Chapter 5 CostVolumeProfit Relationships Chapter 5 CostVolumeProfit Relationships

Chapter 5 Cost-Volume-Profit Relationships

Chapter 5 Cost-Volume-Profit Relationships After studying this chapter, you should be able to: 1 Distinguish between variable and fixed costs. 2 Explain the meaning and importance of the relevant range. 3 Explain the concept of mixed costs. 4 State the five components of cost-volume-profit analysis. 5 Indicate the meaning of contribution margin and the ways it may be expressed.

Chapter 5 Cost-Volume-Profit Relationships After studying this chapter, you should be able to: 6 Identify the three ways that the break-even point may be determined. 7 Define margin of safety and give the formulas for computing it. 8 Give the formulas for determining sales required to earn target net income. 9 Describe the essential features of a cost-volume-profit income statement.

Preview of Chapter 5 COST-VOLUMEPROFIT RELATIONSHIPS Cost Behavior Analysis • Variable Costs • Fixed Costs • Relevant Range • Mixed Costs • Identifying Variable and Fixed Costs

Preview of Chapter 5 COST-VOLUMEPROFIT RELATIONSHIPS Cost-Volume-Profit Analysis • Basic Components • Contribution Margin • Break-Even Analysis • Margin of Safety • Target Net Income • Changes in Business Environment • CVP Income Statement

Cost Behavior Analysis § Cost behavior analysis is the study of how specific costs respond to changes in the level of activity within a company. § The starting point in cost behavior analysis is measuring the key activities in the company’s business. § Activity levels may be expressed in terms of – – sales dollars (retail company), miles driven (trucking company), room occupancy (hotel), or number of dance classes taught (dance studio).

Cost Behavior Analysis § For an activity level to be useful in cost behavior analysis, there should be correlation between changes in the level or volume of activity and changes in the costs. § The activity level selected is referred to as the activity (or volume) index. § The activity index identifies the activity that causes changes in the behavior of costs.

Study Objective 1 Distinguish between variable and fixed costs.

Variable Costs Variable costs are costs that vary in total directly and proportionately with changes in the activity level. A variable cost may also be defined as a cost that remains the same per unit at every level of activity.

Variable Costs § Damon Company manufactures radios that contain a $10 digital clock. The activity index is the number of radios produced. As each radio is manufactured, the total cost of the clocks increases by $10. (b) (a) Unit Variable Costs (Digital Clocks) Cost (000) $100 80 60 40 20 Illustration 5 -1 0 0 2 4 6 8 10 Radios produced in (000) Cost (per unit) Total Variable Costs (Digital Clocks) $25 20 15 10 5 0 0 2 4 6 8 10 Radios produced in (000)

Fixed Costs Fixed costs are costs that remain the same in total regardless of changes in the activity level. Since fixed costs remain constant in total as activity changes, fixed costs per unit vary inversely with activity. As volume increases, unit cost declines and vice versa.

Fixed Costs § Damon Company leases all of its productive facilities at a cost of $10, 000 per month. Total fixed costs of the facilities will remain constant at every level of activity. Cost (000) $25 20 15 10 5 Illustration 5 -2 0 0 2 4 6 8 10 Radios produced in (000) (b) Fixed Costs Per Unit (Rent Expense) Cost (per unit) (a) Total Fixed Costs (Rent Expense) $5 4 3 2 1 0 0 2 4 6 8 10 Radios produced in (000)

Study Objective 2 Explain the meaning and importance of the relevant range.

Nonlinear Behavior of Variable and Fixed Costs Cost ($) In the previous two slides, the assumption was made that total variable costs and total fixed costs were linear, and straight lines were used to represent both types of costs. A straight-line relationship does not usually exist for variable costs throughout the entire range of activity. In the real world, the (a) Total (b) relationship between Variable Costs Total Fixed Costs Curvilinear Nonlinear variable cost behavior and changes in the activity level is often curvilinear, as shown in part (a) on the right. The behavior of total fixed costs through all levels of activity is shown in 0 20 40 60 80 100 part (b). Illustration 5 -3 Activity level (%)

