CPV by Weygandt

7/31/2019 CPV by Weygandt

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John Wiley & Sons, Inc. 2005

Prepared by

Dan R. Ward

Suzanne P. Ward

University of Louisiana at Lafayette

Managerial Accounting

Weygandt Kieso Kimmel

CHAPTER 5

COST-VOLUME-PROFIT


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CHAPTER 5

COSTVOLUME - PROFITStudy Objectives

Distinguish between variable and fixed costs.

Explain the significance of the relevant range.

Explain the concept of mixed costs.

List the five components of cost-volume-profit

analysis.

Indicate what contribution margin is and how it

can be expressed.


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Study Objectives: Continued

Identify the three ways to determine the break-

even point.

Give the formulas for determining sales

required to earn target net income.Define margin of safety, and give the formulas

for computing it.


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COST BEHAVIOR ANALYSIS

Definition: 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 makedecisions

Applies to all types of businesses and entities


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COST BEHAVIOR ANALYSISContinued

Starting point is measuring key businessactivities

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)


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COST BEHAVIOR ANALYSIS

Continued

Many companies use more

than one measurement base

For an activity level

to be useful:

Changes in the level or volume of activity should be

correlated with changes in cost


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COST BEHAVIOR ANALYSISContinued

The activity level selected is calledtheactivity (or volume) index

Identifies the activity that causes

changes in the behavior of costs Allows costs to be classified

according to their response tochanges in activity as:

Variable Costs

Fixed Costs

Mixed Costs


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COST BEHAVIOR ANALYSISVARIABLE COSTS

Study Objective 1

Costs that varyin totaldirectly and proportionately

with changes in the activity level

If the activity level increases 10 percent, total

variable costs increase 10 percent

If the activity level decreases by 25 percent, total

variable costs will decrease by 25 percent


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COST BEHAVIOR ANALYSISVARIABLE COSTS - Continued

Variable costs alsoremainconstant per unit at

every level of activity

Examples of variable costs include Direct material and direct labor for a manufacturer

Sales commissions for a merchandiser

Gasoline in airlines and trucking companies


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Example

Damon Company manufactures radios thatcontain a $10 clock

Activity index is the number of radios produced

For each radio produced, the total cost of theclocks increases by $10

If 2,000 radios are made, the total cost of the clocksis $20,000 (2,000 X $10)

If 10,000 radios are made, the total cost of theclocks is $100,000 (10,000 X $10)


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Example: Continued


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COST BEHAVIOR ANALYSISFIXED COSTS

Costs thatremain the same intotalregardless ofchanges in the activity level.

Per unit costvariesinverselywith activity:

As volume increases,

unit cost decline, and vice versa

Examples include

Property taxes

Insurance

Rent

Depreciation on buildings and equipment


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COST BEHAVIOR ANALYSISFIXED COSTS - Continued

Example

Damon Company leases its productive facilitiesfor $10,000 per month

Total fixed costs of the facilities remain constantat all levels of activity - $10,000 per month

On aper unit basis, the cost of rent decreases asactivity increases and vice versa

At 2,000 radios, the unit cost is $5 ($10,000 2,000units)

At 10,000 radios, the unit cost is $1 ($10,000

10,000 units)


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COST BEHAVIOR ANALYSISFIXED COSTS - Continued

Example:Continued


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COST BEHAVIOR ANALYSISRELEVANT RANGE

Study Objective 2

Throughout the range of possible levels of activity,astraight-line relationship usually doesnot exist for

either variable costs or fixed costs The relationship between variable costs and changes in

activity level is often curvilinear

For fixed costs, the relationship is nonlinearsomefixed costs will not change over the entire range ofactivities, others may


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COST BEHAVIOR ANALYSISRELEVANT RANGE - Continued


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COST BEHAVIOR ANALYSISRELEVANT RANGE - Continued

Defined as the range of activity over which acompany expects to operate during a year

Within this range, a straight-line relationship

usually exists for both variable and fixed costs


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COST BEHAVIOR ANALYSISMIXED COSTS

Study Objective 3

Costs that haveboth a variable costelementanda fixed

cost element

Sometimes calledsemivariable cost

Change in total butnot proportionatelywith changes in

activity level


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COST BEHAVIOR ANALYSISMIXED COSTSHigh-Low Method

Mixed costs must be classified into their fixed andvariable elements

One approach to separate the costs is called thehigh-low method

Uses the total costs incurred at both the high and the lowlevels of activity to classify mixed costs

The difference in costs between the high and low levelsrepresents variable costs, since only variable costs changeas activity levels change


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COST BEHAVIOR ANALYSISMIXED COSTSHigh-Low Method - Continued

