Cost-Volume-Profit Analysis Chapter 7 Cost-Volume-Profit Analysis Chapter 7: Cost-Volume-Profit Analysis McGraw-Hill/Irwin Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Learning Objective 1 Learning Objective 1. Compute a break-even point using the contribution-margin approach and the equation approach. 7-2

The Break-Even Point The break-even point is the point in the volume of activity where the organization’s revenues and expenses are equal. The break-even point is the volume of activity where the organization’s revenues and expenses are equal. At this amount of sales, the organization has no profit or loss; it breaks even. This chapter will introduce an income statement highlighting the distinction between variable and fixed expenses. The statement also shows the total contribution margin, which is total sales revenue minus total variable expenses. Total contribution margin is the amount of revenue that is available to contribute to covering fixed expenses after all variable expenses have been covered. (LO1) 7-3

Equation Approach ($500 × X) ($300 × X) – – $80,000 = $0 ($200X) – Sales revenue – Variable expenses – Fixed expenses = Profit Unit sales price Sales volume in units × Unit variable expense Sales volume in units × ($500 × X) ($300 × X) – The equation approach can be used to find the break-even point. This approach is based on the profit equation. Income (or profit) is equal to sales revenue minus expenses. Expenses can be separated in variable and fixed expenses. At the break-even point, income is $0. (LO1) – $80,000 = $0 ($200X) – $80,000 = $0 X = 400 surf boards 7-4

Learning Objective 2 Learning Objective 2. Compute the contribution-margin ratio and use it to find the break-even point in sales dollars. 7-5

Contribution-Margin Approach Consider the following information developed by the accountant at Curl, Inc.: For each additional surf board sold, Curl generates $200 in contribution margin. Curl, Inc. manufactures surf boards. Each surf board sells for $500 and has variable costs of $300. (LO2) Therefore, the contribution margin per unit is $200. When enough surf boards are sold so that the total contribution margin is $80,000, Curl Inc. will break even for the period. (LO2) 7-6

Contribution-Margin Approach Fixed expenses Unit contribution margin Break-even point (in units) = To compute the break-even volume of surf boards, divide the total fixed expenses by the unit contribution margin. For Curl, Inc., $80,000 is divided by $200, which is 400 surf boards. That means that the break-even point is 400 surf boards. (LO2) $80,000 $200 = 400 surf boards 7-7

Contribution-Margin Approach Here is the proof! 400 × $500 = $200,000 400 × $300 = $120,000 The break-even point of 400 units can be proven by first calculating total sales: multiply $500 x 400 units for $200,000 in total sales. The variable expenses are $300 per unit x 400 units, which is $120,000. Total sales less total variable expenses is total contribution margin of $80,000. When fixed expenses of $80,000 are deducted from the total contribution margin, leaving $0 in net income. (LO2) 7-8

Contribution Margin Ratio Calculate the break-even point in sales dollars rather than units by using the contribution margin ratio. Contribution margin Sales = CM Ratio Sometimes management prefers that the break-even point be expressed in sales dollars rather than units. This can be accomplished by using the contribution margin ratio. The formula for the contribution margin ratio is contribution margin divided by sales. Then divide fixed expenses by the contribution margin ratio to determine the total sales dollars at the break-even point. (LO2) Fixed expense CM Ratio Break-even point (in sales dollars) = 7-9

Contribution Margin Ratio For Curl, Inc., the fixed costs of $80,000 are divided by the contribution margin ratio of 40% to determine the break-even sales of $200,000. (LO2) $80,000 40% $200,000 sales = 7-10

Learning Objective 3 Learning Objective 3. Prepare a cost-volume-profit (CVP) graph and explain how it is used. 7-11

Graphing Cost-Volume-Profit Relationships Viewing CVP relationships in a graph gives managers a perspective that can be obtained in no other way. Consider the following information for Curl, Inc.: While the break-even point conveys useful information to management, it does not show how profit changes as activity changes. Managers will often use a cost-volume-profit (CVP) graph to show the relationship between profit and volume of activity. Consider Curl, Inc. At sales of 300 unit, Curl Inc. incurs a net loss of $20,000. The break-even point occurs at 400 units and a $20,000 profit occurs when sales are at 500 units. (LO3) 7-12

