John Wiley & Sons, Inc. © 2005 Chapter 18 Cost-Volume-Profit Relationships Prepared by Barbara Muller Arizona State University West Principles of Accounting Kimmel Weygandt 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 oSales dollars (retail company) oMiles driven (trucking company) oRoom occupancy (hotel), or oNumber of customers called on (salesperson)  The activity index identifies the activity that causes changes in the behavior of costs

VARIABLE and FIXED COSTS Study 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 Review Variable costs are costs that: a. Vary in total directly and proportionately with changes in the activity level. d. Both (a) and (b) above. c. Neither of the above. b. Remain the same per unit at every activity level.

Let’s Review Variable costs are costs that: a. Vary in total directly and proportionately with changes in the activity level. d. Both (a) and (b) above. c. Neither of the above. b. Remain the same per unit at every activity 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 RANGE Study Objective 2

MIXED COSTS Study 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 activity  The 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 Review One of the following is not involved in CVP analysis. That factor is: a. Sales mix. d. Volume or level of activity. c. Fixed costs per unit. b. Unit selling prices.

Let’s Review One of the following is not involved in CVP analysis. That factor is: a. Sales mix. d. Volume or level of activity. c. Fixed costs per unit. b. Unit selling prices.

CONTRIBUTION MARGIN Study Objective 5  Since CVP is important for management’s decision making process, a CVP income statement is useful  Assists management by classifying costs as variable and fixed  Presents a contribution margin (amount of revenue remaining after deducting variable costs) – = Sales Variable Costs Contribution Margin

– = Unit Selling Price Unit Variable Costs Contribution Margin per Unit  Contribution margin is available to cover fixed costs and to contribute to income  The 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 ANALYSIS Study 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 Costs Break-even Point in Units Contribution Margin per Unit

FORMULA FOR BREAK-EVEN POINT IN DOLLARS USING CONTRIBUTION MARGIN RATIO When the break even point in dollars is desired, contribution margin ratio is used in the following formula ÷ = Fixed Costs Break-even Point in Dollars Contribution Margin Ratio

GRAPHIC PRESENTATION  A cost-volume-profit (CVP) graph shows costs, volume, and profits  Used to visually find the break-even point  To 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 totalcost 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 below  The 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 INCOME Study Objective 8  Target net income is the level of sales necessary to achieve a specified income  The required sales may be expressed either in sales dollars or sales units  The 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 statement  Traditional 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 statements  The major difference is the format for the expenses

TRADITIONAL VERSUS CVP INCOME STATEMENT

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