Linear Behavior Within Relevant Range Operating at zero or at 100% capacity is the exception for most companies. Companies usually operate over a narrower range – such as 40 -80% of capacity. The relevant range of the activity index is the range over which a company expects to operate during a year. Total Variable Costs Curvilinear (b) Total Fixed Costs Nonlinear Relevant Range 0 Illustration 5 -4 Relevant Range Cost ($) Within this range, as shown in both diagrams to the right, a straight-line relationship normally exists for both fixed and variable costs. (a) 20 40 60 80 100 Activity level (%) 0 20 40 60 80 100 Activity level (%)

Study Objective 3 Explain the concept of mixed costs.

Mixed Costs Mixed costs contain both a variable cost element and a fixed cost element. Sometimes called semivariable costs, mixed costs change in total but not proportionately with changes in the activity level.

Behavior of a Mixed Cost The rental of a U-Haul truck is a good example of a mixed cost. $200 e in t. L 150 Cost Local rental terms for a U-Haul truck are $50 per day plus $. 50 per mile. The per diem charge is a fixed cost with respect to miles driven, while the mileage charge is a variable cost. The graphic presentation of the rental cost for a one-day rental is shown on the right. a t To 100 os C l Variable Cost Element 50 Fixed Cost Element 0 0 50 100 150 200 Miles 250 300 Illustration 5 -5

Mixed Cost Classification for CVP Analysis § In CVP analysis, it is assumed that mixed costs must be classified into their fixed and variable elements. § Firms usually ascertain variable and fixed costs on an aggregate basis at the end of a time period, using the company’s past experience with the behavior of the mixed cost at various activity levels. § The high-low method is a mathematical method that uses the total costs incurred at the high and low levels of activity.

The High-Low Method The steps in calculating fixed and variable costs under this method are as follows: 1 Determine variable cost per unit from the following formula: Change in Total Costs High minus Low Activity Level = Variable Cost per Unit Illustration 5 -6 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 activity level.

The High-Low Method: Step 1 To illustrate, assume that Metro Transit Company has the following maintenance costs and mileage data for its fleet of busses over a 4 -month period: 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 Illustration 5 -7 The high and low levels of activity are 50, 000 miles in April and 20, 000 miles in January. The difference in maintenance costs at these levels is $33, 000 ($63, 000 -$30, 000) and the difference in miles is 30, 000 (50, 000 - 20, 000). Therefore, for Metro Transit, variable cost per unit is $1. 10, computed as follows: $33, 000 30, 000 = $1. 10

The High-Low Method: Step 2 Metro Transit Company would compute the fixed portion of its maintenance costs as shown below: Total Cost Less: Variable costs (50, 000 x $1. 10) (20, 000 x $1. 10) Total fixed costs Activity Level High Low $63, 000 $30, 000 55, 000 $ 8, 000 22, 000 $ 8, 000 Illustration 5 -8 Maintenance costs are therefore $8, 000 per month plus $1. 10 per mile. For example at 45, 000 miles, estimated maintenance costs would be $49, 500 variable (45, 000 x $1. 10), and $8, 000 fixed.

The High-Low Method § The high-low method generally produces a reasonable estimate for analysis. § However, it does not produce a precise measurement of the fixed and variable elements in a mixed cost because other activity levels are ignored in the computation. !

Study Objective 4 State the five components of costvolume-profit analysis.

Cost-Volume Profit Analysis § Cost-volume-profit (CVP) analysis is the study of the effects of changes of costs and volume on a company’s profits. § CVP analysis involves a consideration of the interrelationships among the following components: – Volume or activity level – Unit selling price – Variable cost per unit – Total fixed costs – Sales mix

CVP Assumptions The following assumptions underlie each CVP application: When these assumptions are not valid, the results of CVP analysis may be inaccurate. 1 The behavior of both costs and revenues is linear throughout the relevant range of the activity index. 2 All costs can be classified as either variable or fixed with reasonable accuracy. 3 Changes in activity are the only factors that affect costs. 4 All units produced are sold. 5 When more than one type of product is sold, total sales will be in a constant sales mix.