Cost-Volume-Profit Graph In step 1, the horizontal and vertical axes are drawn. The vertical axis of the graph is dollars and the horizontal axis is units of sales. (LO3) In step 2, the fixed-expense line is drawn. It is parallel to the horizontal axis, since fixed expenses do not change with activity. (LO3) In step 3, compute the total expenses at any volume. Plot that point. For Curl, Inc., look at 400 units. Multiply the unit variable expenses of $300 per unit times 400 units for total variable expenses of $120,000. Add the variable expense to the fixed expenses of $80,000. So at the 400 unit level, total expenses are $200,000. (LO3) Fixed expenses 7-13

Cost-Volume-Profit Graph Total expenses In step 4, the total expense line is drawn. Since the total expenses at zero units sold is only the fixed costs, the total expense line crosses the vertical axis at the amount of fixed costs. This line then passes through the point plotted in step 3. (LO3) Fixed expenses 7-14

Cost-Volume-Profit Graph Total expenses In step 5, compute the total sales revenue at any volume. Plot that point. For Curl, Inc., look at 500 units. Multiply the unit sales price of $500 per unit times 500 units for total sales revenue of $250,000. (LO3) Fixed expenses 7-15

Cost-Volume-Profit Graph Total sales Total expenses In Step 6, draw the total revenue line. This line passes through the point plotted in step 5 and the origin. (LO3) Fixed expenses 7-16

Cost-Volume-Profit Graph Total sales Profit area Break-even point Total expenses In step 7, the break-even point, the profit area, and the loss area are all labeled. The break-even point is the point at which total expenses and total sales are equal, which is where the two lines cross. The profit area is the area where the total sales line is above the total expenses line. This is where revenues exceed expenses. The loss area is the area where the total expenses line is above the total sales line. This is where expenses exceeds revenues. (LO3) Fixed expenses Loss area 7-17

Profit-Volume Graph Some managers like the profit-volume graph because it focuses on profits and volume. Break-even point Profit area Yet another approach to graphing cost-volume-profit relationships is called a profit-volume graph. It highlights the amount of profit or loss. The graph intercepts the vertical axis at the amount equal to fixed expenses at the zero activity level. The graph crosses the horizontal axis at the break-even point. The vertical distance between the horizontal axis and the profit line, at a particular level of sales volume, is the profit or loss at that volume. (LO3) Loss area 7-18

Learning Objective 4 Learning Objective 4. Apply CVP analysis to determine the effect on profit of changes in fixed expenses, variable expenses, sales prices, and sales volume. 7-19

Target Net Profit $80,000 + $100,000 $200 = 900 surf boards We can determine the number of surfboards that Curl must sell to earn a profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Unit contribution margin = Units sold to earn the target profit When a company has a net profit they are trying to achieve, or a target net profit, the contribution margin approach can be used to determine the number of units that must be sold. This is very similar to finding the break-even point. The numerator is fixed expenses plus the target profit. The denominator is the contribution margin per unit. The result is the units that need to be sold to earn the targeted net profit. (LO4) $80,000 + $100,000 $200 = 900 surf boards 7-20

Equation Approach Sales revenue – Variable expenses – Fixed expenses = Profit ($500 × X) ($300 × X) – $80,000 = $100,000 The equation approach also can be used to find the units of sales required to earn a target net profit. Recall that in the profit equation, profit is equal to revenues minus variable and fixed expenses. Recall that profit was set to zero to determine the break-even point. When management has determined a target net profit greater than zero, that number becomes profit variable in the equation. (LO4) ($200X) = $180,000 X = 900 surf boards 7-21

Applying CVP Analysis Safety Margin The difference between budgeted sales revenue and break-even sales revenue. The amount by which sales can drop before losses occur. The safety margin of an enterprise is the difference between the budgeted sales revenue and the break-even sales revenue. This is the amount by which sales can drop before losses occur. (LO4) 7-22

Safety Margin Curl, Inc. has a break-even point of $200,000 in sales. If actual sales are $250,000, the safety margin is $50,000, or 100 surf boards. For example, Curl, Inc. has a break-even point when sales are $200,000. If actual sales are $250,000, the margin of safety is $50,000, which is 100 surfboards. (LO4) 7-23

