CHAPTER 18
COST BEHAVIOR AND COST-VOLUME-PROFIT ANALYSIS
Related Assignment Materials
Student Learning Objectives Discussion
Questions
Quick
Studies*
Exercises* Problems* Beyond the
Numbers
Conceptual objectives:
C1. Describe different types of cost
behavior in relation to
production and sales volume.
1,2, 3, 5, 10,
12, 19
18-1, 18-2,
18-1, 18-2,
18-3
18-1, 18-3,
18-5, 18-7
C2. Describe several applications of
cost-volume-profit analysis.
4, 9, 11, 21 18-7, 18-13 18-11, 18-12,
18-13, 18-14,
18-15, 18-16,
18-17, 18-18,
18-19, 18-20,
18-21
18-4, 18-5,
18-4, 18-6
Analytical objectives:
A1. Compute contribution margin
and describe what it reveals
about a company’s cost
structure.
6, 7, 8 18-5, 18-17 18-8 18-1, 18-4,
18-5, 18-6
18-7
A2. Analyze changes in sales using
the degree of operating
leverage.
17, 18 18-16 18-9, 18-24,
18-25
18-2
Procedural objectives:
P1. Determine cost estimates using
the scatter diagram, high-low,
and regression methods of
estimating costs.
13 18-3, 18-4 18-4, 18-5,
18-6, 18-7
18-2
P2. Compute break-even point for a
single product company.
14, 20 18-6, 18-8,
18-9, 18-10,
18-11, 18-12
18-9, 18-16 18-3, 18-4,
18-6
18-2
P3. Graph costs and sales for a
single product company.
15, 16 18-15 18-10 18-3
P4. Compute break-even point for a
multiproduct company.
20 18-14 18-22, 18-23 18-5, 18-7 18-8, 18-9
*See additional information on next page that pertains to these quick studies, exercises and problems.
Additional Information on Related Assignment Material
Connect (Available on the instructor’s course-specific website) repeats all numerical Quick Studies, all
Exercises and Problems Set A. Connect provides new numbers each time the Quick Study, Exercise or
Problem is worked. It allows instructors to monitor, promote, and assess student learning. It can be used
in practice, homework, or exam mode.
Corresponding problems in set B also relate to learning objectives identified in grid on previous page.
Problems 18-3A and 18-6A can be completed using EXCEL. The Serial Problem for Success Systems
starts in this chapter and continues throughout many chapters of the text.
Synopsis of Chapter Revision
Sevenly—New Opener with entrepreneurial assignment.
Revised discussion of fixed and variable costs
Revised discussion of relevant range
Reorganized discussion of the high-low method as a three-step process
Enhanced exhibit on high-low method calculations
Revised discussion of how changes in estimates impact break-even points
Revised target income discussion to focus on pre-tax income
Simplified exhibit on using the contribution margin income statement to compute sales
needed for target income
Revised discussion of sensitivity analyses, buying a new machine
Added example of sensitivity analyses, increasing advertising
Added exhibit on using the contribution margin income statement in sensitivity analysis
Eliminated the weighted-average contribution margin method of computing multi-product
break-even
Added two exhibits on calculations of operating leverage
Added appendix on variable costing versus absorption costing
Added Sustainability section, Volkswagen
Added several new end of chapter assignments
.
18-2
Chapter Outline
I. Identifying Cost Behavior (CVP analysis)
A. Cost-volume-profit analysis is a tool to predict how changes in costs
and sales levels affect profit
1. In its basic form, involves computing the sales level at which the
company neither earns an income nor incurs a loss, call the break-
even point.
2. The concept of relevant range is important when classifying costs
for CVP analysis. The relevant range is the normal operating
range for a business. It excludes extremely high or low operating
levels.
3. Conventional CVP analysis requires that all costs must be
classified as either fixed or variable with respect to production or
sales volume before CVP analysis can be used.