CVP Analysis In CVP analysis applications, the term cost includes manufacturing costs plus selling and administrative expenses. § We will use Vargo Video Company as an example. Relevant data for the VCRs made by this company are as follows: Unit selling price Unit variable costs Total monthly fixed costs $500 $300 $200, 000 Illustration 5 -10

Study Objective 5 Indicate the meaning of contribution margin and the ways it may be expressed.

Contribution Margin One of the key relationships in CVP analysis is contribution margin (CM). Contribution margin is the amount of revenue remaining after deducting variable costs. The CM is then available to cover fixed costs and to contribute income for the company. § For example, assume that Vargo Video sells 1, 000 VCRs in one month, sales are $500, 000 (1, 000 x $500) and variable costs are $300, 000 (1, 000 x $300). Thus, contribution margin is $200, 000, computed as follows: Sales $500, 000 Illustration 5 -11 - Variable Costs = Contribution Margin - $300, 000 = $200, 000

Unit Contribution Margin Views differ as to the best way to express contribution margin (CM). Some favor a per unit basis. § At Vargo Video, the contribution margin per unit is $200. Illustration 5 -12 Unit Selling Price $500 - Unit Variable Cost = Contribution Margin per Unit - $300 = $200 § CM per unit indicates that for every VCR sold, Vargo Video will have $200 to cover fixed costs and contribute to income.

Contribution Margin Ratio Others prefer to use a contribution margin ratio. § At Vargo Video, the contribution margin ratio is 40%. Contribution Margin per Unit $200 Illustration 5 -13 Unit Selling Price = Contribution Margin Ratio $500 = 40% § The CM ratio means that 40 cents of each sales dollar ($1 x 40%) is available to apply to fixed costs and to contribute to income.

Study Objective 6 Identify the three ways that the breakeven point may be determined.

Break-Even Analysis § The second key relationship in CVP analysis is the break-even point, which is the level of activity where total revenues equals total costs, both fixed and variable. § Since no income is involved when the breakeven point is the objective, the analysis is often referred to as break-even analysis.

Break-Even Analysis § The break-even point can be: – Computed from a mathematical equation. – Computed by using contribution margin. – Derived from a CVP graph. § The break-even point can be expressed in either sales dollars or sales units.

Break-Even Analysis: Mathematical Equation In its simplest form, the equation for breakeven sales is: Break-even Sales = Variable Costs + Fixed Costs Illustration 5 -14

Break-Even Analysis: Mathematical Equation for Dollars The break-even point in dollars is found by expressing variable costs as a percentage of unit selling price. § For Vargo Video, the percentage is 60% ($300 $500). Sales must be $500, 000 for Vargo Video to break even. The computation to determine sales dollars at the break -even point is: where: X =. 60 X + $200, 000. 40 X = $200, 000 X = $500, 000 X = sales dollars at the break-even point. 60 = variable costs as a percentage of unit selling price $200, 000 = total fixed costs Illustration 5 -15

Break-Even Analysis: Mathematical Equation for Units The break-even point in units can be computed directly from the mathematical equation by using unit selling prices and unit variable costs. Vargo must sell 1, 000 units to break even. The computation is: $500 X = $300 X + $200, 000 $200 X = $200, 000 X = 1, 000 units where: X = sales volume $500 = unit selling price $300 = variable cost per unit $200, 000 = total fixed costs Illustration 5 -16

Break-Even Analysis: Mathematical Equation Proof The accuracy of the previous computations can be proved as follows: Sales (1, 000 x $500) Total costs: Variable (1, 000 x $300) Fixed Net Income $500, 000 $300, 000 200, 000 500, 000 $ -0 - Illustration 5 -16

Break-Even Analysis: CM Technique for Units Because we know that CM equals total revenues less variable costs, it follows that at the break-even point, contribution margin must equal total fixed costs. When the CM per unit is used, the formula to compute break-even point in units is shown below: § Once again, the CM per unit for Vargo Video is $200. Fixed Costs $200, 000 Contribution Margin per Unit = Break-even Point in Units $200 = 1, 000

Break-Even Analysis: CM Technique for Dollars When the CM ratio is used, the formula to compute break-even point in dollars is shown below: § Again, the CM ratio for Vargo Video is 40%. Fixed Costs $200, 000 Contribution Margin Ratio = Break-even Point in Dollars 40% = $500, 000

Break-Even Analysis: Graphic Presentation § An effective way to derive the break-even point is to prepare a break-even graph. § The graph is referred to as a cost-volumeprofit (CVP) graph since it shows costs, volume, and profits.