Should the company increase the advertising budget? Changes in Fixed Costs Curl is currently selling 500 surfboards per year. The owner believes that an increase of $10,000 in the annual advertising budget, would increase sales to 540 units. Should the company increase the advertising budget? What would happen to a company’s break-even point if fixed expenses change? Suppose the owner wanted to increase advertising by $10,000 per month in hopes that sales will increase to 540 units. (LO4) 7-24

Changes in Fixed Costs 540 units × $500 per unit = $270,000 If the additional advertising is effective and sales increases to 540 boards, sales revenue would be $270,000, variable expenses would be $162,000 and the contribution margin would be $108,000. Fixed expenses would now be $90,000 and therefore, net income would be $18,000. Net income at the current level is $20,000. (LO4) 540 units × $500 per unit = $270,000 $80,000 + $10,000 advertising = $90,000 7-25

Changes in Fixed Costs Sales will increase by $20,000, but net income decreased by $2,000. So even though sales would increase from $250,000 to $270,000, net income would decrease by $2,000. (LO4) 7-26

Changes in Unit Contribution Margin Because of increases in cost of raw materials, Curl’s variable cost per unit has increased from $300 to $310 per surfboard. With no change in selling price per unit, what will be the new break-even point? When the variable cost per unit changes, this effects the contribution margin per unit. In turn, the break-even point would also be changed. Look at Curl, Inc. Suppose the variable cost per unit increases to $310 but there is no change in selling price. Using the equation approach, we find that the new break-even point is 422 units, instead of 400 units. (LO4) ($500 × X) ($310 × X) – $80,000 = $0 X = 422 units (rounded) 7-27

Changes in Unit Contribution Margin Suppose Curl, Inc. increases the price of each surfboard to $550. With no change in variable cost per unit, what will be the new break-even point? Changing the unit sales price will also alter the unit contribution margin. Suppose the price is raised from $500 to $550. This change will raise the unit contribution margin from $200 to $250. The new break-even point will be 320 units ($80,000 / $250). A $50 increase in the sales price will lower the break-even point from 400 to 320 surf boards. But is this change desirable? A lower break-even point may seem like a good thing if sales are slow. However, Curl may be more likely to at least break even with a lower sales price. Maybe sales volume would drop dramatically if the price is raised to $550. Management must try to predict the reaction of the consumers. CVP analysis provides valuable information, but it is only one of several elements that influence management’s decisions. (LO4) ($550 × X) ($300 × X) – $80,000 = $0 X = 320 units 7-28

Predicting Profit Given Expected Volume Fixed expenses Unit contribution margin Target net profit Find: {req’d sales volume} Given: Fixed expenses Unit contribution margin Expected sales volume Find: {expected profit} Given: So far, we have focused on finding the required sales volume to break even or achieve a particular target net profit. We can also use CVP analysis to determine the expected profit if fixed expenses, unit contribution margin, and expected sales volume are known. (LO4) 7-29

Predicting Profit Given Expected Volume In the coming year, Curl’s owner expects to sell 525 surfboards. The unit contribution margin is expected to be $190, and fixed costs are expected to increase to $90,000. Total contribution - Fixed cost = Profit For example, Curl expects to sell 525 surfboards in the coming year. Variable costs are expected to increase, which would reduce the unit contribution margin to $190. Fixed costs are also expected to increase to $90,000. The expected profit can be determined by first determining the total contribution. This is the unit contribution times the number of units sold. By deducting the fixed costs, we can see that the expected profit would be $9,750. (LO4) ($190 × 525) – $90,000 = X X = $99,750 – $90,000 X = $9,750 profit 7-30

Learning Objective 5 Learning Objective 5. Compute the break-even point and prepare a profit-volume graph for a multiproduct enterprise. 7-31

CVP Analysis with Multiple Products For a company with more than one product, sales mix is the relative combination in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. Let’s assume Curl sells surfboards and sail boards and see how we deal with break-even analysis. If a company sells more than one product, the relative combination in which a company’s products are sold is referred to as the sales mix. With different selling prices, contribution margins, and fixed costs, it now becomes more difficult to determine the break-even point. Let’s assume that Curl, Inc. also sells sailboards. (LO5) 7-32

CVP Analysis with Multiple Products Curl provides us with the following: information: The unit selling price, variable cost, and contribution margin are known for each of the two products that Curl sells. Surf boards make up 62.5% of Curl’s total sales and the sailboards make up the other 37.5%. (LO5) 7-33

