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CHAPTER Cost-Volume-Profit ASSIGNMENT CLASSIFICATION TABLE Study Objectives Questions Brief Exercises Distinguish between variable and fixed costs 1, 2, 3, 1, 2, 3, 4, 5, Explain the significance of the relevant range 4, 2 Explain the concept of mixed costs 6, 7, 1, 3, 4, 1, 3, 4, 5, List the five components of cost-volume-profit analysis Indicate what contribution margin is and how it can be expressed 10, 11, 17 6, 8, 9, 10, 11, 1A, 2A, 3A, 12, 13 4A, 5A 1B, 2B, 3B, 4B, 5B Identify the three ways to determine the break-even point 12, 13, 14 8, 8, 9, 10, 11, 1A, 2A, 3A, 12, 13,14, 4A, 5A 16 1B, 2B, 3B, 4B, 5B Give the formulas for determining sales required to earn target net income 16 10, 12 14, 15 2A, 5A 2B, 5B Define margin of safety, and give the formulas for computing it 15 11 16 2A, 4A, 5A 2B, 4B, 5B Exercises A Problems B Problems 1A 1B 1A 1B 5-1 ASSIGNMENT CHARACTERISTICS TABLE Problem Number Description Difficulty Level Time Allotted (min.) 1A Determine variable and fixed costs, compute break-even point, prepare a CVP graph, and determine net income Simple 20–30 2A Prepare a CVP income statement, compute break-even point, contribution margin ratio, margin of safety ratio, and sales for target net income Moderate 30–40 3A Compute break-even point under alternative courses of action Simple 20–30 4A Compute break-even point and margin of safety ratio, and prepare CVP income statement before and after changes in business environment Moderate 20–30 5A Compute break-even point and margin of safety ratio, and prepare a CVP income statement before and after changes in business environment Moderate 20–30 1B Determine variable and fixed costs, compute break-even point, prepare a CVP graph, and determine net income Simple 20–30 2B Prepare a CVP income statement, compute break-even point, contribution margin ratio, margin of safety ratio, and sales for target net income Moderate 30–40 3B Compute break-even point under alternative courses of action Simple 20–30 4B Compute break-even point and margin of safety ratio, and prepare CVP income statement before and after changes in business environment Moderate 20–30 5B Compute break-even point and margin of safety ratio, and prepare a CVP income statement before and after changes in business environment Moderate 20–30 5-2 5-3 Define margin of safety, and give the formulas for computing it * Broadening Your Perspective Give the formulas for determining sales required to earn target net income * * Indicate what contribution margin is and how it can be expressed * Identify the three ways to determine the break-even point List the five components of cost-volume-profit analysis * * Explain the concept of mixed costs E5-4 E5-7 Explain the significance of the relevant range * E5-4 Distinguish between variable and fixed costs E5-1 Real-World Focus Decision Making Exploring the Web Across the Organization E5-16 P5-2A P5-4B P5-5B P5-5B Managerial Analysis Ethics Case All About You P5-4A P5-5A P5-5A P5-5B E5-12 P5-2A E5-14 P5-2B E5-15 Q5-16 BE5-10 BE5-12 Q5-15 BE5-11 P5-3A P5-4A P5-3B P5-4B P5-5A E5-16 P5-1A P5-2A P5-1B P5-2B E5-10 E5-11 E5-12 E5-13 E5-14 Q5-13 BE5-8 BE5-9 E5-8 E5-9 P5-2B P5-1B P5-3A P5-3B P5-4A P5-5A P5-4B P5-5B BE5-3 E5-3 P5-1A Evaluation BE5-6 P5-1A P5-2A P5-1B P5-2B E5-5 E5-6 Synthesis E5-10 E5-11 E5-12 E5-13 Q5-11 Q5-17 BE5-6 BE5-7 E5-8 E5-9 Q5-8 BE5-4 BE5-5 BE5-2 E5-2 Analysis E5-3 E5-6 P5-1A P5-1B Application BE5-1 E5-5 E5-1 E5-2 Communication Q5-12 Q5-14 Q5-10 Q5-9 Q5-6 Q5-7 BE5-1 Q5-4 Q5-5 Q5-1 Q5-2 Q5-3 Q5-6 Knowledge Comprehension * Study Objective Correlation Chart between Bloom’s Taxonomy, Study Objectives and End-of-Chapter Exercises and Problems BLOOM’S TAXONOMY TABLE 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-VOLUMEPROFIT ANALYSIS INDICATE WHAT CONTRIBUTION MARGIN IS AND HOW IT CAN BE EXPRESSED 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 5-4 CHAPTER REVIEW Cost Behavior Analysis Cost behavior analysis is the study of how specific costs respond to changes in the level of business activity A knowledge of cost behavior helps management plan operations and decide between alternative courses of action The activity index identifies the activity that causes changes in the behavior of costs; examples include direct labor hours, sales dollars, and units of output Once an appropriate activity index is chosen, costs can be classified as variable, fixed or mixed Variable and Fixed Costs (S.O 1) Variable costs are costs that vary in total directly and proportionately with changes in the activity level Examples of variable costs include direct materials and direct labor, cost of goods sold, sales commissions, and freight-out A variable cost may also