A cost that changes as volume changes, but at a nonconstant rate, is called a:

Cost Behavior and Cost-Volume-Profit Analysis

Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Chapter 18

Wild and Shaw

Financial and Managerial Accounting

8th Edition

Chapter 18: Cost-Volume-Profit Analysis

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Chapter 18 Learning Objectives

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CONCEPTUAL

C1 Describe different types of cost behavior in relation to production and sales volume.

C2 Describe several applications of cost-volume-profit analysis.

ANALYTICAL

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.

PROCEDURAL

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 Interpret a CVP chart and graph costs and sales for a single-product company.

P4 Compute the break-even point for a multiproduct company.

P5 Appendix 18B—Compute unit cost and income under both absorption and variable costing.

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Describe different types of cost behavior in relation to production and sales volume.

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Learning Objective C1

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Identifying Cost Behavior

Managers use cost-volume-profit analysis to make predictions such as:

How many units must we sell to break-even?

How much does income increase if we install a new machine to reduce labor costs?

What is the change in income if selling prices decline and sales volume increases?

How will income change if we change the sales mix of our products or services?

What sales volume is needed to earn a target income?

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Learning Objective C1: Describe different types of cost behavior in relation to production and sales volume.

Planning a company’s future activities is crucial to successful management. Managers use cost-volume-profit (CVP) analysis, to predict how changes in costs and sales levels affect profit. In its basic form, CVP analysis involves computing the sales level at which a company neither earns an income nor incurs a loss, called the break-even point. For this reason, this basic form of cost-volume-profit analysis is often called break-even analysis.

Managers use CVP analysis to make predictions such as:

How many units must we sell to break-even?

How much does income increase if we install a new machine to reduce labor costs?

What is the change in income if selling prices decline and sales volume increases?

How will income change if we change the sales mix of our products or services?

What sales volume is needed to earn a target income?

We describe in this chapter how to apply CVP analysis. We first review cost classifications like fixed and variable costs, and then we show several methods for measuring these types of costs. The concept of relevant range is important to classifying costs for CVP analysis. The relevant range of operations is the normal operating range for a business.

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Fixed Costs

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Learning Objective C1: Describe different types of cost behavior in relation to production and sales volume.

Exhibit 18.2

Fixed costs remain unchanged despite variations in the volume of activity within a relevant range. For example, $32,000 in monthly rent paid for a factory building remains the same whether the factory operates with a single eight-hour shift or around the clock with three shifts. This means that rent cost is the same each month at any level of output from zero to the plant’s full productive capacity.

When production volume and costs are graphed, units of product are usually plotted on the horizontal axis and dollars of cost are plotted on the vertical axis.

Though the total amount of fixed cost does not change as volume changes, fixed cost per unit of output decreases as volume increases. For instance, if 200 units are produced when monthly rent is $32,000, the average rent cost per unit is $160 (computed as $32,000/200 units). When production increases to 1,000 units per month, the average rent cost per unit decreases to $32 (computed as $32,000/1,000 units).

The upper graph in Exhibit 18.2 shows the relation between total fixed costs and volume, and the relation between total variable cost and volume. We see that total fixed costs of $32,000 remains the same at all production levels up to the company’s monthly capacity of 2,000 units. We also see that total variable costs increase by $20 per unit for each additional unit produced. When variable costs are plotted on a graph of cost and volume, they appear as a straight line starting at the zero cost level.

The lower graph in Exhibit 18.2 shows that fixed costs per unit decrease as production increases. This drop in per unit costs as production increases is known as economies of scale. This lower graph also shows that variable costs per unit remain constant as production levels change.

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Variable Costs

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Learning Objective C1: Describe different types of cost behavior in relation to production and sales volume.

Exhibit 18.2

Variable costs change in proportion to changes in volume of activity. The direct materials cost of a product is one example of a variable cost. If one unit of product requires materials costing $20, total materials costs are $200 when ten units of product are manufactured, $400 for 20 units and so on.

While the total amount of variable cost changes with the level of production, variable cost per unit remains constant as volume changes.

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Mixed Costs

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Learning Objective C1: Describe different types of cost behavior in relation to production and sales volume.

Exhibit 18.2

Are all costs only either fixed or variable? No—another category, mixed costs, includes both fixed and variable cost components. For example, compensation for sales representatives often includes a fixed monthly salary and a variable commission based on sales. Utilities can also be considered a mixed cost; even if no units are produced, it is not likely a manufacturing plant will use no electricity or water. 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.