CVP Analysis with Multiple Products Weighted-average unit contribution margin The sales mix is used to compute a weighted-average unit contribution margin. This is the average of all products’ unit contribution margins, weighted by the relative sales proportion of each product. For Curl, surfboards have a unit contribution margin of $200, which is multiplied by the 62.5% sales proportion. The weighted contribution margin for the surfboards is $125. The same formula is used to calculate the weighted contribution margin for sailboards, which is $206.25. The total weighted average contribution margin for Curl’s products is $331.25. (LO5) $200 × 62.5% $550 × 37.5% 7-34

CVP Analysis with Multiple Products Break-even point Break-even point Fixed expenses Weighted-average unit contribution margin = Break-even point $170,000 $331.25 = The break-even point can be calculated using the contribution margin approach. The total fixed costs are divided by the weighted average unit contribution margin. For Curl, the calculation is $170,000 divided by $331.25, which is 514 total units to be sold. (LO5) Break-even point = 514 combined unit sales 7-35

CVP Analysis with Multiple Products Break-even point Break-even point = 514 combined unit sales The total units are then multiplied by the relative sales proportion to determine the individual product sales. The number of surfboards to be sold at the break-even point, 514 units is multiplied by 62.5%, which equals 321 units. 514 is multiplied by 37.5% to determine that 193 sailboards must be sold to break-even. The break-even point of 514 units per year is valid only for the sales mix assumed in computing the weighted-average unit contribution margin. (LO5) 7-36

Learning Objective 6 Learning Objective 6. List and discuss the key assumptions of CVP analysis. 7-37

Assumptions Underlying CVP Analysis Selling price is constant throughout the entire relevant range. Costs are linear over the relevant range. In multi-product companies, the sales mix is constant. In manufacturing firms, inventories do not change (units produced = units sold). For any cost-volume-profit analysis to be valid, the following important assumptions must be reasonably satisfied within the relevant range. 1. The behavior of total revenue is linear (straight-line). This implies that the price of the product or service will not change as sales volume varies within the relevant range. 2. The behavior of total expenses is linear (straight-line) over the relevant range. This implies the following more specific assumptions. a. Expenses can be categorized as fixed, variable, or semivariable. Total fixed expenses remain constant as activity changes, and the unit variable expense remains unchanged as activity varies. b. The efficiency and productivity of the production process and workers remain constant. 3. In multiproduct organizations, the sales mix remains constant over the relevant range. 4. In manufacturing firms, the inventory levels at the beginning and end of the period are the same. This implies that the number of units produced during the period equals the number of units sold. (LO6) 7-38

Learning Objective 7 Learning Objective 7. Prepare and interpret a contribution income statement. 7-39

CVP Relationships and the Income Statement On a traditional income statement, cost of goods sold includes both variable and fixed manufacturing costs, as measured by the firm’s product-costing system. The gross margin is computed by subtracting cost of goods sold from sales. Selling and administrative expenses are then subtracted; each expense includes both variable and fixed costs. The traditional income statement does not disclose the breakdown of each expense into its variable and fixed components. (LO7) 7-40

CVP Relationships and the Income Statement Many operating managers find the traditional income-statement format difficult to use, because it does not separate variable and fixed expenses. Instead they prefer the contribution income statement. The contribution format highlights the distinction between variable and fixed expenses. On the contribution income statement, all variable expenses are subtracted from sales to obtain the contribution margin. All fixed costs are then subtracted from the contribution margin to obtain net income. Operating managers frequently prefer the contribution income statement, because its separation of fixed and variable expenses highlights cost-volume-profit relationships. It is readily apparent from the contribution-format statement how income will be affected when sales volume changes by a given percentage. (LO7) 7-41

Learning Objective 8 Learning Objective 8. Explain the role of cost structure and operating leverage in CVP relationships. 7-42