be defined as a cost that remains the same per unit at every level of activity Fixed costs are costs that remain the same in total regardless of changes in the activity level Examples include property taxes, insurance, rent, supervisory salaries, and depreciation Fixed costs per unit vary inversely with activity; as volume increases, unit cost declines and vice versa Relevant Range (S.O 2) The range over which a company expects to operate during the year is called the relevant range Within the relevant range a straight-line relationship exists for both variable and fixed costs Mixed Costs (S.O 3) Mixed costs are costs that contain both a variable element and a fixed element; they increase in total as the activity level increases, but not proportionately For purposes of CVP analysis, mixed costs must be classified into their fixed and variable elements The high-low method uses the total costs incurred at the high and low levels of activity The difference in costs represents variable costs, since only the variable cost element can change as activity levels change The steps in computing fixed and variable costs under the high-low method are: a Determine variable cost per unit from the following formula: Change in Total Costs b ÷ High minus Low Activity Level = Variable Cost per Unit 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 Cost-Volume-Profit Analysis (S.O 4) Cost-volume-profit (CVP) analysis is the study of the effects of changes in costs and volume on a company’s profits It is a critical factor in such management decisions as profit planning, setting selling prices, determining product mix, and maximizing use of production facilities 5-5 10 CVP analysis considers the interrelationships among the following components: (a) volume or level of activity, (b) unit selling prices, (c) variable cost per unit, (d) total fixed costs, and (e) sales mix Basic CVP Components 11 The following assumptions underlie each CVP analysis: a The behavior of both costs and revenues is linear throughout the relevant range of the activity index b All costs can be classified as either variable or fixed with reasonable accuracy c Changes in activity are the only factors that affect costs d All units produced are sold e When more than one type of product is sold, the sales mix will remain constant That is, the percentage that each product represents of total sales will stay the same Contribution Margin 12 (S.O 5) Contribution margin is the amount of revenue remaining after deducting variable costs The formula for contribution margin per unit is: Unit Selling Price 13 – Unit Variable Costs = Contribution Margin per Unit Contribution margin per unit indicates the amount available to cover fixed costs and contribute to income The formula for the contribution margin ratio is: Contribution Margin Per Unit ÷ Unit Selling Price = Contribution Margin Ratio The ratio indicates the portion of each sales dollar that is available to apply to fixed costs and to contribute to income Break-Even Analysis 14 (S.O 6) The break-even point is the level of activity at which total revenue equals total costs (both fixed and variable) Knowledge of the break-even point is useful to management when it decides whether to introduce new product lines, change sales prices on established products, or enter new market areas 15 A common equation used for CVP analysis is as follows: Sales = Variable Costs + Fixed Costs + Net Income 16 Under the contribution margin technique, the break-even point can be computed by using either the contribution margin per unit or the contribution margin ratio 17 The formula, using unit contribution margin, is: Fixed Costs ÷ Contribution Margin per Unit 5-6 = Break-even Point in Units 18 The formula using the contribution margin is: Fixed Costs 19 Contribution Margin Ratio ÷ = Break-even Point in Dollars A chart (or graph) can also be used as an effective means to determine and illustrate the breakeven point A cost-volume-profit (CVP) graph is as follows: Dollars (000) Sales Line 900 Total Cost Line 800 700 600 Break-even Point Variable Costs 500 400 300 Fixed Cost Line 200 100 Fixed Costs 200 400 600 800 1000 1200 1400 1600 1800 Units of Sales Target Net Income 20 (S.O 7) Target net income is the income objective for individual product lines The follow-ing equation is used to determine target net income sales: Required Sales = Variable Costs + Fixed Costs + Target Net Income Margin of Safety 21 (S.O 8) Margin of safety is the difference between actual or expected sales and sales at the break-even point a The formula for stating the margin of safety in dollars is: Actual (Expected) – Sales b Break-even Sales = Margin of Safety in Dollars The formula for determining the margin of safety ratio