1. Chapter 20 Cost-Volume-Profit Analysis
© 2016 Pearson Education, Ltd.

2. Learning Objectives Determine how changes in volume affect costs
Calculate operating income using contribution margin and contribution margin ratio
Use cost-volume-profit (CVP) analysis for profit planning

3. Learning Objectives Use CVP analysis to perform sensitivity analysis
Use CVP analysis to calculate margin of safety, operating leverage, and multiproduct breakeven points

4. Learning Objective 1
Determine how changes in volume affect costs

5. How Do Costs Behave When There Is a Change in Volume?
Some costs change as the volume of sales increases or decreases. Other costs are not affected by changes in volume.
Different types of costs are:
Variable costs
Fixed costs
Mixed costs
Managers need to know how a business’s costs are affected by changes in its volume of activity, such as number of products produced and sold, in order to make good decisions about the business. The three different types of costs managers need to manage are variable costs, fixed costs, and mixed costs.
Variable costs are costs that increase or decrease in total in direct proportion to increases or decreases in the volume of activity. On the other hand, a fixed cost is a cost that remains the same in total, regardless of changes over wide ranges of volume of activity. A mixed cost is a cost that has both fixed and variable components.

6. Variable Costs
Variable costs remain constant per unit but change in total as volume changes.
Variable costs are costs that increase or decrease in total in direct proportion to increases or decreases in the volume of activity. Volume is the measure or degree of an activity of a business action that affects costs. In other words, the more volume, the more cost is incurred.
Using Smart Touch Learning as an example, the direct materials that are used to make the tablets are a variable cost. For example, each tablet requires one battery, at a cost of $55 per battery. This chart shows the costs for batteries at various levels of activity.
As you can see, the total variable cost of batteries increases proportionately as the number of tablets produced increases. But the battery cost per tablet does not change.

7. Variable Costs
Exhibit 20-1 graphs total variable cost for batteries as the number of tablets produced increases from 0 to 100.
If Smart Touch Learning does not produce any tablets, it incurs no battery cost. Therefore, the total variable cost line begins at the bottom-left corner. This point is called the origin, and it represents zero volume and zero cost. The slope of the variable cost line is the change in battery cost (on the vertical axis) divided by the change in the number of tablets produced (on the horizontal axis). The slope of the graph equals the variable cost per unit. In this case, the slope of the variable cost line is $55 per tablet.
The graph in Exhibit 20-1 shows how the total variable cost of batteries varies directly with the number of tablets produced. But again, note that the per tablet cost remains constant, at $55.

8. Fixed Costs
In contrast to variable costs, fixed costs are costs that do not change in total over wide ranges of volume of activity. Some common fixed costs include rent, salaries, property taxes, and depreciation.
Exhibit 20-2 graphs Smart Touch Learning’s depreciation on the manufacturing plant and equipment. The company has these fixed costs regardless of the number of tablets produced.
Smart Touch Learning incurs $12,000 of fixed costs each month, and the number of tablets produced monthly is between 0 and 100. As we can see in Exhibit 20-2, fixed costs are graphed as a flat line that intersects the cost axis at $12,000 because Smart Touch Learning will incur the same $12,000 of fixed costs regardless of the number of tablets produced during the month.

9. Fixed Costs
This chart shows the total fixed costs at various levels of activity. Note that the total fixed cost does not change, but the fixed cost per tablet depends on the number of tablets produced. If Smart Touch Learning produces 25 tablets, the fixed cost per tablet is $480 ($12,000 total fixed cost divided by 25 tablets). If the number of tablets produced doubles to 50 tablets, the fixed cost per tablet is cut in half, to $240 ($12,000 total fixed cost divided by 50 tablets).
Therefore, the fixed cost per tablet is inversely proportional to the number of tablets. In other words, as the number of tablets increases, the fixed cost per tablet decreases.

10. Fixed Costs
Exhibit 20-3 provides a summary of the characteristics of variable and fixed costs.

11. Mixed Costs Mixed costs have both fixed and variable components.
Not all costs can be classified as either fixed or variable. Costs that have both variable and fixed components are called mixed costs. For example, Smart Touch Learning’s cell phone provider charges $100 per month to provide the service plus $0.10 for each minute of use. If the cell phone is used for 100 minutes, the company will bill Smart Touch Learning $110 ($100 of fixed cost per month plus the variable cost of 100 minutes at $0.10 per minute).
The table shows the cost for the cell phone at different levels of activity.