Break-Even Analysis: Graphic Presentation The construction of the graph, using the Vargo Video Company data, is as follows: 1 Plot the total revenue line starting at the zero activity level. 2 Plot the total fixed cost by a horizontal line. 3 Plot the total cost line starting at the fixed cost line at zero activity and increasing the amount by the variable cost at each level of activity. 4 Determine the break-even point from the intersection of the total cost line and the total revenue line. In addition to identifying the break-even point, the CVP graph shows both the net income and net loss areas. Thus, the amount of income or loss at each level of sales can be derived from the total sales and total cost lines.

CVP Graph Sales Line $900 Dollars (000) In the graph to the right, sales volume is shown on the horizontal axis. This axis needs to extend to the maximum level of expected sales. Both total revenues (sales) and total costs (fixed plus variable) are recorded on the vertical axis. 700 600 Profit Area Break-even Point Total Cost Line 500 400 300 200 100 Fixed Cost Line Loss Area 200 400 600 800 1000 1200 1400 1600 1800 Units of Sales Illustration 5 -20

Study Objective 7 Define margin of safety and give the formulas for computing it.

Margin of Safety The margin of safety is another relationship that may be calculated in CVP analysis. Margin of safety is the difference between actual or expected sales and sales at the break-even point This relationship measures the “breathing room” or “cushion” that management has in order to break even if actual sales fail to materialize.

Margin of Safety The margin of safety may be expressed in dollars or as a ratio. § Assuming that actual (expected) sales for Vargo Video are $750, 000, the computations are: Margin of Safety in Dollars Actual (Expected) Sales $750, 000 - Break-even Sales = Margin of Safety in Dollars - $500, 000 = $250, 000 = Margin of Safety Ratio = 33% Margin of Safety Ratio Margin of Safety in Dollars Actual (Expected) Sales $250, 000 $750, 000

Study Objective 8 Give the formulas for determining sales required to earn target net income.

Target Net Income § Management usually sets an income objective for individual product lines. This objective, called target net income, is extremely useful to management because it indicates the sales necessary to achieve a specified level of income. § The amount of sales necessary to achieve target net income can be determined from each of the approaches used in determining break-even sales.

Target Net Income: Mathematical Equation We know that at the break-even point no profit or loss results for the company. By adding a factor for target net income to the break-even equation, we obtain the formula shown below for determining required sales. Required Sales = Variable Costs + Fixed Costs + Target Net Income Illustration 5 -23 Required sales may be expressed in either sales dollars or sales units.

Target Net Income: Mathematical Equation Assuming the target net income is $120, 000 for Vargo Video, the computation of required sales in dollars is as follows: where: X =. 60 X + $200, 000 + $120, 000. 40 X = $320, 000 X = $800, 000 X = required sales. 60 = variable costs as a percentage of unit selling price $200, 000 = total fixed costs $120, 000 = target net income Illustration 5 -24 The sales volume in units at the target income level is found by dividing the sales dollars by the unit selling price. $800, 000 $500 = $1, 600

Target Net Income: CM Technique As in the case of break-even sales, the sales required to meet a target net income can be computed in either dollars or units. § The formula using the CM ratio for Video Vargo is as follows: Required Sales = Fixed Costs + Target Net Income $320, 000 = 40% Contribution Margin Ratio $800, 000

Target Net Income: Graphic Presentation § A CVP graph can also be used to derive the sales required to meet target net income. § In the profit area of the graph, the distance between the sales line and the total cost line at any point equals net income. Required sales are found by analyzing the differences between the two lines until the desired net income is found.

