1. Financial and Managerial Accounting
In presentations for each chapter in this text, we will provide you with sound to go along with the material on your screen. There will be sound on every slide you view. Please make sure your computer speakers are set-up properly when viewing the material. Good luck and we hope you enjoy this new format.
Wild, Shaw, and Chiappetta
Fifth Edition
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. 1

2. Cost Behavior and Cost-Volume-Profit Analysis
Chapter 18
Cost Behavior and Cost-Volume-Profit Analysis
This chapter shows how information on both costs and sales behavior is useful to managers in performing cost-volume-profit analysis. This analysis is an important part of successful management and sound business decisions.

3. Conceptual Learning Objectives
C1: Describe different types of cost behavior in relation to production and sales volume.
C2: Describe several applications of cost-volume-profit analysis.
Conceptual Learning Objectives:
C1: Describe different types of cost behavior in relation to production and sales volume.
C2: Describe several applications of cost-volume-profit analysis.
18-3

4. Analytical Learning Objectives
A1: Compute the contribution margin and describe what it reveals about a company’s cost structure.
A2: Analyze changes in sales using the degree of operating leverage.
Analytical Learning Objectives:
A1: Compute the contribution margin and describe what it reveals about a company’s cost structure.
A2: Analyze changes in sales using the degree of operating leverage.
18-4

5. Procedural Learning Objectives
P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.
P2: Compute the break-even point for a single product company.
P3: Graph costs and sales for a single product company.
P4: Compute the break-even point for a multiproduct company.
Procedural Learning Objectives:
P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.
P2: Compute the break-even point for a single product company.
P3: Graph costs and sales for a single product company.
P4: Compute the break-even point for a multiproduct company.
18-5

6. Questions Addressed by Cost-Volume-Profit Analysis
CVP analysis is used to answer questions such as:
What sales volume is needed to earn a target income?
What is the change in income if selling prices decline and sales volume increases?
How much does income increase if we install a new machine to reduce labor costs?
Will income change if we change the sales mix of our products or services?
Cost-volume-profit analysis will allow us to answer many questions and make important decisions involving the relationships between the volume of activity, costs, and revenues. Before we can answer these questions using cost-volume-profit analysis, we must first study cost behavior.
18-6

7. Monthly Basic Telephone Bill
Total Fixed Cost C1
Total fixed costs remain unchanged when activity changes. $
Monthly Basic Telephone Bill
We begin our study of cost behavior with fixed costs. Your basic land-line telephone has a monthly connect charge that remains constant regardless of the number of local calls that you might make. The monthly charge that is independent of call activity is a fixed cost.
Your monthly basic telephone bill probably does not change when you make more local calls.
Number of Local Calls
18-7

8. Monthly Basic Telephone Bill per Local Call
Fixed Cost per Unit C1
Fixed costs per unit decline as activity increases. $
Monthly Basic Telephone Bill per Local Call
Fixed costs per unit decline as activity increases. Dividing your monthly connect fee by more local calls reduces the cost per call by spreading the fixed amount over a higher number of calls. For example, if your monthly connect charge is $20 and you make 40 local calls in a month, your cost per local call is 50 cents. If you make 100 local calls in a month, your cost per local call is 20 cents.
Your average cost per local call decreases as more local calls are made.
Number of Local Calls
18-8

9. Total Long Distance Telephone Bill
Total Variable Cost C1
Total variable costs change when activity changes. $
Total Long Distance Telephone Bill
Total variable costs increase as activity increases. For most people, the total land-line long distance telephone bill is based on the number of minutes talked. So there’s a direct relationship between the number of minutes talked and your total bill. You can see a graph of that relationship in the lower left-hand part of this slide.
Your total long distance telephone bill is based on how many minutes you talk. #
Minutes Talked
18-9

10. Per Minute Telephone Charge
Variable Cost per Unit C1
Variable costs per unit do not change as activity increases. $
Per Minute Telephone Charge
The cost per land-line long distance minute talked is normally constant. For example, for your service, it may be seven cents per minute. Talking more or less minutes will not change the per minute charge. So, on a per unit basis, variable costs remain unchanged. You can see the graph of that in the right-hand side of this slide.
The cost per long distance minute talked is constant. For example, 7 cents per minute.
Minutes Talked
18-10

11. Cost Behavior Summary C1
We know that some of the language we use to differentiate fixed and variable costs in total and per unit can be very confusing when you first see it. So we’ve prepared this chart to help you identify how those costs behave.
18-11