12. Mixed Costs
Exhibit 20-4 graphs shows how Smart Touch Learning can separate its cell phone bill into fixed and variable components. The $100 monthly charge is a fixed cost because it is the same no matter how many minutes the company uses the cell phone. The $0.10-per-minute charge is a variable cost that increases in direct proportion to the number of minutes of use. If Smart Touch Learning uses the phone for 100 minutes, its total variable cost is $10 (100 minutes at $0.10 per minute). If it doubles the use to 200 minutes, total variable cost also doubles to $20 (200 minutes at $0.10 per minute), and the total bill rises to $120 ($100 plus $20).

13. High-Low Method
A method to separate mixed costs into variable and fixed components is the high-low method.
When companies have mixed costs, it is helpful to separate the costs into their variable and fixed components so managers can use the information to make planning and control decisions. An easy method to separate mixed costs into variable and fixed components is the high-low method. This method requires you to identify the highest and lowest levels of activity over a period of time.
To illustrate the high-low method, we will look at the maintenance costs for Smart Touch Learning’s manufacturing equipment. Looking at the data for the year, we identify the quarter with the highest activity (the third quarter, with 480 tablets) and the quarter with the lowest activity (the fourth quarter, with 240 tablets). 
The high-low method is used to separate mixed costs into their variable and fixed components, using the highest and lowest activity levels.

14. High-Low Method
Use three steps to separate the variable and fixed costs.
Step 1: Identify the highest and lowest levels of activity and calculate the variable cost per unit.
We can use the high-low method, which requires three steps, to estimate Smart Touch Learning’s fixed and variable costs of manufacturing equipment maintenance. Step 1: Identify the highest and lowest levels of activity and calculate the variable cost per unit. The highest volume is 480 tablets produced in the third quarter of the year, and the lowest volume is 240 tablets produced in the fourth quarter. Using the high and low points, find the change in costs and divide by the change in volume of activity.

15. High-Low Method
Now that we have calculated the variable costs per unit, we can calculate the portion of the mixed costs that relates to the fixed costs.
Step 2: Calculate the total fixed costs.
In step 2, we calculate the total fixed costs. This example uses the highest volume and its mixed cost to calculate the total fixed costs, but you can also use the lowest volume and its mixed cost to calculate the same $1,000 total fixed cost.

16. High-Low Method
Using the variable costs per unit and the fixed costs per unit, we can determine the total mixed costs at various levels of productivity.
Step 3: Create and use an equation to show the behavior of a mixed cost.
This method provides a rough estimate of fixed and variable costs that can be used for planning purposes. The high and low activity volumes become the relevant range, which is discussed in the next section. Managers find the high-low method to be quick and easy, but there are other more complex methods that provide better estimates.

17. Relevant Range and Relativity
The relevant range is the range of volume where total fixed costs and variable costs per unit remain constant.
The relevant range is the range of volume where total fixed costs remain constant and the variable cost per unit remains constant. To estimate costs, managers need to know the relevant range because total fixed costs can differ from one relevant range to another, and the variable cost per unit can differ in various relevant ranges.
Exhibit 20-5 shows fixed costs for Smart Touch Learning over three different relevant ranges. If the company expects to produce 2,400 tablets next year, the relevant range is between 2,001 and 4,000 tablets, and managers will plan for fixed costs of $144,000. To produce more than 4,000 tablets, Smart Touch Learning will have to expand the company. This will increase total fixed costs for added rent, supervisory salaries, and equipment costs. Exhibit 20-5 shows that total fixed cost increases to $216,000 as the relevant range shifts to this higher band of volume. Conversely, if the company expects to produce fewer than 2,001 tablets, the company will budget only $72,000 of fixed cost. Managers will have to lay off employees or take other actions to cut fixed costs.
Variable cost per unit can also change outside the relevant range. For example, Smart Touch Learning may get a quantity discount for batteries if it purchases more than 4,000 batteries.
We also need to remember that costs are classified as fixed or variable relative to some activity. However, if the frame of reference shifts, then the classification can shift, too. For example, Smart Touch Learning may lease cars for sales representatives to use when making sales calls. The amount of the lease is the same each month, $500. Therefore, relative to the number of tablets produced, the cost is fixed. Increasing or decreasing the number of tablets produced does not change the total amount of the lease. It remains constant at $500 per month. However, relative to the number of sales representatives, the cost is variable as it is directly proportional to the number of sales representatives. If there is one sales representative, the total cost is $500 per month. If there are two sales representatives, then two cars are required, and the cost doubles to $1,000 per month. While the cost per unit remains constant, $500 per sales representative, the total cost changes with the change in volume (the number of sales representatives).
For all examples and problems in this textbook, when classifying costs as fixed or variable, classify as relative to the number of units produced and sold unless told otherwise.