CVP and Changes in the Business Environment § Business conditions change rapidly and management must respond intelligently to these changes. § CVP analysis can be used in responding to change. § The original VCR sales and cost data for Vargo Video Company are shown below. Unit selling price Unit variable cost Total fixed costs Break-even sales $ 500 $ 300 $ 200, 000 $ 500, 000 or 1, 000 units Illustration 5 -26

CVP and Changes in the Business Environment: Case I § A competitor is offering a 10% discount on the selling price of its VCRs. Management must decide whether or not to offer a similar discount. § Question: What effect will a 10% discount on selling price have on the break-even point for VCRs? § Answer: A 10% discount on selling price reduces the selling price per unit to $450 [$500 – ($500 x 10%)]. Variable cost per unit remains unchanged at $300. Therefore, the contribution margin per unit is $150. Assuming no change in fixed costs, break-even sales are 1, 333 units, calculated as follows: Fixed Costs ÷ Contribution Margin per Unit = Break-even Sales $ 200, 000 ÷ $ 150 = 1, 333 units (rounded) Illustration 5 -27

CVP and Changes in the Business Environment: Case II § Management invests in new robotic equipment that will significantly lower the amount of direct labor required to make the VCRs. It is estimated that total fixed costs will increase 30% and that variable cost per unit will decrease 30%. § Question: What effect will the new equipment have on the sales volume required to break even? § Answer: Total fixed costs become $260, 000 [$200, 000 + ($200, 000 x 30%)], and variable cost per unit is now $210 [$300 – ($300, 000 x 30%)]. The new break-even point about 900 units, calculated as follows: Fixed Costs ÷ Contribution Margin per Unit = Break-even Sales $ 260, 000 ÷ ($500 - $210) = 900 units (rounded) Illustration 5 -28

CVP and Changes in the Business Environment: Case III § An increase in the price of raw materials will increase the unit variable cost of VCRs by an estimated $25. Management is striving to hold the line on the selling price of the VCRs, and plans a cost-cutting program that will save $17, 500 in fixed costs per month. Vargo Video Company is currently realizing monthly net income of $80, 000 on sales of 1, 400 VCRs. § Question: What increase in sales will be needed to to maintain the same level of net income? § Answer: The variable cost per unit increases to $325 ($300 + $25), and fixed costs are reduced to $182, 500 ($200, 000 – $17, 500). Because of the change in variable cost, the variable cost becomes 65% of sales ($325 ÷ $500). Using the equation for target net income, required sales are calculated to be $750, 000, as follows: Required Sales = Variable Costs + Fixed Costs + Target Net Income X =. 65 X + $182, 500 + $80, 000. 35 X = $262, 500 X = $750, 000 Illustration 5 -29

Study Objective 9 Describe the essential features of a cost-volume-profit income statement.

CVP Income Statement § The CVP income statement classifies costs and expenses as variable or fixed and specifically reports contribution margin in the body of the statement. § The CVP income statement format is sometimes called the contribution margin format. § This format is for internal management use only.

CVP Income Statement § For purposes of illustrating the CVP income statement, assume that Vargo Video Company reaches its target net income of $120, 000. From an analysis of the transactions, the following information is obtained on the $680, 000 of costs that were incurred in June: Cost of goods sold Selling expenses Administrative expenses Variable Fixed Total $ 400, 000 60, 000 20, 000 $ 120, 000 40, 000 $ 520, 000 100, 000 60, 000 $ 480, 000 $ 200, 000 $ 680, 000 Illustration 5 -30

Traditional versus CVP Income Statement § The CVP income statement and the traditional income statement based on this data are shown side-by-side on the next slide. § Note that net income is the same ($120, 000) in both of the statements. § The major difference is the format for the expenses. § Also, the traditional statement shows gross profit, whereas the CVP statement shows contribution margin.

Traditional versus CVP Income Statement Traditional Format Sales $ 800, 000 Cost of goods sold 520, 000 Gross profit 280, 000 Operating expenses Selling expenses $ 100, 000 Administrative expenses 60, 000 Total operating expenses 160, 000 Net income $ 120, 000 CVP Format Sales $ 800, 000 Variable expenses Cost of goods sold $ 400, 000 Selling expenses 60, 000 Administrative expenses 20, 000 Total variable expenses 480, 000 320, 000 Contribution margin Fixed expenses Cost of goods sold 120, 000 Selling expenses 40, 000 Administrative expenses 40, 000 Total fixed expenses 200, 000 Net income $ 120, 000 Illustration 5 -31

Appendix 5 A Variable Costing

Appendix 5 A Study Objective 10 Explain the difference between absorption costing and variable costing.

