John Wiley & Sons, Inc. © 2005

Chapter 18Chapter 18

Cost-Volume-Profit Relationships

Prepared by Barbara MullerPrepared by Barbara MullerArizona State University WestArizona State University West

Principles of AccountingPrinciples of Accounting

Kimmel Kimmel •• Weygandt Weygandt •• Kieso Kieso

CHAPTER 18 COST-VOLUME-PROFIT RELATIONSHIPS

After studying this chapter, you should be able to:

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.

CHAPTER 18 COST-VOLUME-PROFIT RELATIONSHIPS

After studying this chapter, you should be able to:

Identify the three ways to determine the break-even point.Define margin of safety and give the formulas for computing it.Give the formulas for determining sales required to earn target net income.Describe the essential features of a cost-volume-profit

income statement.

COST BEHAVIOR ANALYSIS

Cost behavior analysis• the study of how specific costs respond to changes in

the level of business activity• begins with a measurement of key business activities• these activities can be expressed in terms of

o Sales dollars (retail company)

o Miles driven (trucking company)

o Room occupancy (hotel), or

o Number of customers called on (salesperson)

The activity index identifies the activity that causes changes in the behavior of costs

VARIABLE and FIXED COSTSStudy Objective 1

Variable costs•Vary in total directly and proportionately with changes in the activity level

•A variable cost remains the same per unit at every level of activity

Fixed costs•Remain the same in total regardless of changes in the activity level

•Vary per unit inversely with activity

VARIABLE and FIXED COSTS

Let’s ReviewLet’s Review

Variable costs are costs that:Variable costs are costs that:

a.a. Vary in total directly and proportionately Vary in total directly and proportionately with with changes in the activity level.changes in the activity level.

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

c.c. Neither of the above.Neither of the above.

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

Let’s ReviewLet’s Review

Variable costs are costs that:Variable costs are costs that:

a.a. Vary in total directly and proportionately Vary in total directly and proportionately with with changes in the activity level.changes in the activity level.

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

c.c. Neither of the above.Neither of the above.

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

Relevant range•Range of activity over which the company expects to operate during a year

•Within this range, a straight-line relationship usually exists for both variable and fixed costs

•Throughout the entire range of activity, this straight-line relationship usually does not exist for variable and fixed costs

RELEVANT RANGEStudy Objective 2

MIXED COSTSStudy Objective 3

Mixed costs (semivariable costs)•Contain both variable and fixed cost elements•Costs change, but not proportionately with changes in activity level•Usually classified into their fixed and variable elements using the high-low method

HIGH-LOW METHOD

The high-low method uses total costs incurred at the high and low levels of activityThe high-low method produces a reasonable estimate for analysis purposes

HIGH-LOW METHOD

÷ =Change in Total Costs

High minus Low Activity Level

Variable Cost per Unit

STEP 1•Determine variable cost per unit using the following formula:

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 level

Cost-volume-profit (CVP) analysis • is the study of the effects of changes of costs and

volume on a company’s profits• is a critical factor in management decisions• is important in profit planning

Components of CVP ANALYSIS

Study Objective 4

Assumptions underlying CVP analysis• The behavior of both costs and revenues is linear

throughout the relevant range of the activity index• All costs can be classified as either variable or fixed with

reasonable accuracy

• Changes in activity are the only factors that affect costs

• All units produced are sold

• When more than one type of product is sold, the sales mix will remain constant

Assumptions of CVP Analysis

COMPONENTS OF CVP ANALYSIS

CVP considers relationships among the following components

Let’s ReviewLet’s Review

One of the following is not involved in One of the following is not involved in CVP analysis. That factor is:CVP analysis. That factor is:

a.a. Sales mix.Sales mix.

d.d. Volume or level of activity.Volume or level of activity.

c.c. Fixed costs per unit.Fixed costs per unit.

b.b. Unit selling prices.Unit selling prices.

Let’s ReviewLet’s Review

One of the following is not involved in One of the following is not involved in CVP analysis. That factor is:CVP analysis. That factor is:

a.a. Sales mix.Sales mix.

d.d. Volume or level of activity.Volume or level of activity.

c.c. Fixed costs per unit.Fixed costs per unit.

b.b. Unit selling prices.Unit selling prices.