18. Learning Objective 2
Calculate operating income using contribution margin and contribution margin ratio

19. What Is Contribution Margin, And How Is It Used to Compute Operating Income?
A traditional income statement classifies costs by function:
Product costs
Period costs
A contribution margin income statement classifies costs by behavior:
Variable costs
Fixed costs
The traditional income statement format does not always provide enough information for managers, so another format is used. A contribution margin income statement classifies costs by behavior; that is, costs are classified as either variable costs or fixed costs. The contribution margin highlights contribution margin income, which is net sales less variable costs.

20. Contribution Margin
The difference between net sales revenue and variable costs is the contribution margin.
It is called contribution margin because it is the amount that contributes to covering fixed costs.
The contribution margin is the amount that contributes to covering the fixed costs and then to providing operating income. Contribution margin = Net sales revenue – Variable costs. Contribution margin is often expressed in total.

21. Unit Contribution Margin
The contribution margin can be expressed as a unit amount.
Note: The terms unit contribution margin and contribution margin per unit are used interchangeably.
The contribution margin is often expressed as a unit amount. Unit contribution margin = Net sales revenue per unit – Variable costs per unit. Note that the terms unit contribution margin and contribution margin per unit are used interchangeably.

22. Contribution Margin Ratio
A third way to express contribution margin is as a ratio.
Contribution margin ratio is the ratio of contribution margin to net sales revenue.
A third way to express contribution margin is as a ratio. The contribution margin ratio is the ratio of contribution margin to net sales revenue. Contribution margin ratio = Contribution margin / Net sales revenue. The ratio can be calculated using either the total amount of sales price and variable costs or the unit amounts.

23. Contribution Margin Income Statement
A traditional income statement classifies cost by function; that is, costs are classified as either product costs or period costs. Remember that product costs are those costs that are incurred in the purchase or production of the product sold.
For a manufacturing company such as Smart Touch Learning, the product costs are direct materials, direct labor, and manufacturing overhead. These costs accumulate in the inventory accounts until the product is sold. At that point, the costs are transferred to the expense account Cost of Goods Sold. The period costs are the selling and administrative costs.
The traditional income statement is required by GAAP, the Generally Accepted Accounting Principles, and is the format you have been using in your accounting studies thus far.
The contribution margin income statement is the income statement that groups costs by behavior—variable or fixed—and highlights the contribution margin.

24. Learning Objective 3
Use cost-volume-profit (CVP) analysis for profit planning

25. How Is Cost-Volume-Profit (CVP) Analysis Used?
Managers use information about cost behavior to make business decisions.
Cost-volume-profit (CVP) analysis is a planning tool that looks at the relationships among costs and volume and how they affect profits (or losses).
Let’s see how managers use the information of cost behavior to make business decisions. Cost-volume-profit (CVP) analysis is a planning tool that looks at the relationships among costs and volume and their effects on profits and losses. Smart Touch Learning uses CVP analysis to estimate how changes in sales prices, variable costs, fixed costs, and volume will affect profits.

26. Assumptions The price per unit does not change as volume changes.
Managers can classify each cost as variable, fixed, or mixed.
The only factor that affects total costs is change in volume, which increases or decreases variable and mixed costs.
Fixed costs do not change.
There are no changes in inventory levels.
Five assumptions are made with cost-volume-profit analysis. First, the price per unit does not change as volume changes. For example, Smart Touch Learning assumes that all tablets will sell for $500 each.
Second, managers can classify each cost as variable, fixed, or mixed.
Another assumption is that the only factor that affects total costs is change in volume, which increases variable and mixed costs. For example, Smart Touch Learning assumes the variable cost per tablet is $275.
Similarly, it is assumed that fixed costs do not change. In our example, Smart Touch Learning assumes fixed costs are $12,000 per month.
Finally, there are no changes in inventory levels. Smart Touch Learning assumes the number of tablets produced equals the number of tablets sold.
Most business conditions do not perfectly meet these general assumptions, so managers regard cost-volume-profit analysis as approximate, not exact.

27. Target Profit—Three Approaches
CVP analysis can be used to estimate the amount of sales needed to achieve a target profit.
There are three methods of estimated sales required to make a profit:
Equation approach
Contribution margin approach
Contribution margin ratio approach
CVP analysis can be used to estimate the amount of sales needed to achieve a target profit. Target profit is the operating income that results when sales revenue minus variable and fixed costs equals management’s profit goal. Required sales can be expressed either as a number of units or as a total dollar figure. We will look at three methods of estimating sales required to make a target profit:
• Equation approach
• Contribution margin approach
• Contribution margin ratio approach

28. The Equation Approach
An equation can be used to estimate the number of units a company needs to sell to achieve target profit or total sales revenue.
We can further break down total costs into its components: variable costs and fixed costs.

