a) and (b) above.

Question

CVP INCOME STATEMENT

LO 3

11-47

Ampco Industries produces and sells a cell phone-operated

thermostat. Information regarding the costs and sales of

thermostats during September 2017 are provided below.

Unit selling price of thermostat $85

Unit variable costs $32

Total monthly fixed costs $190,000

Units sold 4,000

Prepare a CVP income statement for Ampco Industries for the

month of September. Provide per unit values and total values.

LO 3

DO IT! 3 CVP Income Statement

11-48

Prepare a CVP income statement for Ampco Industries for the

month of September. Provide per unit values and total values.

LO 3

DO IT! 3 CVP Income Statement

11-49

 Process of finding the break-even point level of activity

at which total revenues equal total costs (both fixed and

variable).

 Can be computed or derived

► from a mathematical equation,

► by using contribution margin, or

► from a cost-volume profit (CVP) graph.

 Expressed either in sales units or in sales dollars.

Break-Even Analysis

LO 4

LEARNING

OBJECTIVE

Compute the break-even point using three

approaches. 4

11-50

ILLUSTRATION 11-20

Computation

of break-

even point in

units.

Break-even occurs where total sales equal variable costs

plus fixed costs; i.e., net income is zero

MATHEMATICAL EQUATION

LO 4

11-51

 At the break-even point, contribution margin must equal

total fixed costs

(CM = total revenue – variable costs)

 Break-even point can be computed using either

contribution margin per unit or contribution margin ratio.

CONTRIBUTION MARGIN TECHNIQUE

LO 4 11-52

 When the break-even-point in units is desired,

contribution margin per unit is used in the following

formula which shows the computation for Vargo Video:

ILLUSTRATION 11-21 Formula for break-even point in units using unit contribution margin

Contribution Margin In Units

LO 4

CONTRIBUTION MARGIN TECHNIQUE

11-53

 When the break-even-point in dollars is desired,

contribution margin ratio is used in the following

formula which shows the computation for Vargo Video:

Contribution Margin Ratio

ILLUSTRATION 11-22 Formula for break-even point in dollars using contribution margin ratio

LO 4

CONTRIBUTION MARGIN TECHNIQUE

11-54 LO 4

11-55

Because this

graph also shows

costs, volume, and

profits, it is

referred to as a

cost-volume-profit

(CVP) graph.

ILLUSTRATION 11-23 CVP graph

GRAPHIC PRESENTATION

LO 4 11-56

Gossen Company is planning to sell 200,000 pliers for $4

per unit. The contribution margin ratio is 25%. If Gossen

will break even at this level of sales, what are the fixed

costs?

a. $100,000.

b. $160,000.

c. $200,000.

d. $300,000.

Question

Break-Even Analysis

LO 4

11-57

1,125 units

Lombardi Company has a unit selling price of $400, variable

costs per unit of $240, and fixed costs of $180,000. Compute

the break-even point in units using (a) a mathematical equation

and (b) contribution margin per unit.

$400Q $240Q $180,000 0

$160Q $180,000

Q

-

-

=

- =

ILLUSTRATION 11-19

Sales Variable

Costs

Fixed

Costs

Net

Income - - =

LO 4

DO IT! 4 Break-Even Analysis

11-58

1,125 units$180,000 $160 =

ILLUSTRATION 11-21

Lombardi Company has a unit selling price of $400, variable

costs per unit of $240, and fixed costs of $180,000. Compute

the break-even point in units using (a) a mathematical equation

and (b) contribution margin per unit.

Fixed

Costs Contribution

Margin per Unit

Break-Even

Point in Units ÷ =

÷

LO 4

DO IT! 4 Break-Even Analysis

11-59

 Level of sales necessary to achieve a specified

income.

 Can be determined from each of the approaches used

to determine break-even sales/units:

► from a mathematical equation,

► by using contribution margin technique, or

► from a cost-volume profit (CVP) graph.

 Expressed either in sales units or in sales dollars.

TARGET NET INCOME

LO 5

LEARNING

OBJECTIVE

Determine the sales required to earn target

net income and determine margin of safety. 5

11-60

Mathematical Equation

Formula for required sales to meet target net income.