CONTRIBUTION MARGINStudy Objective 5

Since CVP is important for management’s decision making process, a CVP income statement is usefulAssists management by classifying costs as variable and fixedPresents a contribution margin (amount of revenue remaining after deducting variable costs)

– =Sales Variable CostsContribution

Margin

– =Unit Selling Price

Unit Variable Costs

Contribution Margin per Unit

Contribution margin is available to cover fixed costs and to contribute to incomeThe formula for contribution margin per unit is shown below

CONTRIBUTION MARGIN PER UNIT

CONTRIBUTION MARGIN RATIO

Contribution margin ratio shows the percentage of each sales dollar available to apply toward fixed costs and profits

÷ = Contribution Margin Ratio

Unit Selling Price

Contribution Margin per Unit

The break-even point is the level of activity at which total revenues equal total costs – both fixed and variable

It can be• Computed from a mathematical equation• Computed by using contribution margin• Derived from a cost-volume-profit (CVP) graph• Expressed either in sales units or in sales dollars

BREAK-EVEN ANALYSISStudy Objective 6

FORMULA FOR BREAK-EVEN POINT IN UNITS USING CONTRIBUTION MARGIN

At the break-even point, contribution margin must equal total fixed costs (CM = total revenues – variable costs)

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

• When the break even point in units is desired, contribution margin per unit is used in the following formula

÷ =Fixed CostsBreak-even

Point in UnitsContribution

Margin per Unit

FORMULA FOR BREAK-EVEN POINT IN DOLLARS USING

CONTRIBUTION MARGIN RATIOWhen the break even point in dollars is desired, contribution margin ratio is used in the following formula

÷ =Fixed CostsBreak-even

Point in DollarsContribution Margin Ratio

GRAPHIC PRESENTATION

A cost-volume-profit (CVP) graph shows costs, volume, and profitsUsed to visually find the break-even pointTo construct a graph,•Plot the total revenue line starting at the zero activity level

•Plot the total fixed cost by a horizontal line

•Plot the total cost line. This starts at the fixed cost line at zero activity

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

CVP GRAPH

MARGIN OF SAFETY IN DOLLARS

Study Objective 7

The margin of safety is the difference between actual or expected sales and sales at the break-even point

It may be expressed in dollars or as a ratio The formula for determining the margin of

safety in dollars is shown below

– = Margin of Safety in Dollars

Break-even Sales

Actual (Expected) Sales

MARGIN OF SAFETY RATIO

The formula for determining the margin of safety ratio is shown belowThe higher the dollars or the percentage, the greater the margin of safety

÷ = Margin of Safety Ratio

Actual (Expected) Sales

Margin of Safety in Dollars

TARGET NET INCOMEStudy Objective 8

Target net income is the level of sales necessary to achieve a specified incomeThe required sales may be expressed either in sales dollars or sales unitsThe formula for required sales in dollars is as follows

÷ =Required Sales in Dollars

Contribution Margin Ratio

Fixed Costs + Target Net Income

The formula for required sales in units is as follows

÷ =Required Sales in

Units

Contribution Margin per Unit

Fixed Costs + Target Net Income

FORMULA FOR REQUIRED SALES IN UNITS

ESSENTIALS OF A COST-VOLUME-PROFIT INCOME STATEMENT

Study Objective 9

The CVP income statement classifies costs and expenses as variable or fixed and specifically reports contribution margin in the body of the statementTraditional and CVP income statements based on the data for the Vargo Video example in the text are next shown side-by-side for comparative purposes Net income is $120,000 in both statementsThe major difference is the format for the expenses

TRADITIONAL VERSUS CVP INCOME STATEMENT

T r a d i t i o n a l F o r m a tS a l e s $ 8 0 0 , 0 0 0C o s t o f g o o d s s o l d 5 2 0 , 0 0 0G r o s s p r o f i t 2 8 0 , 0 0 0O p e r a t i n g e x p e n s e s S e l l i n g e x p e n s e s $ 1 0 0 , 0 0 0 A d m i n i s t r a t i v e e x p e n s e s 6 0 , 0 0 0 T o t a l o p e r a t i n g e x p e n s e s 1 6 0 , 0 0 0N e t i n c o m e $ 1 2 0 , 0 0 0

C V P F o r m a tS a l e s $ 8 0 0 , 0 0 0V a r i a b l e e x p e n s e s C o s t o f g o o d s s o l d $ 4 0 0 , 0 0 0 S e l l i n g e x p e n s e s 6 0 , 0 0 0 A d m i n i s t r a t i v e e x p e n s e s 2 0 , 0 0 0 T o t a l v a r i a b l e e x p e n s e s 4 8 0 , 0 0 0C o n t r i b u t i o n m a r g i n 3 2 0 , 0 0 0F i x e d e x p e n s e s C o s t o f g o o d s s o l d 1 2 0 , 0 0 0 S e l l i n g e x p e n s e s 4 0 , 0 0 0 A d m i n i s t r a t i v e e x p e n s e s 4 0 , 0 0 0 T o t a l f i x e d e x p e n s e s 2 0 0 , 0 0 0N e t i n c o m e $ 1 2 0 , 0 0 0

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Copyright © 2005 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written consent of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.