Cost Behavior and Cost-Volume-Profit Analysis Chapter 4

Learning Objectives Classify costs as variable costs, fixed costs, or mixed costs. Compute the contribution margin, the contribution margin ratio, and the unit contribution margin. Determine the break-even point and sales necessary to achieve a target profit. Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit. Compute the break-even point for a company selling more than one product, the operating leverage, and the margin of safety.

Learning Objective 1 Classify costs as variable costs, fixed costs, or mixed costs.

Cost Behavior Cost behavior is the manner in which a cost changes as a related activity changes. Understanding the behavior of a cost depends on: Identifying the activities that cause the cost to change, called activity bases (or activity drivers). Specifying the range of activity over which the changes in the cost are of interest. This range of activity is called the relevant range.

Variable Costs Variable costs are costs that vary in proportion to changes in the level of activity.

Variable Costs Jason Sound Inc. produces stereo systems. The parts for the stereo systems are purchased from suppliers for $10 per unit (a variable cost) and are assembled by Jason Sound Inc. For Model JS-12, the direct materials costs for the relevant range of 5,000 to 30,000 units of production are shown on the next slide.

Variable Costs

Variable Costs As shown in the previous slides, the variable costs have the following characteristics: Cost per unit remains the same regardless of changes in the activity base. Total cost changes in proportion to changes in the activity base.

Variable Costs $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $20 $15 $10 $5 Cost per Unit Total Direct Materials Cost 10 20 30 Units Produced (000) 10 20 30 Units Produced (000) Number of Units of Model JS-12 Produced Direct Materials Cost per Unit Total Direct Materials Cost 5,000 units $10 $ 50,000 10,000 10 l00,000 15,000 10 150,000 20,000 10 200,000 25,000 10 250,000 30,000 10 300,000

Fixed Costs Fixed costs are costs that remain the same in total dollar amount as the activity base changes.

Fixed Costs Minton Inc. manufactures, bottles, and distributes perfume. The production supervisor is Jane Sovissi. She is paid $75,000 per year. The plant produces from 50,000 to 300,000 bottles of perfume.

The more units produced, the lower the fixed cost per unit. Fixed Costs The more units produced, the lower the fixed cost per unit.

Fixed Costs Fixed costs have the following characteristics: Cost per unit changes inversely to changes in the activity base. Total cost remains the same regardless of changes in the activity base.

Fixed Costs $150,000 $125,000 $100,000 $75,000 $50,000 $25,000 $1.50 $1.25 $1.00 $.75 $.50 $.25 Total Salary Salary per Unit 100 200 300 100 200 300 Units Produced (000) Units Produced (000) Number of Bottles of Perfume Produced Total Salary for Jane Sovissi Salary per Bottle of Perfume Produced 50,000 bottles $75,000 $1.500 100,000 75,000 0.750 150,000 75,000 0.500 200,000 75,000 0.375

Mixed Costs Mixed costs have characteristics of both a variable and a fixed cost. Mixed costs are sometimes called semivariable or semifixed costs. Over one range of activity, the total mixed cost may remain the same. Over another range of activity, the mixed cost may change in proportion to changes in the level of activity.

Mixed Costs Simpson Inc. manufactures sails, using rented equipment. The rental charges are $15,000 per year, plus $1 for each machine hour used over 10,000 hours.

Mixed Costs The rental charges for various hours used within the relevant range of 8,000 hours to 40,000 hours are as follows:

Mixed Costs

Mixed Costs The high-low method is a cost estimation method that may be used to separate mixed costs into their fixed and variable components.

Mixed Costs The Equipment Maintenance Department of Kason Inc. incurred the following costs during the past five months:

Mixed Costs The number of units produced is the activity base, and the relevant range is the units produced between June and October. The next four slides illustrate how the high-low method is used to determine the fixed and variable costs.