is: Margin of Safety in Dollars – Actual (Expected) = Sales Margin of Safety Ratio The higher the dollars or the percentage, the greater the margin of safety 5-7 LECTURE OUTLINE A Cost Behavior Analysis Cost behavior analysis is the study of how specific costs respond to changes in the level of business activity The activity index identifies the activity that causes changes in the behavior of costs With an appropriate activity index, companies can classify the behavior of costs into three categories: variable, fixed, or mixed TEACHING TIP Use ILLUSTRATION 5-1 to define and graphically illustrate variable and fixed cost classifications Emphasize total cost behavior with changes in activity levels, then demonstrate unit cost behavior with activity level changes Point out that for internal analysis of operations by management, having costs classified into variable and fixed classifications facilitates CVP analysis Variable costs are costs that 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 are costs that remain the same in total regardless of changes in the activity level a Because total fixed costs remain constant as activity changes, it follows that fixed costs per unit vary inversely with activity b Examples of fixed costs include property taxes, insurance, rent, supervisory salaries, and depreciation on buildings and equipment 5-8 The relevant range is the range of activity over which a company expects to operate during a year It is important in CVP analysis because the behavior of costs is assumed to be linear (straight-line) throughout the relevant range Although the linear relationship may not be completely realistic, the linear assumption produces useful data for CVP analysis as long as the level of activity remains within the relevant range Mixed costs are costs that contain both a variable element and a fixed element Mixed costs change in total but not proportionately with changes in the activity level a For purposes of CVP analysis, mixed costs must be classified into their fixed and variable elements One method that management may use to classify these costs is the high-low method TEACHING TIP Use ILLUSTRATION 5-2 to define and graphically illustrate the mixed costs classification Point out that for CVP analysis, the variable and fixed elements of a mixed cost should be separated using a method such as the high-low method b B The high-low method uses the total costs incurred at the high and low levels of activity The difference in costs between the high and low levels represents variable costs, since only the variable cost element can change as activity levels change Fixed costs are determined by subtracting the total variable cost at either the high or low activity level from the total cost at that activity level Cost-Volume-Profit Analysis Cost-volume-profit (CVP) analysis is the study of the effects of changes in costs and volume on a company’s profits CVP analysis is important in profit planning It is useful in setting selling prices, determining product mix, and maximizing use of production facilities 5-9 TEACHING TIP ILLUSTRATION 5-3 lists the basic components and assumptions that underlie CVP analysis CVP analysis considers the interrelationships among the following components: a Volume or level of activity b Unit selling prices c Variable cost per unit d Total fixed costs e Sales mix The following assumptions underlie each CVP analysis: a The behavior of both costs and revenues is linear throughout the relevant range of the activity index b Costs can be classified accurately as either variable or fixed c Changes in activity are the only factors that affect costs d All units produced are sold e When more than one type of product is sold, the sales mix will remain constant (the percentage that each product represents of total sales will stay the same) Contribution margin is the amount of revenue remaining after deducting variable costs It can be expressed as a per unit amount or as a ratio 5-10 TEACHING TIP Use ILLUSTRATION 5-4 to demonstrate the calculation of the contribution margin on a unit basis and as a ratio Emphasize the importance of the contribution margin in CVP analysis C a Contribution Margin per Unit = Unit Selling Price – Unit Variable Costs b Contribution Margin Ratio = Contribution Margin per Unit ÷ Unit Selling Price Break-even Analysis At the break-even point, the company will realize no income but will suffer no loss Knowledge of the break-even point is useful to management when it decides whether to introduce new product lines, change sales prices on established products, or enter new market areas The break-even point can be: a Computed from a mathematical equation: Break-even Point in Dollars = Total Variable Costs + Total