12. Mixed Costs C1
Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage.
Example: monthly electric utility charge
Fixed service fee
Variable charge per kilowatt hour used
Many costs are mixed in nature. That is, they have both a fixed and variable component. Like a fixed cost, a mixed cost is greater than zero when volume is zero; but unlike a fixed cost, it increases steadily in proportion to increases in volume. Think about your utility bill. You have a fixed monthly charge for the hook-up, and the variable portion of your bill depends upon the number of kilowatt hours you consume. The more the kilowatt hours you use, the higher your total utility bill will be.
18-12

13. Total cost remains constant within a narrow range of activity.
Step-Wise Costs C1
Total cost remains constant within a narrow range of activity.
Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity.
Cost
Activity
18-13

14. Identifying and Measuring Cost BehaviorP1
The objective is to classify all costs as either fixed or variable.
When presented with a mixed cost, the fixed and variable components must be separated.
Identifying and measuring cost behavior requires careful analysis and judgment. An important part of this process is to identify costs that can be classified as either fixed or variable, which often requires analysis of past cost behavior. When a cost has both a fixed and a variable component, we must separate the variable portion of the cost from the fixed portion of the cost. There are a number of ways to do this. We will use a scatter diagram and the high-low method. A more sophisticated method, the least squares regression model, is also available.
18-14

15. Total Cost in 1,000’s of Dollars
Scatter Diagram P1
Unit variable cost = Slope =
Change in cost Change in units *
Total Cost in 1,000’s of Dollars 10 20
Activity, 1,000’s of Units Produced
Vertical distance is the change in cost.
A scatter diagram is a plot of cost data points on a graph. It is almost always helpful to plot cost data to be able to observe a visual picture of the relationship between cost and activity. We begin by plotting the data points on our graph. The vertical axis is cost and the horizontal axis is activity.
Next, we draw a straight line through the data points with about an equal number of observations above and below the line. Fitting this line demands judgment. We continue the line past the observed points until it intersects with the vertical axis. The intercept in this case is our fixed cost, which is estimated to be $10,000.
Next, we determine the slope of the line. The slope of the line is the change in cost divided by the change in units. The slope, the amount of change in cost for a one unit change in activity, is the variable cost per unit of activity.
Horizontal distance is the change in activity.
18-15

16. The High-Low Method P1
The following relationships between units produced and costs are observed:
Using these two levels of activity, we can compute:
The variable cost per unit.
The total fixed cost.
Now let’s look at the high-low method. In our example, we’re going to look at a company’s relationship between cost and sales activity. During the year, the company reports sales and costs on a monthly basis. The month with the highest level of sales shows sales of 67,500 units and a corresponding cost of $29,000, and the month with the lowest level of sales show sales of 17,500 units with a corresponding cost of $20,500. We will use this information to compute the variable cost per unit and the total fixed cost.
18-16

17. The High-Low Method (Exhibit 18.6)P1
Unit variable cost = = = $0.17 /unit
Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per unit × 67,500 units) Fixed cost = $29,000 – $11,475 = $17,525
Δin cost Δin units
$8, ,000
To determine the variable cost per unit of activity, we divide the change in cost by the change in units. In our case, the change in cost is $8,500 and the change in units is 50,000. The result is a variable cost rate of $0.17 per unit.
Next, we calculate the fixed cost by subtracting the total variable cost from the total cost. Since total cost and total variable cost are different amounts at different sales levels, we must choose either the high level or the low level for our computations.
Let’s choose the high level of activity, 67,500 units. Our first step is to calculate the total variable cost. At 67,500 units, the total variable cost is .17 per dollar per unit times 67,500 units, resulting in a total variable cost of $11,475. Next, we subtract $11,475 from the total cost at the high sales activity, to get the fixed cost. Total fixed cost is $17,525. You will obtain the same result if you select the low level of activity to compute fixed cost. Why don’t you compute fixed cost using the low level of activity before advancing to the next screen. You should wind up with the exact same result.
18-17

18. Least-Squares RegressionP1
Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators.
The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost.
If we have a large number of observations, we’ll probably want to use computer software that can do regression analysis to determine cost volume relationships. Least-squares regression is a statistical method for identifying cost behavior. Excel is a wonderful tool to carry out this computation. You can review the chapter’s appendix if this is of interest to you.
18-18

19. Using Break-Even AnalysisP2
The break-even point (expressed in units of product or dollars of sales) is the sales level at which a company neither earns a profit nor incurs a loss.
Now that we have improved our knowledge of cost behavior, we are ready to apply the concepts to break-even analysis. The break-even point is the level of sales where a company’s income is exactly equal to zero. At breakeven, total costs equal total revenues.
18-19