29. The Equation Approach
If Smart Touch Learning desires a target profit of $6,000, using the equation approach, it finds it needs to sell 80 units.
Sales revenue equals the unit sales price ($500 per tablet in this case) multiplied by the number of units (tablets) sold. Variable costs equal variable costs per unit ($275 in this case) times the number of units (tablets) sold. Smart Touch Learning’s fixed costs total $12,000 per month. If the company desires to earn $6,000 in profits each month, how many tablets must it sell? Using the equation approach, it determines that 80 units must be sold to earn a target profit of $6,000.

30. The Contribution Margin Approach
The contribution margin approach is a shortcut method of computing the required sales in units.
The equation approach is rewritten to derive the following equation:
The contribution margin approach is a shortcut method of computing the required sales in units. Previously, we proved our answer using the equation approach. We can rewrite the equation approach to be (Fixed costs + Target profit) / Contribution margin per unit = Required sales in units. Using the contribution margin approach, we find that the number of units to sell to achieve a target profit of $6,000 is 80 units because ($12,000 + $6,000) / $225 = 80 units.

31. Contribution Margin Ratio Approach
The contribution margin ratio approach computes required sales in terms of sales dollars rather than in units.
Companies can use the contribution margin ratio approach to compute required sales in terms of sales dollars rather than in units. The formula is the same as when using the contribution margin approach, except that the denominator is the contribution margin ratio rather than the contribution margin per unit.

32. Breakeven Point—A Variation of Target Profit
The breakeven point calculation is a variation of the target profit calculation.
The breakeven point is the point at which total revenues equal total costs.
The same three approaches used for target profit can be used to determine the breakeven point.
A variation of the target profit calculation is the breakeven point calculation. The breakeven point is the sales level at which the company does not earn a profit or a loss but has an operating income of zero. It is the point at which total revenues equal total costs. The same three approaches can be used. The only difference is that the target profit is $0.
Exhibit 20-7 shows the calculation of the breakeven point for Smart Touch Learning, using the three approaches.

33. Breakeven Point—A Variation of Target Profit
Exhibit 20-7 shows the calculation of the breakeven point for Smart Touch Learning, using the three approaches. Using the equation approach and substituting Smart Touch Learning’s information into the equation, we see that the company must sell 54 units per month in order to break even. Note that the actual result is , but we must round up to the next full unit as it is not possible to sell partial tablets

34. CVP Graph—A Graphic Portrayal
Exhibit 20-8 shows a cost-volume-profit graph. This graph shows how changes in the levels of sales will affect profits. As in the variable, fixed, and mixed cost graphs of Exhibits 20-1, 20-2, and 20-4, the volume of units is on the horizontal axis, and dollars are on the vertical axis.
To graph the cost-volume-profit relations for Smart Touch Learning, we draw the sales revenue line, the fixed cost line, and the total cost line.
Then we identify the breakeven point. The breakeven point is where the sales revenue line intersects the total cost line. This is where revenue exactly equals total costs. In this case, it is at 54 tablets, or $26,667 in sales (based on rounded figures from Exhibit 20-7).
Finally, we mark the operating loss area and operating income area on the graph. To the left of the breakeven point, total costs exceed sales revenue, leading to an operating loss, indicated by the orange zone. To the right of the breakeven point, the business earns a profit because sales revenue exceeds total cost, as shown by the green zone.
Graphs like Exhibit 20-8 are helpful to managers because the managers can use the graphs to prepare quick estimates of the profit or loss earned at different levels of sales. The three target profit formulas are also useful, but they indicate income or loss only for a single sales amount.

35. Learning Objective 4
Use CVP analysis to perform sensitivity analysis

36. How Is CVP Analysis Used for Sensitivity Analysis?
Managers can use CVP relationships to conduct sensitivity analysis.
Sensitivity analysis is a “what if” technique that estimates profit or loss results if sales price, cost, volume, or underlying assumptions change.
Managers often want to predict how changes in sales price, costs, or volume affect their profits. Managers can use CVP relationships to conduct sensitivity analysis. Sensitivity analysis is a “what if” technique that estimates profit or loss results if sales price, costs, volume, or underlying assumptions change. Sensitivity analysis allows managers to see how various business strategies will affect how much profit the company will make and, thus, empowers managers with better information for decision making.