First, select the highest and lowest levels of activity. Mixed Costs Production Total (Units) Cost Actual costs incurred June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 First, select the highest and lowest levels of activity. Variable Cost per Unit = Difference in Total Cost Difference in Production

Difference in Total Cost Difference in Production Mixed Costs Production Total (Units) Cost Next, fill in the formula for difference in total cost. June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 $61,500 41,250 $20,250 Variable Cost per Unit = Difference in Total Cost Difference in Production $20,250

Difference in Total cost Difference in Production Mixed Costs Production Total (Units) Cost Then, fill in the formula for difference in production. June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 2,100 750 1,350 Variable Cost per Unit = Difference in Total cost Difference in Production $20,250 1,350

Mixed Costs Variable cost per unit is $15 Production Total (Units) Cost June 1,000 $45,550 July 1,500 52,000 August 2,100 61,500 September 1,800 57,500 October 750 41,250 Variable cost per unit is $15 Variable Cost per Unit = $20,250 1,350 = $15

Mixed Costs The fixed cost is estimated by subtracting the total variable costs from the total costs for the units produced as shown below: Fixed Cost = Total Costs – (Variable Cost per Unit x Units Produced)

Mixed Costs The fixed cost is the same at the highest and the lowest levels of production as shown below for Kason Inc. Highest Level Fixed Cost = Total Costs – (Variable Cost per Unit x Units Produced) Fixed Cost = $61,500 – ($15 x 2,100 units) Fixed Cost = $61,500 – $31,500 Fixed Cost = $30,000

Mixed Costs The fixed cost is the same at the highest and the lowest levels of production as shown below for Kason Inc. Lowest Level Fixed Cost = Total Costs – (Variable Cost per Unit x Units Produced) Fixed Cost = $41,250 – ($15 x 750 units) Fixed Cost = $41,250 – $11,250 Fixed Cost = $30,000

Mixed Costs With fixed costs and variable costs estimated at $30,000 plus $15 per unit, a formula is in place to estimate production at any level. If the company is expected to produce 2,000 units in November, the estimated total cost would be calculated as follows: Total Cost = ($15 x Units Produced) + $30,000 Total Cost = ($15 x 2,000) + $30,000 Total Cost = $30,000 + $30,000 Total Cost = $60,000

Summary of Cost Behavior Concepts Total variable costs increase and decrease proportionately with activity level. Total Variable Costs Total Costs Total Units Produced Per-unit variable costs remain the same regardless of activity level. Unit Variable Costs Per-Unit Cost Total Units Produced

Summary of Cost Behavior Concepts Total fixed costs remain the same regardless of activity level. Total Fixed Costs Total Costs Total Units Produced Per-unit fixed costs decrease as activity level increases. Unit Fixed Costs Per-Unit Cost Total Units Produced

Summary of Cost Behavior Concepts Some examples of variable, fixed, and mixed costs for the activity base units produced are as follows:

Summary of Cost Behavior Concepts One method of reporting variable and fixed costs is called variable costing or direct costing. Under variable costing, only the variable manufacturing costs are included in the product cost. The fixed factory overhead is treated as an expense of the period in which it is incurred.

Learning Objective 2 Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.

Cost-Volume-Profit Relationships Cost-volume-profit analysis is the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits.

Cost-Volume-Profit Relationships Some of the ways cost-volume-profit analysis may be used include the following: Analyzing the effects of changes in selling prices on profits Analyzing the effects of changes in costs on profits Analyzing the effects of changes in volume on profits Setting selling prices Selecting the mix of products to sell Choosing among marketing strategies

Contribution Margin Contribution margin is the excess of sales over variable costs, as shown in the formula below. Contribution Margin = Sales – Variable Costs

Contribution Margin Assume the following data for Lambert, Inc.:

Contribution Margin

Contribution Margin Ratio The contribution margin ratio, sometimes called the profit-volume ratio, indicates the percentage of each sales dollar available to cover fixed costs and to provide income from operations. It is computed as follows: Contribution Margin Ratio = Contribution Margin Sales

Contribution Margin Ratio The contribution margin ratio is 40% for Lambert Inc., computed as follows: Contribution Margin Ratio = Contribution Margin Sales Contribution Margin Ratio = $400,000 $1,000,000 Contribution Margin Ratio = 40%

Contribution Margin Ratio 100% 60% 40% 30% 10% Contribution Margin Ratio = Sales – Variable Costs Sales $1,000,000 – $600,000 $1,000,000 Contribution Margin Ratio = Contribution Margin Ratio = 40%

Contribution Margin Ratio If Lambert Inc. adds $80,000 in sales from the sale of an additional 4,000 units, its income will increase by $32,000, as computed below. Change in Income from Operations Change in Sales Dollars x Contribution Margin Ratio = Change in Income from Operations $80,000 x 40% = $32,000 =

