University of Louisiana at Lafayette Managerial Accounting Weygandt • Kieso • Kimmel CHAPTER 5 COST-VOLUME-PROFIT Prepared by Dan R. Ward Suzanne P. Ward University of Louisiana at Lafayette John Wiley & Sons, Inc. © 2005

CHAPTER 5 COST – VOLUME - PROFIT Study 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.

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.

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 make decisions Applies to all types of businesses and entities

COST BEHAVIOR ANALYSIS Continued Starting point is measuring key business activities 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)

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

COST BEHAVIOR ANALYSIS Continued The activity level selected is called the activity (or volume) index Identifies the activity that causes changes in the behavior of costs Allows costs to be classified according to their response to changes in activity as: Variable Costs Fixed Costs Mixed Costs

COST BEHAVIOR ANALYSIS VARIABLE COSTS Study Objective 1 Costs that vary in total directly 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

COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued Variable costs also remain constant 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

COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued Example Damon Company manufactures radios that contain a $10 clock Activity index is the number of radios produced For each radio produced, the total cost of the clocks increases by $10 If 2,000 radios are made, the total cost of the clocks is $20,000 (2,000 X $10) If 10,000 radios are made, the total cost of the clocks is $100,000 (10,000 X $10)

COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued Example: Continued

COST BEHAVIOR ANALYSIS FIXED COSTS Costs that remain the same in total regardless of changes in the activity level. Per unit cost varies inversely with activity: As volume increases, unit cost decline, and vice versa Examples include Property taxes Insurance Rent Depreciation on buildings and equipment

COST BEHAVIOR ANALYSIS FIXED COSTS - Continued Example Damon Company leases its productive facilities for $10,000 per month Total fixed costs of the facilities remain constant at all levels of activity - $10,000 per month On a per unit basis, the cost of rent decreases as activity increases and vice versa At 2,000 radios, the unit cost is $5 ($10,000 ÷ 2,000 units) At 10,000 radios, the unit cost is $1 ($10,000 ÷ 10,000 units)

COST BEHAVIOR ANALYSIS FIXED COSTS - Continued Example: Continued

COST BEHAVIOR ANALYSIS RELEVANT RANGE Study Objective 2 Throughout the range of possible levels of activity, a straight-line relationship usually does not 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 nonlinear – some fixed costs will not change over the entire range of activities, others may

COST BEHAVIOR ANALYSIS RELEVANT RANGE - Continued

COST BEHAVIOR ANALYSIS RELEVANT RANGE - Continued Defined as the range of activity over which a company expects to operate during a year Within this range, a straight-line relationship usually exists for both variable and fixed costs

COST BEHAVIOR ANALYSIS MIXED COSTS Study Objective 3 Costs that have both a variable cost element and a fixed cost element Sometimes called semivariable cost Change in total but not proportionately with changes in activity level

COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method Mixed costs must be classified into their fixed and variable elements One approach to separate the costs is called the high-low method Uses the total costs incurred at both the high and the low levels of activity to classify mixed costs The difference in costs between the high and low levels represents variable costs, since only variable costs change as activity levels change

COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued Steps in Method 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 ÷ = Change in Total Costs High minus Low Activity Level Variable Cost per Unit

COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued Example Data 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 Month January February Miles Driven 20,000 40,000 Total Cost $30,000 $48,000 Month March April Miles Driven 35,000 50,000 Total Cost $49,000 $63,000

COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued 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

COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued 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.

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

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

COST-VOLUME-PROFIT ANALYSIS Study Objective 4 Study of the effects of changes of costs and volume on a company’s profits A critical factor in management decisions Important in profit planning

COST-VOLUME-PROFIT ANALYSIS Considers the interrelationships among the five components of CVP analysis:

ASSUMPTIONS UNDERLYING CVP ANALYSIS 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

CVP INCOME STATEMENT Study Objective 5 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 Example Vargo Video Company produces DVD players. Relevant data for June 2005: Unit selling price of DVD player $500 Unit variable costs $300 Total monthly fixed costs $200,000 Units sold 1,600

CVP INCOME STATEMENT Contribution Margin Per Unit Contribution margin is available to cover fixed costs and to contribute to income Formula for contribution margin per unit: Example: Computation for Vargo Video – = Unit Selling Price Unit Variable Costs Contribution Margin per Unit – = Unit Selling Price $500 Unit Variable Costs $300 Contribution Margin per Unit $200