TARGET NET INCOME

LO 5

ILLUSTRATION 11-24 Formula for required sales to meet target net income

11-61

Using the formula for the break-even point, simply include the

desired net income as a factor. ILLUSTRATION 11-25 Computation of required sales

LO 5

Mathematical Equation

TARGET NET INCOME

11-62

To determine the required sales in units for Vargo Video:

Contribution Margin Technique

ILLUSTRATION 11-26 Formula for required sales in units using unit contribution margin

LO 5

TARGET NET INCOME

11-63

To determine the required sales in dollars for Vargo Video:

ILLUSTRATION 11-27 Formula for required sales in dollars using contribution margin ratio

LO 5

TARGET NET INCOME

Contribution Margin Technique

11-64

Suppose Vargo Video

sells 1,400 camcorders.

ILLUSTRATION 11-23

shows that a vertical line

drawn at 1,400 units

intersects the sales line at

$700,000 and the total

cost line at $620,000. The

difference between the

two amounts represents

the net income (profit) of

$80,000.

ILLUSTRATION 11-23

Graphic

Presentation

LO 5

TARGET NET INCOME

11-65

The mathematical equation for computing required sales to

obtain target net income is:

Required sales =

a. Variable costs + Target net income.

b. Variable costs + Fixed costs + Target net income.

c. Fixed costs + Target net income.

d. No correct answer is given.

Question

LO 5

TARGET NET INCOME

11-66

 Difference between actual or expected sales and sales at

the break-even point.

 Measures the “cushion” that a particular level of sales

provides.

 May be expressed in dollars or as a ratio.

 Assuming actual/expected sales are $750,000:

MARGIN OF SAFETY

ILLUSTRATION 11-28 Formula for margin of safety in dollars

LO 5

11-67

 Computed by dividing the margin of safety in dollars by

the actual (or expected) sales.

 Assuming actual/expected sales are $750,000: ILLUSTRATION 11-29 Formula for margin of

safety ratio

 The higher the dollars or percentage, the greater the

margin of safety.

Margin of Safety Ratio

LO 5 11-68

Marshall Company had actual sales of $600,000 when break-

even sales were $420,000. What is the margin of safety ratio?

a. 25%.

b. 30%.

c. 33 1/3%.

d. 45%.

Question

MARGIN OF SAFETY

LO 5

11-69 LO 5 11-70

Zootsuit Inc. makes travel bags that sell for $56 each. For the

coming year, management expects fixed costs to total

$320,000 and variable costs to be $42 per unit. Compute the

following:

a) break-even point in dollars using the contribution margin

(CM) ratio;

b) the margin of safety and margin of safety ratio assuming

actual sales are $1,382,400; and

c) the sales dollars required to earn net income of

$410,000.

Comprehensive

LO 5

DO IT! 5 Break-Even, Margin of Safety, and

Target Net Income

11-71

Comprehensive

Zootsuit Inc. makes travel bags that sell for $56 each. For the

coming year, management expects fixed costs to total

$320,000 and variable costs to be $42 per unit. Compute

break-even point in dollars using the contribution margin (CM)

ratio.

Contribution margin ratio = [($56 - $42) ÷ $56] = 25%

Break-even sales in dollars = $320,000 ÷ 25% = $1,280,000

LO 5

DO IT! 5 Break-Even, Margin of Safety, and

Target Net Income

11-72

Margin of safety = $1,382,400 - $1,280,000 = $102,400

Margin of safety ratio = $102,400 ÷ $1,382,400 = 7.4%

ComprehensiveComprehensive

Zootsuit Inc. makes travel bags that sell for $56 each. For the

coming year, management expects fixed costs to total

$320,000 and variable costs to be $42 per unit. Compute the

margin of safety and margin of safety ratio assuming actual

sales are $1,382,400.

LO 5

DO IT! 5 Break-Even, Margin of Safety, and

Target Net Income

11-73

Required sales in dollars =

($320,000 + $410,000) ÷ 25% = $2,920,000

ComprehensiveComprehensive

Zootsuit Inc. makes travel bags that sell for $56 each. For the

coming year, management expects fixed costs to total

$320,000 and variable costs to be $42 per unit. Compute the

sales dollars required to earn net income of $410,000.

LO 5

DO IT! 5 Break-Even, Margin of Safety, and

Target Net Income

11-74

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