Contribution Margin Ratio Proof

Unit Contribution Margin The unit contribution margin is useful for analyzing the profit potential of proposed decisions. The unit contribution margin is computed as follows: Unit Contribution Margin = Sales Price per Unit Variable Cost per Unit –

Unit Contribution Margin The unit contribution margin is most useful when the increase or decrease in sales volume is measured in sales units (quantities). The change in income from operations can be determined using the following formula: Change in Income from Operations Change in Sales Units = x Unit Contribution Margin

Unit Contribution Margin Lambert Inc.’s sales could be increased by 15,000 units, from 50,000 to 65,000 units. Lambert’s income from operations would increase by $120,000 (15,000 x $8), as shown below. Change in Income from Operations Change in Sales Units = x Unit Contribution Margin Change in Income from Operations = 15,000 units x $8 = $120,000

Unit Contribution Margin Lambert Inc.’s contribution margin income statement, shown below, confirms that income increased to $220,000 when 65,000 units are sold.

Review Sales (50,000 units) $1,000,000 Variable costs 600,000 Contribution margin $ 400,000 Fixed costs 300,000 Income from operations $ 100,000 100% 60% 40% 30% 10% $20 12 $ 8 Unit contribution margin analyses can provide useful information for managers.

Review Sales (50,000 units) $1,000,000 100% $20 Variable costs 600,000 60% 40% 30% 10% $20 12 $ 8 Sales (50,000 units) $1,000,000 Variable costs 600,000 Contribution margin $ 400,000 Fixed costs 300,000 Income from operations $ 100,000 The contribution margin can be expressed in three ways: Total contribution margin in dollars. Contribution margin ratio (percentage). Unit contribution margin (dollars per unit).

Learning Objective 3 Determine the break-even point and sales necessary to achieve a target profit.

Break-Even Point The break-even point is the level of operations at which a company’s revenues and expenses are equal.

Break-Even Point Assume the following data for Baker Corporation: Fixed costs $90,000 Unit selling price $25 Unit variable cost 15 Unit contribution margin $10

Unit Contribution Margin Break-Even Point The break-even point (in sales units) is calculated using the following equation: Break-Even Sales (units) = Fixed Costs Unit Contribution Margin Break-Even Sales (units) = $90,000 $10 Break-Even Sales (units) = 9,000 units

Break-Even Point Income from operations is zero when 9,000 units are sold—hence, the break-even point is 9,000 units.

Contribution Margin Ratio Break-Even Point The break-even point (in sales dollars) is calculated using the following equation: Break-Even Sales (dollars) = Fixed Costs Contribution Margin Ratio $90,000 .40 Break-Even Sales (dollars) = $10 $25 Break-Even Sales (dollars) = $225,000

Effect of Changes in Fixed Costs

Effect of Changes in Fixed Costs Bishop Co. is evaluating a proposal to budget an additional $100,000 for advertising. The data for Bishop Co. are as follows:

Effect of Changes in Fixed Costs Break-Even Sales (units) = Fixed Costs Unit Contribution Margin Without additional advertising: Break-Even Sales (units) = $600,000 $20 = 30,000 units With additional advertising: Break-Even Sales (units) = $700,000 $20 = 35,000 units

Effect of Changes in Unit Variable Costs

Effect of Changes in Unit Variable Costs Park Co. is evaluating a proposal to pay an additional 2% commission on sales to its salespeople (a variable cost) as an incentive to increase sales. Fixed costs are estimated at $840,000. The other data for Park Co. are as follows:

Effect of Changes in Unit Variable Costs Break-Even Sales (units) = Fixed Costs Unit Contribution Margin Without additional 2% commission: Break-Even Sales (units) = $840,000 $105 = 8,000 units With additional 2% commission: Break-Even Sales (units) = $840,000 $100 = 8,400 units $250 – [$145 + ($250 x 2%)] = $100

Effect of Changes in Unit Selling Price

Effect of Changes in Unit Selling Price Graham Co. is evaluating a proposal to increase the unit selling price of a product from $50 to $60. The estimated fixed costs are $600,000. The following additional data have been gathered:

Effect of Changes in Unit Selling Price Fixed Costs Unit Contribution Margin Break-Even Sales (units) = Without price increase: Break-Even Sales (units) = $600,000 $20 = 30,000 units With price increase: Break-Even Sales (units) = $600,000 $30 = 20,000 units

Summary of Effects of Changes on B/E Point

Target Profit The sales volume required to earn a target profit is determined by modifying the break- even equation. Sales (units) = Fixed Costs + Target Profit Unit Contribution Margin

Target Profit Assume the following data for Waltham Co.: What would be the necessary sales to earn the target profit of $100,000?