Cost Structure and Operating Leverage The cost structure of an organization is the relative proportion of its fixed and variable costs. Operating leverage is: the extent to which an organization uses fixed costs in its cost structure. greatest in companies that have a high proportion of fixed costs in relation to variable costs. The cost structure of an organization is the relative proportion of its fixed and variable costs. Cost structures differ widely among industries and among firms within an industry. A company using a computer-integrated manufacturing system has a large investment in plant and equipment, which results in a cost structure dominated by fixed costs. In contrast, a home builder contractor’s cost structure has a much higher proportion of variable costs. The highly automated manufacturing firm is capital-intensive, whereas the home building contractor is labor-intensive. An organization’s cost structure has a significant effect on the sensitivity of its profit to changes in volume. The extent to which an organization uses fixed costs in its cost structure is called operating leverage. The operating leverage is greatest in firms with a large proportion of fixed costs, low proportion of variable costs, and the resulting high contribution margin ratio. (LO8) 7-43

Measuring Operating Leverage factor Contribution margin Net income = The managerial accountant can measure a firm’s operating leverage, at a particular sales volume, using the operating leverage factor. The formula is contribution margin divided by net income. At sales of 500 surfboards, Curl’s contribution margin is $100,000 and net income is $20,000; therefore, its operating leverage factor is 5. (LO8) $100,000 $20,000 = 5 7-44

Measuring Operating Leverage A measure of how a percentage change in sales will affect profits. If Curl increases its sales by 10%, what will be the percentage increase in net income? The operating leverage factor is a measure, at a particular level of sales, of the percentage impact on net income of a given percentage change in sales revenue. Multiplying the percentage change in sales revenue by the operating leverage factor yields the percentage change in net income. At Curl, Inc., a 10% increase in sales would be multiplied by the operating leverage of 5. Therefore, if Curl experiences a 10% increase in sales, it can expect a 50% increase in net income. (LO8) 7-45

Measuring Operating Leverage A firm’s cost structure plays an important role in determining its cost-volume-profit relationships. A company with proportionately high fixed cost has relatively high operating leverage. The result of high operating leverage is that the firm can generate a large percentage increase in net income from a relatively small percentage increase in sales revenue. On the other hand, a firm with high operating leverage has a relatively high break-even point. This entails some risk to the firm. (LO8) A firm with proportionately high fixed costs has relatively high operating leverage. On the other hand, a firm with high operating leverage has a relatively high break-even point. 7-46

Learning Objective 9 Learning Objective 9. Understand the implications of activity-based costing for CVP analysis. 7-47

CVP Analysis, Activity-Based Costing, and Advanced Manufacturing Systems An activity-based costing system provides a much more complete picture of cost-volume-profit relationships and, thus, it provides better information to managers. Break-even point = Fixed costs Unit contribution margin Traditional cost-volume-profit analysis focuses on the number of units sold as the only cost and revenue driver. Sales revenue is assumed to be linear in units sold. Moreover, costs are categorized as fixed or variable, with respect to the number of units sold, within the relevant range. This approach is consistent with traditional product-costing systems, in which cost assignment is based on a single, volume-related cost driver. In CVP analysis, as in product costing, the traditional approach can be misleading or provide less than adequate information for various management purposes. An activity based costing system provides a much more complete picture of cost-volume-profit relationships and, thus, it provides better information to managers. (LO9) 7-48

Learning Objective 10 Learning Objective 10. Be aware of the effects of advanced manufacturing technology on CVP relationships. 7-49

A Move Toward JIT and Flexible Manufacturing Overhead costs like setup, inspection, and material handling are fixed with respect to sales volume, but they are not fixed with respect to other cost drivers. This is the fundamental distinction between a traditional CVP analysis and an activity-based costing CVP analysis. The point of this section is that activity-based costing provides a richer description of a company’s cost behavior. Just as ABC can improve an organization’s product-costing system, it also can facilitate a deeper understanding of cost behavior and CVP relationships. (LO10) 7-50

Learning Objective 11 Learning Objective 11. Understand the effect of income taxes on CVP analysis (appendix). 7-51

Effect of Income Taxes Target after-tax net income 1 - t = Income taxes affect a company’s CVP relationships. To earn a particular after-tax net income, a greater before-tax income will be required. Target after-tax net income 1 - t = Before-tax net income The requirement that companies pay income taxes affects their cost-volume-profit relationships. To earn a particular after-tax net income, a greater before-tax income will be required. To determine what the before-tax net income is, the after-tax net income is divided by 1 minus the tax rate. The formulas presented in this chapter can now be used with the before-tax net income to provide for the effect of taxes. (LO11) 7-52

End of Chapter 7 We made it! 7-53