20. Computing The Break-Even Point
We’re going to concentrate exclusively on the contribution format income statement for our break-even analysis. Contribution margin is the amount remaining after we deduct all our variable expenses from sales revenue. Contribution margin can be expressed as a total amount, $60,000 in this example, or as an amount per unit, $30 in this example. Each unit sold contributes $30 toward covering fixed costs and providing for profits.
Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.
18-20

21. Understanding the Contribution Margin
Part I
Contribution margin goes to cover our fixed costs. If all our fixed costs are covered, the company will operate in the profit area. If we fail to cover our fixed expenses, we will operate in the loss area. How much contribution must this company have to cover its fixed costs?
Part II
Fixed costs are $24,000, so this company must generate $24,000 in contribution margin to cover its fixed costs. When contribution margin is exactly $24,000, the company’s sales are at breakeven as its income will be zero.
How much contribution margin must this company have to cover its fixed costs (break even)?
Answer: $24,000
18-21

22. Computing The Break-Even Point
Part I
This company is earning $36,000 income by selling 2,000 units. The breakeven point will obviously occur at a sales volume less than 2,000 units. If each unit contributes $30 to covering fixed costs, can you compute the number of units that must be sold to cover the $24,000 in fixed costs and allow the company to breakeven?
Part II
We compute the break-even sales volume in units by dividing the fixed costs of $24,000 by the $30 unit contribution margin. This company must sell 800 units to break even.
How many units must this company sell to cover its fixed costs (break even)?
Answer: $24,000 ÷ $30 per unit = 800 units
18-22

23. Computing The Break-Even Point (Exhibit 18.11)
We have just seen one of the basic CVP relationships – the break-even computation.
Break-even point in units =
Fixed costs
Contribution margin per unit
The results of the previous question can be expressed in equation form as seen on your screen. The break-even point in units is equal to fixed costs divided by the contribution margin per unit.
Unit sales price less unit variable cost ($30 in previous example)
18-23

24. The break-even formula may also be expressed in sales dollars.
Computing The
Break-Even Point (Exhibit 18.12) P2
The break-even formula may also be expressed in sales dollars.
Break-even point in dollars =
Fixed costs
Contribution margin ratio
The break-even point in sales dollars is equal to fixed costs divided by the contribution margin ratio. The contribution margin ratio is equal to the unit contribution divided by the unit sales price. In the earlier example, the contribution margin ratio is 30 percent, resulting from dividing the $30 unit contribution margin by the $100 unit sales price. You might want to refer back to the example to verify these numbers. The contribution margin ratio tells us that 30 cents of each sales dollar contributes to covering fixed costs and providing for income.
Unit contribution margin Unit sales price
18-24

25. Computing the Margin of Safety
Margin of safety is the amount by which sales can drop before the company incurs a loss.
Margin of safety may be expressed as a percentage of expected sales.
All companies wish to sell more than the break-even number of units. The excess of expected sales over the break-even sales level is called a company’s margin of safety, the amount that sales can drop before the company incurs a loss. It can be expressed in units, dollars, or even as a percent of the predicted level of sales. The margin of safety percentage is equal to the margin of safety in dollars divided by the expected sales in dollars.
Margin of safety Expected sales - Break-even sales percentage Expected sales =
18-25

26. Preparing a Cost-Volume- Profit Chart
Plot total fixed costs on the vertical axis.
Total fixed costs
Total costs
Draw the total cost line with a slope equal to the unit variable cost.
Costs and Revenue in Dollars
The relationships between cost, volume and profit can also be shown in a graph. In this graph, we have plotted costs and revenues on the vertical axis and number of units produced on the horizontal axis. The total costs line has a slope equal to the variable cost per unit and intercepts the vertical cost axis at the fixed cost.
Number of Units Produced
18-26

27. Preparing a Cost-Volume-Profit Chart
Starting at the origin, draw the sales line with a slope equal to the unit sales price.
Sales
Total fixed costs
Costs and Revenue in Dollars
Total costs
When we add the sales line to our graph, we see the break-even point where the sales line crosses the total costs line. The sales line begins at the origin and has a slope equal to the unit sales price. The sales line is steeper, that is, it increases at a faster rate than the total cost line. This is because the unit sales price is greater than the unit variable cost.
Break-even point
Number of Units Produced
18-27

28. Assumptions of CVP Analysis
A limited range of activity called the relevant range, where CVP relationships are linear.
Unit selling price remains constant.
Unit variable costs remain constant.
Total fixed costs remain constant.
Production = Sales (no inventory changes).
There are some basic assumptions related to cost-volume-profit analysis that we are studying in this chapter. Some of these assumptions may be very restrictive. First, within a relevant range of activity, costs and revenues are assumed to be linear in nature, meaning that the selling price is assumed to be constant, the unit variable cost is assumed to be constant, and total fixed costs are assumed to be constant. If the expected costs and sales behavior differ from these assumptions, the results of CVP analysis can be limited. Also, for manufacturing companies, we sometimes assume that the production level is the same as the sales level. That is, inventory levels do not change.
18-28