Steps in Method

STEP 1: Determine variable cost per unit using thefollowing formula:

STEP 2: Determine the fixed cost by subtractingthe total variable cost at either the high or the lowactivity level from the total cost at that level

=Change inTotal CostsHigh minus Low

Activity LevelVariable Cost

per Unit


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ExampleData for Metro Transit Company

for the last 4-month period:

High Level of Activity: April $63,000 50,000 miles

Low Level of Activity: January 30,000 20,000 miles

Difference $33,000 30,000 miles

Step 1: Using the formula, variable costs per unit are

$33,000 30,000 = $1.10 variable cost per mile

MonthJanuaryFebruary

Miles Driven20,00040,000

Total Cost$30,000$48,000

MonthMarchApril

Miles Driven35,00050,000

Total Cost$49,000$63,000


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Example: Continued

Step 2: Subtract total variable costs at either the high or low

activity level from the total cost at that same level

Total Cost

Less: Variable costs(50,000 x $1.10)(20,000 x $1.10)

Total fixed costs

High$63,000

55,000

$ 8,000

Low$30,000

22,000

$ 8,000

Activity Level


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Example: Continued

Maintenance costs: $8,000 per month plus $1.10 per mile

To determine maintenance costs at a particular activity level:

multiply the activity level times the variable cost per unit

then add that total to the fixed cost

EXAMPLE: If the activity level is 45,000 miles, the estimated

maintenance costs would be $8,000 fixed and $49,500

variable ($1.10 X 45,000 miles) for a total of $57,500.


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Lets Review

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


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Lets Review

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



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COST-VOLUME-PROFIT

ANALYSISStudy Objective 4

Study of the effects of changes of costs and

volumeon a companys profits

A critical factor in management decisions

Important in profit planning


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COST-VOLUME-PROFIT

ANALYSIS

Considers the interrelationships among thefive

components of CVP analysis:


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ASSUMPTIONS UNDERLYINGCVP ANALYSIS

Behavior of both costs and revenues is linearthroughout the relevant range of the activity index

All costs can be classified as either variable or fixedwith reasonable accuracy

Changes in activity are the only factors that affectcosts

All units produced are sold

When more than one type of product is sold, thesales mix will remain constant


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CVP INCOME STATEMENTStudy Objective 5

A statement for internal use

Classifies costs and expenses as fixed or variable

Reportscontribution margin in the body of the

statement.

Contribution margin amount of revenueremaining after

deducting variable costs

Reports the same netincome as a traditionalincome statement


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CVP INCOME STATEMENT

Example

Vargo Video Company produces DVD players.

Relevant data for June 2005:Unit selling price of DVD player $500Unit variable costs $300Total monthly fixed costs $200,000

Units sold 1,600


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CVP INCOME STATEMENTContribution Margin Per Unit

Contribution margin is availableto cover fixed costsand to contribute to income

Formula forcontribution margin per unit:

Example: Computation for Vargo Video

=Unit Selling Price Unit VariableCosts

Contribution

Margin per Unit

=Unit Selling Price$500

Unit Variable

Costs $300

ContributionMargin per Unit

$200


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CVP INCOME STATEMENTContribution Margin Ratio

Shows the percentage of each sales dollar available

to apply toward fixed costs and profits

Example: Computation for Vargo Video

= ContributionMargin RatioUnit Selling PriceContributionMargin per Unit

=Contribution

Margin Ratio

40%

Unit Selling Price

$500

Contribution

Margin per Unit

S200


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CVP INCOME STATEMENTContribution Margin Ratio - Example

Ratio helps to determine the effect of changes in sales on net income


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BREAK-EVEN ANALYSISStudy Objective 6

Process of finding thebreak-even point

Break-even point

Level of activity at whichtotal revenues equaltotal

costs (both fixed and variable)

Can be computed or derived

from amathematical equation

by using contribution margin from a cost-volume-profit (CVP) graph

Expressed either insales units or insalesdollars

BREAK EVEN ANALYSIS


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BREAK-EVEN ANALYSISMathematical Equation

Variable Costs

$300 Q

Fixed Costs

$200,000

Net Income

$0

Sales

$500 Q = + +

Example using the Vargo Video data:

Where:

Q = sales volume; $500 = selling price; $300 = variable cost per unit; $200,000 total fixed costs

To findsales dollars required to break-even:1000 units X $500 = $500,000 (break-even sales dollars)

$200 Q $200,000

Q 1000 units

=

=

BREAK EVEN ANALYSIS


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BREAK-EVEN ANALYSISContribution Margin Technique

At the break-even point,contribution margin must equaltotal fixed costs(CM = total revenuesvariable costs)