Absorption versus Variable Costing § All manufacturing costs are charged to and absorbed by the product under full or absorption costing. This is how costs were handled in previous chapters. § Under variable costing only direct materials, direct labor, and variable manufacturing overhead costs are considered product costs. Fixed manufacturing overhead costs are recognized as period costs when incurred. § The difference between absorption costing and variable costing is graphically shown below. Absorption Costing Product Cost Fixed Manufacturing Overhead Variable Costing Period Cost Illustration 5 A-1

Absorption versus Variable Costing: An Illustration § As an illustration, Premium Products Corporation manufactures a polyurethane sealant called Fix-it for car windshields. Relevant data for Fix-it in January 1996, the first month of production, is as follows: – Selling Price: $20 per unit. – Units: Produced 30, 000; sold 20, 000; beginning inventory zero. – Variable unit costs: Manufacturing $9 (direct materials $5, direct labor $3, and variable overhead $1) and selling and administrative expenses $2. – Fixed costs: Manufacturing overhead $120, 000, and selling and administrative expenses $15, 000.

Absorption versus Variable Costing: Unit Production Cost § The per unit production cost under each costing approach is: Absorption Type of Costing $ 5 Direct materials 3 Direct labor 1 Variable manufacturing overhead 4 Fixed manufacturing overhead ($120, 000 ÷ 30, 000 units produced) Total unit cost $ 13 Variable Costing $ 5 3 1 0 $ 9 Illustration 5 A-2 § The difference in total unit cost of $4 ($13 - $9) occurs because fixed manufacturing costs are a product cost under absorption costing and a period cost under variable costing.

Absorption versus Variable Costing: Effects on Income § The income statements under the two costing approaches are shown on the next two slides. § Income from operations under absorption costing is $40, 000 higher than under variable costing ($85, 000 – $45, 000). There is a $40, 000 difference in the ending inventories ($130, 000 under absorption costing and $90, 000 under variable costing). § Under absorption costing, $40, 000 of the fixed overhead costs have been deferred to a future period as a product cost.

Absorption Costing Income Statement Sales (20, 000 units X $20) Cost of goods sold Inventory, January 1 Cost of goods manufactured (30, 000 units X $13) Cost of goods available for sale Inventory, January 31 (10, 000 units X $13) Cost of goods sold (20, 000 units X $13) Gross profit Selling and administrative expenses (Variable 20, 000 units X $2 + fixed $15, 000) Income from operations $ 400, 000 $ – 0– 390, 000 130, 000 260, 000 140, 000 55, 000 $ 85, 000 Illustration 5 A-3

Variable Costing Income Statement Sales (20, 000 units X $20) Variable expenses Variable cost of goods sold Inventory, January 1 Variable manufacturing costs (30, 000 units X $9) Cost of goods available for sale Inventory, January 31 (10, 000 units X $9) Variable cost of goods sold Variable selling and administrative expenses (20, 000 units X $2) Total variable expenses Contribution margin Fixed expenses Manufacturing overhead Selling and administrative expenses Total fixed expenses Income from operations $ 400, 000 – 0– 270, 000 90, 000 180, 000 40, 000 220, 000 180, 000 120, 000 15, 000 135, 000 $ 45, 000 Illustration 5 A-4

Summary of Income Effects = > < Illustration 5 A-5

Rationale for Variable Costing § The rationale for variable costing focuses on the purpose of fixed manufacturing costs, which is to have productive facilities available for use. § Defenders of absorption costing justify the assignment of fixed manufacturing overhead costs to inventory on the basis that these costs are as much a cost of getting a product ready for sale as direct materials or direct labor. § The use of variable costing in product costing is acceptable only for internal use by management.

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Chapter 5 Cost-Volume-Profit Relationships