The total cost line in the top graph in this slide starts on the vertical axis at the $32,000 fixed cost point. Thus, at the zero volume level, total cost equals the fixed costs. As the volume of activity increases, the total cost line increases at an amount equal to the variable cost per unit. This total cost line is a “mixed cost”—and it is highest when the volume of activity is at 2,000 units (the end point of the relevant range). In CVP analysis, mixed costs should be separated into fixed and variable components. The fixed component is added to other fixed costs, and the variable component is added to other variable costs.

We show how to separate costs later in this chapter.

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Step-Wise Costs

Total cost increases to a new higher cost for the next higher range of activity, but remains constant within a range of activity.

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Learning Objective C1: Describe different types of cost behavior in relation to production and sales volume.

Exhibit 18.3

A step-wise cost (or stair-step cost) reflects a step pattern in costs. Salaries of production supervisors are fixed within a relevant range of the current production volume. However, if production volume expands significantly (for example, with the addition of another shift), additional supervisors must be hired. This means that the total cost for supervisory salaries steps up by a lump-sum amount. Similarly, if production volume takes another significant step up, supervisory salaries will increase by another lump sum. This behavior is graphed in this slide. See how the step-wise cost line is flat within ranges, called the relevant range. Then, when volume significantly changes, the cost steps up to another level for that range.

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Curvilinear Costs

Costs that increase when activity increases, but in a nonlinear manner.

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Learning Objective C1: Describe different types of cost behavior in relation to production and sales volume.

Exhibit 18.3

Curvilinear costs also increase as volume increases, but at a nonconstant rate. The curved line in this slide shows a curvilinear cost beginning at zero (when production is zero) and increasing at different rates as volume increases.

One example of a curvilinear cost is total direct labor cost. At low levels of production, employees can specialize in certain tasks. This efficiency results in a flatter slope in the curvilinear cost graph at lower levels of production in Exhibit 18.3. At some point, adding more employees creates inefficiencies (they get in each other’s way or do not have special skills). This inefficiency is reflected in a steeper slope at higher levels of production in the curvilinear cost graph in Exhibit 18.3.

In CVP analysis, step-wise costs are usually treated as either fixed or variable costs. Curvilinear costs are typically treated as variable costs, and thus constant per unit. These treatments involve manager judgment and depend on the width of the relevant range and the expected volume.

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Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

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Learning Objective P1

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Measuring Cost Behavior

The objective is to classify all costs as either fixed or variable. We will look at three methods:

Scatter diagram

High-low method

Regression

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Learning Objective P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

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. A goal of classifying costs is to develop a cost equation. The cost equation expresses total costs as a function of fixed costs plus variable cost per unit. Three methods are commonly used to analyze past costs:

scatter diagram

high-low method

regression

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Scatter Diagrams

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Learning Objective P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

Exhibit 18.5

Scatter diagrams are graphs of unit volume and cost data. Units are plotted on the horizontal axis and costs are plotted on the vertical axis. Each point on a scatter diagram reflects the cost and number of units for a prior period.

In this graph, the prior 12 months’ costs and numbers of units are graphed. Each point reflects total costs incurred and units produced in that month. For instance, the point labeled March had units produced of 25,000 and costs of $25,000.

The estimated line of cost behavior is drawn on a scatter diagram to reflect the relation between cost and unit volume. This line best visually “fits” the points in a scatter diagram. Fitting this line demands judgment, or can be done with spreadsheet software.

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The High-Low Method (1 of 2)

The following relationships between units produced and total cost are observed:

Using these two levels of volume, compute:

the variable cost per unit.

the total fixed cost.

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Learning Objective P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

Exhibit 18.4

The high-low method is a way to estimate the cost equation using just two points to estimate the cost equation: the highest and lowest volume levels. The high-low method follows these steps:

Step 1: Identify the highest and lowest volume levels. These might not be the highest or lowest levels of costs.

Step 2: Compute the slope (variable cost per unit) using the high and low volume levels.

Step 3: Compute the total fixed costs by computing the total variable cost at either the high or low volume level, and then subtracting that amount from the total cost at that volume level.

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The High-Low Method (2 of 2)

Total cost = $14,125 + $0.25 per unit produced

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Learning Objective P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

Exhibit 18.7

Exhibit 18.6

We illustrate the high-low method here.

Step 1: In our case, the lowest number of units is 17,500 and the highest is 67,500. The costs corresponding to these unit volumes are $18,500 and $31,000, respectively (see the data in Exhibit 18.4).

Step 2: The variable cost per unit is calculated using a simple formula: change in cost divided by the change in units. Using the data from the high and low unit volumes, this results in a slope, or estimated variable cost per unit, of $0.25 as computed in Exhibit 18.6.

Step 3: To estimate the fixed cost for the high-low method, we know that total cost equals fixed cost plus variable cost per unit times the number of units. Then we pick either the high or low volume point to determine the fixed cost. This computation is shown in Exhibit 18.7—where we use the high point (67,500 units) in determining the fixed cost of $14,125.