37. Changes in the Sales Price
If the sales price changes from $500 to $475, the number of units needed to breakeven increases from 54 to 60.
If competition for a particular product is fierce, a company may need to cut the sales price of its product to remain competitive. Assume the competition in the touch screen tablet computer business is fierce, and Smart Touch Learning believes it must cut the price to $475 per tablet to maintain market share. The breakeven point in units increases from 54 units at a sales price of $500 to 60 units at a sales price of $475.

38. Changes in Variable Costs
If one of Smart Touch Learning’s suppliers raises prices and variable costs increase from $275 to $285, the number of units needed to break even increases from 54 to 56.
Assume that one of Smart Touch Learning’s suppliers raises prices, which increases the variable costs for each tablet to $285 from the original cost of $275. Assuming the original sales price of $500 is used, the number of units required to break even due to the change in variable costs increases from 54 units to 56 units, rounded.
When variable costs change, the contribution margin per unit changes, as does the contribution margin ratio.

39. Changes in Fixed Costs
If Smart Touch Learning’s fixed costs increase from $12,000 to $15,000, the number of units needed to break even increases from 54 to 67.
Assume that Smart Touch Learning is considering spending an additional $3,000 on Web site banner ads. This would increase fixed costs from $12,000 to $15,000. Assuming the original sales price of $500 per unit and unit variable costs of $275, the new breakeven point is 67 units, rounded.

40. How Is CVP Analysis Used for Sensitivity Analysis?
Exhibit 20-9 shows how all these changes affect the contribution margin per unit and the breakeven point.

41. Learning Objective 5
Use CVP analysis to calculate margin of safety, operating leverage, and multiproduct breakeven points

42. What Are Some Other Ways CVP Analysis Can Be Used?
CVP analysis can be used for estimating target profits and breakeven points, as well as sensitivity analysis.
Three additional applications of CVP are:
Margin of safety
Operating leverage
Sales mix
We have learned how CVP analysis can be used for estimating target profits and breakeven points, as well as sensitivity analysis. Three additional applications of CVP analysis are margin of safety, operating leverage, and sales mix.

43. Margin of Safety
Margin of safety is the excess of expected sales over breakeven sales.
Used to evaluate the risk of current operations and their plans for the future.
We have learned how cost-volume-profit analysis can be used for estimating target profits and breakeven points, as well as sensitivity analysis. Let’s look at three more applications of this analysis.
The margin of safety is the excess of expected sales over breakeven sales. It is the amount sales can decrease before the company incurs an operating loss. It is the cushion between profit and loss. Managers use the margin of safety to evaluate the risk of both their current operations and their plans for the future.
The margin of safety focuses on the sales part of the equation—that is, how many sales dollars the company is generating above breakeven sales dollars. We can calculate the margin of safety in units, in dollars, or as a ratio.

44. Operating Leverage
The cost structure of a company is the proportion of fixed costs to variable costs.
Operating leverage predicts the effects that fixed costs will have on changes in operating income when sales volume changes.
The degree of operating leverage can be measured by dividing the contribution margin by the operating income.
Companies can predict the expected change in operating income due to a change in sales volume based on their cost structure. Operating leverage predicts the effects that fixed costs will have on changes in operating income when sales volume changes. The degree of operating leverage is the ratio that measures the effects that fixed costs have on changes in operating income when sales volume changes. It is found using the following formula: Operating leverage = Contribution margin / Operating income.

45. Operating Leverage
Using two companies providing horse-drawn carriage tours in Charleston, South Carolina, we will calculate the degree of operating leverage to determine the change in net income due to changes in sales. The contribution margin for Company A is $10,000, and the operating income is $4,000, resulting in a degree of operating leverage of The contribution margin for Company B is $5,000, and the operating income is $4,000, resulting in a degree of operating leverage of 1.25.
For Company A, the percentage change in operating income will be 2.5 times the percentage change in sales.

46. Sales Mix Most companies sell more than one product.
Sales price and variable costs differ for each product.
Sales mix, or product mix, is the combination of products that make up total sales.
Most companies sell more than one product. Sales price and variable costs differ for each product, so each product makes a different contribution to profits. The same CVP formulas we used earlier can apply to a company with multiple products. To calculate the breakeven point for the company, we must compute the weighted-average contribution margin of all the company’s products. The sales mix provides the weights that make up total product sales.

47. Sales Mix
To compute breakeven sales in units for both products, Cool Cat completes the following three steps. Step 1 is to calculate the weighted-average contribution margin per unit. To do this, compute the unit contribution margin for each product and then multiply by the sales mix in units. The weighted contribution margins for the cat beds and scratching posts are added together, for a total of $200. Next, this $200 is divided by 5, for a weighted-average contribution margin of $40.