B. Fixed Costs
1. Total fixed costs remain unchanged in amount when volume of
activity varies from period to period within a relevant range.
2. The fixed cost per unit of output decreases as volume increases
(and vice versa).
3. When production volume and cost are graphed, units of product
are usually plotted on the horizontal axis and dollars of cost are
plotted on the vertical axis. (Exhibit 18.1) The fixed cost is
represented by a horizontal line with no slope (cost remains
constant at all levels of volume within the relevant range).
4. It is likely that amount of fixed cost will change when outside of
relevant range.
C. Variable Costs
1. Variable costs change in proportion to changes in volume of
activity
2. Variable cost per unit remains constant but the total amount of
variable cost changes with the level of production.
3. When production volume and cost are graphed, (Exhibit 18.1)
a. Variable cost is represented by a straight line starting at the
zero cost level.
b. The straight line is upward (positive) sloping. The line rises as
volume increases.
D. Mixed Costs
1. Include both fixed and variable cost components.
2. When volume and cost are graphed, the mixed cost is represented
by a straight line with an upward (positive) slope. Start of line is at
fixed cost point (or amount of total cost when volume is zero) on
cost (vertical) axis. As activity level increases, mixed cost line
increases at an amount equal to the variable cost per unit.
3. Mixed costs are often separated into fixed and variable
Notes
18-3
Chapter Outline
E. Step-wise Costs
1. Fixed within a relevant range of the current production volume. If
production volume expands significantly, total costs go up by a
lump-sum amount (stair-step cost).
2. Treated as either fixed or variable cost in conventional CVP
analysis; depends on width of range, and requires judgment.
F. Curvilinear (or Nonlinear) Costs
1. Increase at a non-constant rate as volume increases.
2. When volume and costs are graphed, curvilinear costs appear as a
curved line that starts at intersection point of cost axis and volume
axis (total cost is zero when volume is zero) and increases at
different rates.
3. Often treated as variable costs in CVP analysis within a relevant
range.
II. Measuring Cost BehaviorAfter establishing that cost data are reliable
and useful in predicting future costs, three methods are commonly used to
analyze past cost behavior. Goal is to develop a cost equation.
A. Scatter Diagrams
1. Display past cost and unit data in graphical form. (Exhibit 18-4)
2. Units are plotted on horizontal axis, cost on the vertical axis.
3. Each point reflects the number of units for a prior period.
4. Estimated line of cost behaviordrawn with a line that best “fits”
the points visually.
a. Intersection point of line on cost axis is at fixed cost amount.
b. The variable cost per unit of volume equals the slope of the
line.
i. Select any two points on horizontal axis.
ii. Draw a vertical line from each of these points to intersect
the estimated line of cost behavior.
iii. The slope of the line, or variable cost per unit is computed
as follows:
Change in Costs = variable cost per unit
Change in volume (units)
c. Cost equation (useful to predict future cost levels at different
volumes):
Total costs = Fixed costs + variable cost per unit x #of units
d. Deficiency of scatter diagram methodestimates are based on
“visual fit” of cost line, subject to interpretation.
Notes
.
18-4
Chapter Outline
B. High-low Method
1. Step 1: Identify the highest and lowest volume levels. Note that
these may not be the highest or lowest level of costs.
2. Step 2: Compute the slope (variable cost per unit) using the high
low activity levels
Variable cost = high volume costs – low volume costs
per unit high volume units – low volumes units
3. Step #3: Compute the estimated fixed costs by first computing the
total variable costs at either the high or low activity level and then
subtracting that amount from the total costs at that activity level.
Use the cost equation.
Total costs = Fixed costs + variable cost per unit x #of units
4. Deficiency of high-low methodignores all cost points except the
highest and lowest resulting in less precision.
C. Least-Squares Regressioncomputation details covered in advanced
cost accounting courses.
1. Statistical method of identifying cost behavior.
2. Cost equation readily calculated using most spreadsheet programs.
Illustrated in Appendix 18A using Excel®
3. Cost equation may differ slightly from those determined using the
scatter diagram and high-low methods; may be superior due to use
of all data points available.