The break-even point can be computed using eithercontribution margin per unit or contribution margin ratio

When the break even point in units is desired, contribution marginper unit is used in the following formula

When the break even point in dollars is desired, contributionmarginratio is used in the following formula

=Fixed CostsBreak-even Point

in Units

Contribution

Margin per Unit

=Fixed CostsBreak-even Point

in Dollars

Contribution

Margin Ratio


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BREAK-EVEN ANALYSISContribution Margin Technique

Example using Vargo Video data:

=Fixed Costs$200,000

Break-even Point

in Units1,000 units

Contribution

Margin per Unit$200

=Fixed Costs$200,000

Break-even Point

in Dollars

$500,000

Contribution

Margin per Unit

40%


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BREAK-EVEN ANALYSISGraphic Presentation

A cost-volume-profit (CVP) graph shows costs,volume, and profits

Used to visually find the break-even point

To construct a CVP graph,

Plot the total revenue linestarting at the zero activity level

Plot the total fixed costby a horizontal line

Plot the total cost line.(Starts at the fixed cost lineat zero activity)

Determine the break-even point from the intersection ofthe total cost line and the total revenue line

BREAK EVEN ANALYSIS


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BREAK-EVEN ANALYSISCVP Graph for Vargo Video


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BREAK-EVEN ANALYSISTarget Net Income

Study Objective 7

Level of sales necessaryto achieve a specifiedincome

Can be determinedfrom each of theapproaches used todetermine break-even

sales/units

May be expressed eitherinsales dollars or salesunits

S S


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BREAK-EVEN ANALYSISTarget Net Income - Example

Using the Contribution Margin Approach

and the Vargo Video Data:

Formula forrequired sales in units:

Formula forrequired sales in dollars

=ContributionMargin Ratio

40%

Fixed Costs + TargetNet Income

$200,000 + $120,000

Required Sales inDollars

$800,000

=Contribution

Margin Per Unit

$200

Fixed Costs + TargetNet Income

$200,000 + $120,000

Required Salesin Units

1,600 units


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Lets Review

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



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Lets Review

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



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BREAK-EVEN ANALYSISMargin of Safety

Difference betweenactual or expected sales and salesat thebreak-even point

May be expressed in dollarsor as a ratio

Example -

To determine themargin of safety in dollars for Vargo Video

assuming that actual (expected) sales are $750,000:

=Margin of Safety

in Dollars

$250,000

Break-even

Sales

$500,000

Actual (Expected)

Sales

S750,000


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BREAK-EVEN ANALYSISMargin of Safety Ratio

Study Objective 8

Computed by dividing the margin of safety in dollarsby the actual or expected sales (using Vargo Video data)

Results indicate that Vargo Videos sales could fallby33 percent before it would be operating at a loss.

Thehigher the dollars or the percentage, the greaterthe margin of safety.

= Margin of SafetyRatio33%

Actual (Expected)Sales

$750,000

Margin of Safetyin Dollars

$250,000


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Summary of Study Objectives

Distinguish between variable and fixed costs. Variable costs:

Costs that vary in total directly and proportionately with changes

in the activity index, but remain constant on a per unit basis

Fixed costs:

Costs that remain the same in total regardless of changes in the

activity index, but, on a per unit basis, vary inversely with

changes in the activity index

Explain the significance of the relevant range.

Relevant rangeRange of activity within which the company expects to operate

Cost behavior assumed to be linear through this range


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Explain the concept of mixed costs. Containsboth a variable cost and a fixed cost component

For CVP analysis, must be divided into its fixed and variableamounts

One method used to classify these costs is thehigh-low method

List the five components of CVP analysis.

Volume or level of activity

Unit selling price

Variable cost per unit

Total fixed costs

Sales mix


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Indicate what contribution margin is andhow it can be expressed.

Contribution margin is the excess of revenueover all variable costs

Can be expressed either as aper unit amountor as aratio

Identify the three ways to determine thebreak-even point.

Using amathematical equation

Thecontribution margin technique

From a CVP graph


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Summary of Study Objectives Give the formulas for determining sales required to earn

target net income. General formula:

Required sales= Variable costs + Fixed costs + Target Net Income

Other formulas:Required sales in units= (Fixed costs + Target Net Income)

Contribution margin per unit

andRequired sales in dollars= (Fixed costs + Target Net Income) Contribution margin ratio

Define the margin of safety and give the formulas forcomputing it. Excess of actual or expected sales over sales at break-even

Formulas:

Actual (expected) sales Break-even sales =Margin of safety in dollars

and

Margin of safety in dollars Actual (expected) sales =Margin of safetyratio


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CPV by Weygandt