Fixed Costs The break-even point in units can be computed by using unit selling prices and unit variable costs TEACHING TIP ILLUSTRATION 5-5 provides an example of break-even analysis calculated by the equation approach The break-even point can be stated in terms of units or sales dollars 5-11 b Computed by using contribution margin: Break-even Point in Units = Fixed Costs ÷ Contribution Margin per Unit Break-even Point in Dollars = Fixed Costs ÷ Contribution Margin Ratio TEACHING TIP ILLUSTRATION 5-6 provides an example of computing the break-even point in dollars and units using the contribution margin approach c Derived from a CVP graph at the intersection of the total-cost line and the total-sales line TEACHING TIP ILLUSTRATION 5-7 provides an example of determining the break-even point in dollars and units by using a CVP graph Point out that the equation approach (Illustration 5-5), the contribution margin technique (Illustration 5-6), and the CVP graph all provide the same answer and are alternative approaches to CVP analysis The income objective set by management is called target net income To meet target net income, required sales must be determined a Mathematical equation: Required Sales = Variable Costs + Fixed Costs + Target Net Income Required sales may be expressed in either sales units or sales dollars b Contribution margin technique: Fixed Costs + Target Net Income ÷ Contribution Margin Ratio = Required Sales in Dollars c Graphic presentation: In the profit area of the CVP graph, the distance between the sales line and the total cost line at any point equals net income A company can find required sales by analyzing the differences between the two lines until the desired net income is found 5-12 TEACHING TIP ILLUSTRATION 5-8 provides an example of calculating target net income using the mathematical equation approach, contribution margin technique, and the CVP graph (see Illustration 5-7 at 14,000 units of activity) Margin of safety is the difference between actual or expected sales and sales at the break-even point The margin of safety can be expressed in dollars or as a ratio a Margin of Safety in Dollars = Actual (Expected) Sales – Break-even Sales b Margin of Safety Ratio = Margin of Safety in Dollars ÷ Actual (Expected) Sales 5-13 20 MINUTE QUIZ Circle the correct answer True/False The range over which a company is expected to operate is called the relevant range of the activity index True A mixed cost contains both selling and administrative cost elements True False In a CVP income statement, contribution margin is reported in the body of the statement True 10 False If the unit contribution margin is $300 and fixed costs are $240,000 then the break-even point in units would be 800 units True False Sales mix is the percentage that each product represents of total sales True False The contribution margin is the amount of revenue remaining after deducting fixed costs True False If revenue = $80 and variable cost = 40% of revenue, then contribution margin = $48 True False If a salesperson incurs $2,000 of expenses in servicing two customers and $4,000 of expenses in servicing four customers, the fixed costs are $1,000 True False Variable costs are costs that remain the same per unit at every level of activity True False False Margin of safety is the difference between actual sales and contribution margin True False 5-14 Multiple Choice Which of the following is a false statement regarding assumptions of CVP analysis? a Total fixed costs remain constant over the relevant range b Unit selling prices are constant c Changes in volume or level of activity increase variable costs per unit d All units produced are sold Mixed costs may be separated into fixed costs and variable costs by using a the relevant range method b the high-low method c the contribution margin method d all of the above If the unit selling price is $500, the unit variable cost is $300, and the total monthly fixed costs are $300,000, then the contribution margin ratio is a 30% b 40% c 50% d 60% If activity level increases 25% and a specific cost increases from $40,000 to $50,000, this cost would be classified as a a variable cost b mixed cost c fixed cost d none of the above If total fixed costs are $900,000 and variable costs as a percentage of unit selling price are 40%, then the break-even point in dollars is a $1,500,000 b $360,000 c $2,250,000 d not determinable with the information given 5-15 ANSWERS TO QUIZ True/False True False True False True 10 False True True True False Multiple Choice c b b a a 5-16 ILLUSTRATION 5-1 COST CLASSIFICATIONS—VARIABLE AND FIXED COSTS VARIABLE COST TOTAL COST BEHAVIOR Cost $ Costs that vary in total directly and proportionately with changes in activity