29. Computing Income from Expected Sales
Did someone say income?
Sales
– Variable costs
Contribution margin
– Fixed costs
Income (pretax)
We have seen what it takes for a company to breakeven, but we are not in business just to breakeven. Hopefully our business will earn an income. The break-even relationships that we have studied can be slightly altered to include income.
18-29

30. Computing Sales (Dollars) for a Target Net Income
Target net income is income after income tax. But we can use target income before tax in our calculations.
Target income before tax (Target pretax income) = Net income (after tax) + Income taxes paid on the pretax income
A company needs to be able to compute the sales needed to earn a target net income. To solve for sales necessary to earn a target income, they will use a target pretax income in their formulas. Pretax income has two components, net income (after tax) and the income taxes paid on the pretax income.
18-30

31. Computing Sales (Dollars) for a Target Net Income
To convert target net income to pretax income, use the following formula:
Target after-tax net income =
Target pretax Income
1 - Tax rate
If our target income is stated as after-tax net income, we can covert to pretax income by dividing the target after-tax net income by one minus the tax rate.
18-31

32. Computing Sales for a Target Income
Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income.
Dollar sales at target after-tax income
Fixed costs + Target pretax income =
We can adjust the break-even formulas that we used earlier to incorporate income. Recall that we calculated breakeven by dividing fixed costs by contribution margin per unit. When we incorporate a target pretax income into our calculation, the total contribution must cover the fixed costs as well as provide for the target income. To adapt the break-even formulas for income, we add the desired amount of target pretax income to the numerator.
Contribution margin ratio
Unit sales at target after-tax income
Fixed costs + Target pretax income =
Contribution margin per unit
18-32

33. Sensitivity Analysis C2
The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost.
This sensitivity analysis can be used to generate different sets of revenue and cost estimates that are optimistic, pessimistic, and most likely.
Our basic assumptions related to cost-volume-profit analysis such as the selling price is assumed to be constant, the unit variable cost is assumed to be constant, and total fixed costs are assumed to be constant, can be restrictive. Instead management can utilize CVP relationships to examine strategies that impact several estimates in the CVP analysis. This sensitivity analysis can be used to generate different sets of revenue and cost estimates that are optimistic, pessimistic, and most likely.
18-33

34. Computing Multiproduct Break-Even Point
The CVP formulas may be modified for use when a company sells more than one product.
The unit contribution margin is replaced with the contribution margin for a composite unit.
A composite unit is composed of specific numbers of each product in proportion to the product sales mix.
Sales mix is the ratio of the sales volumes for the various products.
To this point, we’ve assumed that a company sells a single product. We can extend the cost-volume-profit relationships to cover multiproduct companies. Instead of unit contribution margin for one unit, we will have a composite unit contribution for all units. The composite unit contribution margin is dependent on the sales mix of the products sold. .
18-34

35. Computing Multiproduct Break-Even Point
The resulting break-even formula for composite unit sales is:
Fixed costs Contribution margin per composite unit
Break-even point in composite units =
Note that the break-even formula looks the same for a multiproduct company. The only difference is the denominator. The unit contribution margin for one unit is replaced by a composite unit contribution for all units. A composite unit is composed of specific numbers of each product in proportion to the product sales mix.
A composite unit is composed of specific numbers of each product in proportion to the product sales mix.
18-35

36. Total contribution margin (in dollars)
Operating Leverage A2
The extent, or relative size, of fixed costs in the total cost structure of an organization.
A measure of how a percentage change in sales will affect profits.
Operating leverage is an important concept for managers to understand. It’s a measure of how sensitive operating income is to changes in sales. Companies having a higher proportion of fixed costs in their total cost structure are said to have higher operating leverage. An example of this is a company that chooses to automate its processes instead of using direct labor, increasing its fixed costs and lowering its variable costs. The degree of operating leverage is equal to total contribution margin in dollars divided by pretax net income. When operating leverage is high, a small percentage increase in sales can result in a much larger percentage increase in operating income.
Total contribution margin (in dollars)
Pretax income
Degree of operating leverage =
18-36

37. End of Chapter 18
The understanding of cost behavior, and the relationships between costs, volume, and profit are some of the basic concepts and principles of managerial accounting. They are important ones for you to understand.
18-37