Fixed Costs + Target Profit Unit Contribution Margin Sales (units) = Fixed Costs + Target Profit Unit Contribution Margin Sales (units) = $200,000 + $100,000 $30 Sales (units) = 10,000 units

Target Profit Proof )

Unit Contribution Margin Target Profit Unit Contribution Margin Unit Selling Price Contribution Margin Ratio = Contribution Margin Ratio = $30 $75 From an earlier slide Contribution Margin Ratio = 40% Sales (dollars) = Fixed Costs + Target Profit Contribution Margin Ratio Sales (dollars) = $200,000 + $100,000 40% = $750,000 Necessary sales to earn a $100,000 target profit

Learning Objective 4 Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit.

Cost-Volume-Profit (Break-Even) Chart A cost-volume-profit chart, sometimes called a break-even chart, graphically shows sales, costs, and the related profit or loss for various levels of units sold.

Cost-Volume-Profit (Break-Even) Chart The cost-volume-profit charts in this section are based on Exhibit 5, which was constructed using the following data: (continued)

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Dollar amounts are indicated along the vertical axis. Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Volume is shown along the horizontal axis.

Cost-Volume-Profit (Break-Even) Chart Using maximum sales of $500,000 and knowing that each unit sells for $50, we can find the values on the two axes. Where the horizontal sales and costs line intersects the vertical 10,000 units of sales line is Point A in the next slide. (continued)

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Point A Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Point A could have been plotted at any sales level, because linearity is assumed.

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Point A Total Revenue Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Beginning at zero on the left corner of the graph, connect a straight line to the dot (Point A). This is the total revenue or total sales line.

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) Fixed Cost 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Fixed cost of $100,000 is a horizontal line.

Cost-Volume-Profit (Break-Even) Chart A point on the chart is needed to establish the cost line. An arbitrary sales amount is picked of 10,000 units. At this sales level, the cost should be $400,000, calculated as follows: [(10,000 x $30) + $100,000] = $400,000. (continued)

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) A point is marked at $400,000, where 10,000 units are sold. (continued)

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Sales and Costs (in thousands) Total Costs 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) A line is drawn from fixed costs at zero sales ($100,000) to this point. This is the total costs line. (continued)

Cost-Volume-Profit (Break-Even) Chart The line would be the same if another point had been picked. For example, assume that 8,000 units had been chosen. At this sales level, the cost should be $340,000 [(8,000 x $30) + $100,000]. (continued)

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 $340,000 Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) The 8,000 units line drawn vertically intersects the total costs line at $340,000.

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Break-even Point Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) The point where the revenue (blue) line and the total costs (orange) line intersect is the break-even point. (continued)

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Break-even Point Sales and Costs (in thousands) 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands) Break-even is sales of 5,000 units or $250,000.

Cost-Volume-Profit (Break-Even) Chart $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Operating Loss Area Break-even Point Sales and Costs (in thousands) Operating Profit Area 1 2 3 4 5 6 7 8 9 10 Units of Sales (in thousands)

Cost-Volume-Profit (Break-Even) Chart

Cost-Volume-Profit (Break-Even) Chart A proposal to reduce fixed costs by $20,000 is to be evaluated. The cost-volume-profit chart in Exhibit 6 (next slide) was designed to assist in this evaluation. Note that the total costs line has been drawn from fixed costs at zero sales of $80,000, reducing the break-even point to dollar sales of $200,000, or 4,000 units.