levels Activity UNIT COST BEHAVIOR: Variable cost per unit remains constant for all activity levels FIXED COST TOTAL COST BEHAVIOR Cost $ Costs that remain the same in total regardless of changes in activity levels Activity UNIT COST BEHAVIOR: Fixed cost per unit varies inversely with changes in activity levels Note: Cost behavior assumptions are valid only in the relevant range 5-17 ILLUSTRATION 5-2 COST CLASSIFICATION—MIXED COSTS MIXED COST TOTAL COST BEHAVIOR Cost $ Costs that contain both variable and fixed elements, and increase in total but not proportionately with changes in activity levels Activity EXAMPLE High Change in activity level 5,000 hours Low Jan Feb Mar Apr May June Machine Hours 5,000 8,000 4,000 6,000 3,000 6,500 Power Costs $ 800 1,100 700 $500 900 600 950 Change in costs Determine variable cost per unit: Change in Total Cost $500 ÷ Determine fixed cost: High – Low Activity Levels 5,000 = Variable Cost per Unit $.10 per hour Activity Level High Low $1,100 $600 Total cost Less: Variable cost 8,000 × $.10 = 800 3,000 × $.10 = 300 Total fixed cost $ 300 $300 Power costs are $300 per month plus $.10 per hour 5-18 ILLUSTRATION 5-3 BASIC COMPONENTS AND ASSUMPTIONS THAT UNDERLIE CVP ANALYSIS INTERRELATIONSHIPS AMONG THE BASIC COMPONENTS Volume or level of activity Unit selling prices Variable cost per unit Total fixed costs Sales mix ASSUMPTIONS FOR CVP ANALYSIS The behavior of both costs and revenues is linear throughout the relevant range of the activity index All costs can be classified accurately as either variable or fixed 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 5-19 ILLUSTRATION 5-4 CONTRIBUTION MARGIN CONTRIBUTION MARGIN: REVENUE REMAINING AFTER DEDUCTING VARIABLE COSTS Example: Selling price Variable costs Contribution margin Per Unit % $25 15 $10 100% 60% 40% CONTRIBUTION MARGIN PER UNIT Unit Selling Price – $25 Unit Variable Costs = $15 Contribution Margin Per Unit $10 CONTRIBUTION MARGIN RATIO Contribution Margin Per Unit $10 ÷ Unit Selling Price $25 5-20 = Contribution Margin Ratio 40% ILLUSTRATION 5-5 BREAK-EVEN ANALYSIS—EQUATION APPROACH EXAMPLE: Per Unit % $25 100% 15 60% $10 40% $100,000 Selling price Variable costs Contribution margin Fixed costs Break-even point in dollars: Let X = sales dollars at break-even point X = 60 X + $100,000 40 X = $100,000 X = $250,000 Break-even point in units: Let X = number of units to sell to break-even $25 X = $15 X + $100,000 $10 X = $100,000 X = 10,000 units Proof: Sales Variable costs Contribution margin Fixed costs Net income $250,000 (10,000 units × $25) 150,000 (10,000 units × $15) 100,000 (10,000 units × $10) 100,000 $ 5-21 ILLUSTRATION 5-6 BREAK-EVEN ANALYSIS—CONTRIBUTION MARGIN TECHNIQUE EXAMPLE: Per Unit % $25 100% 60% 15 40% $10 $100,000 Selling price Variable costs Contribution margin Fixed costs Break-even point in dollars: Fixed Costs ÷ Contribution Margin Ratio $100,000 = 40 Break-even Point in Dollars $250,000 Break-even point in units: Fixed Costs $100,000 ÷ Contribution Margin per Unit $10 5-22 = Break-even Point in Units 10,000 units ILLUSTRATION 5-7 CVP GRAPH Sales Line 450 400 Profit Area 350 Dollars (000) 300 Break-even Point 250 200 150 Loss Area Variable Costs Fixed Cost Line 100 Fixed Costs 50 Total Cost Line 2,000 6,000 10,000 14,000 Units of Sales 5-23 18,000 ILLUSTRATION 5-8 TARGET NET INCOME EXAMPLE: Target net income — $40,000 Per Unit % $25 100% Selling price 15 60% Variable costs $10 40% Contribution margin Fixed costs $100,000 EQUATION APPROACH Required sales in units: Let X = unit sales for target net income of $40,000 $25 X = $15 X + $100,000 + $40,000 $10 X = $140,000 X = 14,000 units Required sales in dollars: Let X = sales dollars for target net income of $40,000 X = 60 X + $100,000 + $40,000 40 X = $140,000 X = $350,000 CONTRIBUTION MARGIN TECHNIQUE Required sales in units: Fixed Costs + Target Income $140,000 ÷ Contribution Margin per Unit $10 = Required Sales in Units 14,000 units = Required Sales in Dollars $350,000 Required sales in dollars: Fixed Costs + Target Income $140,000 ÷ Contribution Margin Ratio 40 5-24 ... point in units can be computed by using unit selling prices and unit variable costs TEACHING TIP ILLUSTRATION 5-5 provides an example of break-even analysis calculated by the equation approach The... Total Costs b ÷ High minus Low Activity Level = Variable Cost per Unit Determine the fixed cost by subtracting the total variable cost at either the high or the low activity level from the total... Costs + Net Income 16 Under the contribution margin technique, the break-even point can be computed by using either the contribution margin per unit or the contribution margin ratio 17 The formula,
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