III. Break-Even Analysis
A. Contribution Margin
1. Requires separating costs and expenses by behavior (fixed or
variable).
2. The amount by which a product’s unit selling prices exceeds its
total unit variable cost. (This excess amount contributes to
covering fixed costs and generating profits on a per unit basis).
3. Contribution margin per unit is computed as:
CM per unit = Selling price per unit – variable cost per unit
B. Contribution margin ratio
1. The percent of a unit’s selling price that exceeds total unit variable
cost. (Interpreted as what proportion of each sales dollars remains
after deducting total unit variable costs).
2. Contribution margin ratio is computed as:
CM % = CM per unit
Notes
18-5
Chapter Outline
C. Computing Break-Even Point
1. Break-even point
a. Sales level at which company neither earns a profit nor incurs
a loss.
b. Can be expressed either in units or dollars of sales.
2. Computation of break-even point
a. Break-even units = Fixed costs
CM per unit
b. Break-even sales dollars = Fixed costs
CM%
D. Contribution Margin Income Statement (Exhibit 18.13)
1. Differs from a conventional income statement in two ways:
i. Classifies costs and expenses as variable and fixed
ii. Reports contribution margin
Revenues
– Variable Costs
Contribution Margin
– Fixed Costs
Net Income
E. Margin of safety can be expressed in units, dollars, or as a percent of
predicted level of sales. It is the excess of expected sales over break-
even sale. It is the amount that sales can drop before the company
incurs a loss.
1. Expected Unit Sales Expected Sales Dollars
– Break-even Unit sales – Break-even Sales Dollars
Margin of safety (units) Margin of Safety (dollars)
2. Margin of Safety Rate (%) = Margin of Safety
Expected Sales
F. Preparing a Cost-Volume-Profit Chart (also called a break-even graph
or chart) (Exhibit 18.15)
1. Horizontal axisnumber of units produced and sold (volume)
2. Vertical axisdollars of sales and costs.
3. Three steps:
a. Plot fixed costs on vertical axis; draw horizontal line at this
level to show that FC remains unchanged regardless of output
volume.
b. Draw line reflecting total costs (variable costs plus fixed
costs) for a relevant range of volume levels.
i. Line starts at fixed costs on vertical axis.
ii. Slope equals variable cost per unit
Notes
.
18-6
Chapter Outline
iii. Compute total costs for any volume level, and connect
this point with the vertical axis intercept.
iv. Stop line at productive capacity for the planning period.
c. Draw sales line.
i. Line starts at origin (zero units and zero dollars of sales).
ii. Slope of line is equal to selling price per unit; compute
total revenues for any volume level, and connect this
point with the origin.
iii. Stop line at productive capacity for the planning period
4. The break-even point is at the intersection of total cost line and
sales line.
5. On either side of break-even point, the vertical distance between
sales line and total cost line at any specific sales volume reflects
the profit or loss expected at that point.
a. Volume levels to left of break-even pointvertical distance is
amount of loss expected because the total costs line is above
the total sales line.
b. Volume levels to right of break-even pointvertical distance
is amount of profit expected because the total sales line is
above the total costs line.
IV. Applying Cost-Volume-Profit Analysis Useful in helping managers
evaluate likely effects of strategies considered in planning business
operations.
A. Computing Income from Sales and Costs
1. Sales (# units sold x unit selling price)
– Variable Costs (# units sold x unit variable cost)
Contribution Margin
– Fixed Costs
Income (pretax)
B. Computing Sales for a Target Income
1. Sales (in dollars) required for target pretax income equals:
fixed costs + target pretax income
CM%
2. Sales (in units) required for target income equals
fixed costs + target pretax income
CM
3. Can also use the contribution margin income statement to
compute sales for a target income (exhibit 18.24)
Notes
.
18-7