Thus, the cost equation from the high-low method is $14,125 plus $0.25 per unit produced. This cost equation differs from that determined from the scatter diagram method. A weakness of the high-low method is that it ignores all data points except the highest and lowest volume levels.

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The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost.

Regression

Regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators.

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Learning Objective P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

Least-squares regression is a statistical method for identifying cost behavior. For our purposes, we use the cost equation estimated from this method but leave the computational details for more advanced courses. Such computations for least-squares regression are readily done using most spreadsheet programs or calculators. We illustrate this using Excel in this chapter’s Appendix. Using least-squares regression, the cost equation for the data presented in Exhibit 18.3 is $16,688 plus $0.20 per unit produced; that is, the fixed cost is estimated as $16,688 and the variable cost at $0.19 per unit.

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Comparison of Cost Estimation Methods

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Learning Objective P1: Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs.

Exhibit 18.8

The different cost estimation methods result in different estimates of fixed and variable costs as summarized in this slide. Estimates from the high-low method use only two sets of values corresponding to the lowest and highest unit volumes. Sometimes these two extreme activity levels do not reflect the more usual conditions likely to recur. Estimates from least-squares regression use a statistical technique and all available data points.

We must remember these methods use past data. Thus, cost estimates resulting from these methods are only as good as the data used for estimation. Managers must establish that the data are reliable in deriving cost estimates for the future. If the data are reliable, the use of more data points, as in the regression method, should yield more accurate estimates than the high-low method. However, the high-low method is easier to apply and thus might be useful for obtaining a quick cost equation estimate.

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Compute the contribution margin and describe what it reveals about a company’s cost structure.

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Learning Objective A1

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Contribution Margin and Its Measures

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Learning Objective A1: Compute the contribution margin and describe what it reveals about a company’s cost structure.

Exhibit 18.9

Exhibit 18.10

After we classify costs as fixed or variable we can compute the contribution margin, which equals total sales minus total variable costs. The contribution margin contributes to covering fixed costs and generating profits. Contribution margin per unit, or unit contribution margin, is the amount by which a product’s unit selling price exceeds its variable cost per unit. The top graphic shows the formula to calculate contribution margin per unit.

The contribution margin ratio is the percent of a unit’s selling price that exceeds total unit variable cost. It can be interpreted as the percent of each sales dollar that remains after deducting the unit variable cost. The second graphic shows the formula for the contribution margin ratio.

To illustrate the use of contribution margin, let’s consider Rydell, which sells footballs for $100 each and incurs variable costs of $70 per football sold. Its fixed costs are $24,000 per month with monthly capacity of 1,800 units (footballs). Rydell’s contribution margin per unit is $30, computed as shown.

Thus, at a selling price of $100 per unit, Rydell covers its per unit variable costs and makes $30 per football to contribute to fixed costs and profit. Rydell’s contribution margin ratio is 30%, computed as $30/$100. A contribution margin ratio of 30% implies that for each $1 in sales, Rydell has $0.30 that contributes to fixed cost and profit.

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Compute the break-even point for a single product company.

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Learning Objective P2

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Break-Even Point

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Learning Objective P2: Compute the break-even point for a single product company.

Sales level at which total sales equal total costs.

Company neither earns a profit nor incurs a loss.

Can be expressed in units or dollars of sales.

Three methods to find break-even point:

Formula

Contribution margin income statement

Cost-volume-profit chart

The break-even point is the sales level at which total sales equal total costs and a company neither earns a profit nor incurs a loss. Break-even applies to nearly all organizations, activities, and events. A key concern when launching a project is whether it will break even—that is, whether sales will at least cover total costs. The break-even point can be expressed in either units or dollars of sales.

To illustrate break-even analysis, let’s again look at Rydell, which sells footballs for $100 per unit and incurs $70 of variable costs per unit sold. Its fixed costs are $24,000 per month. Three different methods are used to find the break-even point.

Formula

Contribution margin income statement

Cost-volume-profit chart

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Formula Method

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Learning Objective P2: Compute the break-even point for a single product company.

Exhibit 18.11

Exhibit 18.12

We compute the break-even point using the formula in this slide. This formula uses the contribution margin per unit (calculated above), which for Rydell is $30 ($100 - $70). The break-even sales volume in units is $24,000 / $30 = 800 units per month.

If Rydell sells 800 units, its profit will be zero. Profit increases or decreases by $30 for every unit sold above or below that break-even point; if Rydell sells 801 units, profit will equal $30. We also can calculate the break-even point in dollars. Also called break-even sales dollars, it uses the contribution margin ratio to determine the required sales dollars needed for the company to break even.

The second graphic shows the formula and Rydell’s break-even point in dollars.