Cost-Volume-Profit (Break-Even) Chart

Profit-Volume Chart Another graphic approach to cost-volume- profit analysis, the profit-volume chart, plots only the difference between total sales and total costs (or profits). Again, data from Exhibit 5 are used. Unit selling price $ 50 Unit variable cost 30 Unit contribution margin $ 20 Total fixed costs $100,000

Profit-Volume Chart The maximum operating loss is equal to the fixed costs of $100,000. Assuming that the maximum unit sales within the relevant range is 10,000 units, the maximum operating profit is $100,000, as shown below. Maximum profit

Profit-Volume Chart

Revised Maximum profit Profit-Volume Chart Assume that an increase in fixed costs of $20,000 is to be evaluated. The maximum operating profit would be $80,000, as shown below: Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20) $200,000 Fixed costs 120,000 Operating profit $ 80,000 Revised Maximum profit

Profit-Volume Chart

Assumptions of Cost-Volume-Profit Analysis The primary assumptions are as follows: Total sales and total costs can be represented by straight lines. Within the relevant range of operating activity, the efficiency of operations does not change. Costs can be divided into fixed and variable components. The sales mix is constant. There is no change in the inventory quantities during the period.

Learning Objective 5 Compute the break-even point for a company selling more than one product, the operating leverage, and the margin of safety.

Sales Mix Considerations Many companies sell more than one product at different selling prices. In addition, the products normally have different unit contribution margins. The sales mix is the relative distribution of sales among the various products sold by a company.

Sales Mix Considerations Cascade Company sold Products A and B during the past year as follows:

Sales Mix Considerations It is useful to think of the individual products as components of one overall enterprise product. For Cascade Company, the overall enterprise product is called E. The unit selling price, unit variable cost, and unit contribution margin for E are computed as follows:

Sales Mix Considerations Fixed Costs Unit Contribution Margin Break-Even Sales (units) = Break-Even Sales (units) = $200,000 $25 Break-Even Sales (units) = 8,000 units

Sales Mix Considerations Break-even point

Income from Operations Operating Leverage The relationship of a company’s contribution margin to income from operations is measured by operating leverage. A company’s operating leverage is computed as follows: Contribution Margin Income from Operations Operating Leverage =

Operating Leverage Both companies have the same contribution margin.

Income from Operations Operating Leverage 5 Contribution Margin Income from Operations Jones Inc.: $100,000 $20,000 = 5

Income from Operations Operating Leverage 5 2 Contribution Margin Income from Operations Wilson Inc.: $100,000 $50,000 = 2

Percent Change in Sales Operating Leverage Operating leverage can be used to measure the impact of changes in sales on income from operations. This measure can be computed as follows: Percent Change in Income from Operations Percent Change in Sales Operating Leverage = x

Operating Leverage Assume that sales increased 10%, or $40,000 ($400,000 x 10%), for Jones Inc. and Wilson Inc. Jones Inc.: Percent Change in Income from Operations = 10% x 5 = 50% Wilson Inc.: Percent Change in Income from Operations = 10% x 2 = 20%

Operating Leverage 50% increase ($10,000/$20,000)

Operating Leverage 20% increase ($10,000/$50,000)

Operating Leverage The impact of a change in sales on income from operations for companies with high and low operating leverage can be summarized as follows:

Margin of Safety The margin of safety indicates the possible decrease in sales that may occur before an operating loss results. The margin of safety may be expressed in the following ways: Dollars of sales Units of sales Percent of current sales

Sales – Sales at Break-Even Point Margin of Safety If sales are $250,000, the unit selling price is $25, and the sales at the break-even point are $200,000, the margin of safety is 20%, computed as follows: Margin of Safety = Sales – Sales at Break-Even Point Sales Margin of Safety = $250,000 – $200,000 $250,000 Margin of Safety = 20%

Appendix Variable Costing

Variable Costing The cost of manufactured products consists of direct materials, direct labor, and factory overhead. The reporting of all these costs in financial statements is called absorption costing. Absorption costing is required by GAAP.

Variable Costing In variable costing, also called direct costing, the cost of goods manufactured consists of direct materials, direct labor, and variable factory overhead. In a variable costing income statement, fixed factory overhead costs do not become a part of the cost of goods manufactured.

Variable Costing Instead, fixed factory overhead costs are treated as a period expense.

Variable Costing The form of a variable costing income statement is as follows:

Variable Costing Assume that 15,000 units are manufactured and sold at a price of $50. The related costs and expenses are as follows:

Variable Costing

Variable Costing

Variable Costing

Variable Costing

Cost Behavior and Cost-Volume-Profit Analysis The End