CVP INCOME STATEMENT Contribution Margin Ratio Shows the percentage of each sales dollar available to apply toward fixed costs and profits Example: Computation for Vargo Video ÷ = Contribution Margin Ratio Unit Selling Price Contribution Margin per Unit ÷ = Contribution Margin Ratio 40% Unit Selling Price $500 Contribution Margin per Unit S200

CVP INCOME STATEMENT Contribution Margin Ratio - Example Ratio helps to determine the effect of changes in sales on net income

BREAK-EVEN ANALYSIS Study Objective 6 Process of finding the break-even point 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 from a cost-volume-profit (CVP) graph Expressed either in sales units or in sales dollars

BREAK-EVEN ANALYSIS Mathematical Equation Example using the Vargo Video data: Where: Q = sales volume; $500 = selling price; $300 = variable cost per unit; $200,000 total fixed costs To find sales dollars required to break-even: 1000 units X $500 = $500,000 (break-even sales dollars) Variable Costs $300 Q Fixed Costs $200,000 Net Income $0 Sales $500 Q = + + $200 Q $200,000 = Q 1000 units =

BREAK-EVEN ANALYSIS Contribution Margin Technique 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 When the break even point in dollars is desired, contribution margin ratio is used in the following formula ÷ = Fixed Costs Break-even Point in Units Contribution Margin per Unit ÷ = Fixed Costs Break-even Point in Dollars Contribution Margin Ratio

BREAK-EVEN ANALYSIS Contribution Margin Technique Example using Vargo Video data: ÷ = Fixed Costs $200,000 Break-even Point in Units 1,000 units Contribution Margin per Unit $200 ÷ = Fixed Costs $200,000 Break-even Point in Dollars $500,000 Contribution Margin per Unit 40%

BREAK-EVEN ANALYSIS Graphic 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 line starting at the zero activity level Plot the total fixed cost by a horizontal line Plot the total cost line. (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

BREAK-EVEN ANALYSIS CVP Graph for Vargo Video

BREAK-EVEN ANALYSIS Target Net Income Study Objective 7 Level of sales necessary to achieve a specified income Can be determined from each of the approaches used to determine break-even sales/units May be expressed either in sales dollars or sales units

BREAK-EVEN ANALYSIS Target Net Income - Example Using the Contribution Margin Approach and the Vargo Video Data: Formula for required sales in units: Formula for required sales in dollars ÷ = Contribution Margin Per Unit $200 Fixed Costs + Target Net Income $200,000 + $120,000 Required Sales in Units 1,600 units ÷ = Contribution Margin Ratio 40% Fixed Costs + Target Net Income $200,000 + $120,000 Required Sales in Dollars $800,000

Let’s Review Contribution margin: Is revenue remaining after deducting variable costs May be expressed as contribution margin per unit Is selling price less cost of goods sold Both (a) and (b) above

Let’s Review Contribution margin: Is revenue remaining after deducting variable costs May be expressed as contribution margin per unit Is selling price less cost of goods sold Both (a) and (b) above

BREAK-EVEN ANALYSIS Margin of Safety Difference between actual or expected sales and sales at the break-even point May be expressed in dollars or as a ratio Example - To determine the margin 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

BREAK-EVEN ANALYSIS Margin of Safety Ratio Study Objective 8 Computed by dividing the margin of safety in dollars by the actual or expected sales (using Vargo Video data) Results indicate that Vargo Video’s sales could fall by 33 percent before it would be operating at a loss. The higher the dollars or the percentage, the greater the margin of safety. ÷ = Margin of Safety Ratio 33% Actual (Expected) Sales $750,000 Margin of Safety in Dollars $250,000

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 range Range of activity within which the company expects to operate Cost behavior assumed to be linear through this range

Summary of Study Objectives Explain the concept of mixed costs. Contains both a variable cost and a fixed cost component For CVP analysis, must be divided into its fixed and variable amounts One method used to classify these costs is the high-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

Summary of Study Objectives Indicate what contribution margin is and how it can be expressed. Contribution margin is the excess of revenue over all variable costs Can be expressed either as a per unit amount or as a ratio Identify the three ways to determine the break-even point. Using a mathematical equation The contribution margin technique From a CVP graph

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 and Required sales in dollars = (Fixed costs + Target Net Income) ÷ Contribution margin ratio Define the margin of safety and give the formulas for computing it. Excess of actual or expected sales over sales at break-even Formulas: Actual (expected) sales – Break-even sales = Margin of safety in dollars Margin of safety in dollars ÷ Actual (expected) sales = Margin of safety ratio

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