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Contribution margin income statement method

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Learning Objective P2: Compute the break-even point for a single product company.

Exhibit 18.13

The center of Exhibit 18.13 shows the general format of a contribution margin income statement. It differs in format from a traditional income statement in two ways. First, it separately classifies costs and expenses as variable or fixed. Second, it reports contribution margin (sales – variable costs). A traditional income statement classifies costs as product or period.

We can use this statement as another way to find the break-even point. For Rydell to break even, its contribution margin must exactly equal its fixed costs of $24,000. For Rydell’s contribution margin to equal $24,000, it must sell 800 units ($24,000/$30). The resulting contribution margin income statement shows that the $80,000 revenue from sales of 800 units exactly equals the sum of variable and fixed costs.

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Interpret a CVP chart and graph costs and sales for a single product company.

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Learning Objective P3

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Graphing – Cost-volume-profit Chart

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Learning Objective P3: Interpret a CVP chart and graph costs and sales for a single product company.

Exhibit 18.14

A third way to find the break-even point is by examining a cost-volume-profit (CVP) chart (break-even chart). Exhibit 18.14 shows Rydell’s CVP chart. In a CVP chart, the horizontal axis is the number of units produced and sold, and the vertical axis is dollars of sales and costs. The lines in the chart show both sales and costs at different output levels.

The CVP chart provides several key observations.

1. Break-even point, where the total cost line and total sales line intersect—at 800 units, or $80,000, for Rydell.

2. Profit or loss expected, measured as the vertical distance between the sales line and the total cost line at any level of units sold (a loss is to the left of the break-even point, a profit is to the right). As the number of units sold increases, the loss area decreases and the profit area increases.

3. Maximum productive capacity, which is 1,800 units (the last point on the CVP chart). At this point Rydell expects sales of $180,000 and its largest profit.

Total costs. This line starts at the fixed costs level on the vertical axis ($24,000 for Rydell). The slope of this line is the variable cost per unit ($70 per unit for Rydell).

Total sales. This line starts at zero on the vertical axis (zero units and zero dollars of sales). The slope of this line equals the selling price per unit ($100 per unit for Rydell). This line must not extend beyond the company’s productive capacity.

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Changes in Estimates

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Exhibit 18.15

Exhibit 18.16

Exhibit 18.17

Learning Objective P3: Interpret a CVP chart and graph costs and sales for a single product company.

Because CVP analysis uses estimates, knowing how changes in those estimates impact break-even is useful. For example, a manager might form three estimates for each of the components of break-even: optimistic, most likely, and pessimistic. Then ranges of break-even points in units can be computed, using any of the three methods shown. To illustrate, assume Rydell’s managers provide the set of estimates in this slide.

If, for example, Rydell’s managers believe they can raise the selling price of a football to $105, without any change in unit variable or total fixed costs, then the revised contribution margin per football is $35 ($105 - $70), and the revised break-even in units is shown in the middle graphic.

Repeating this calculation using each of the other eight separate estimates above (and keeping other estimates unchanged from their original amounts), and graphing the results, yields the three graphs as shown.

These graphs show how changes in selling prices, variable costs, and fixed costs impact break-even. When selling prices can be increased without impacting unit variable costs or total fixed costs, break-even decreases (graph A). When competition reduces selling prices, and the company cannot reduce costs, break-even increases (graph A). Increases in either variable (graph B) or fixed costs (graph C), if they cannot be passed on to customers via higher selling prices, will increase break-even. If costs can be reduced and selling prices held constant, the break-even point decreases.

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Describe several applications of cost-volume-profit analysis.

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Learning Objective C2

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Computing the Margin of Safety

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Learning Objective P2: Compute the break-even point for a single product company.

All companies desire results in excess of break-even. 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 is often expressed in dollars or as a percent of the expected sales level.

To illustrate, recall that Rydell’s break-even point in dollars is $80,000. If its expected sales are $100,000, the margin of safety is $20,000 ($100,000 - $80,000). As a percent, the margin of safety is 20% of expected sales as shown in this slide.

Management must assess whether the margin of safety is adequate in light of factors such as sales variability, competition, consumer tastes, and economic conditions.

Review what you have learned in the following NEED-TO-KNOW Slides.

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Computing Income from Sales and Costs

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Learning Objective C2: Describe several applications of cost-volume-profit analysis.

Exhibit 18.20

Exhibit 18.21

Exhibit 18.19

Managers often use contribution margin income statements to forecast future sales or income. Exhibit 118.19 shows the key variables in CVP analysis—sales, variable costs, contribution margin, and fixed costs, and their relations to income (pretax). To answer the question “What is the predicted income from a predicted level of sales?” we work our way down this income statement to compute income.