Chapter 21 – Cost-Volume-Profit Analysis
CHAPTER 21
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
21-1, 21-2,
21-1, 21-2,
21-3
21-1, 21-3,
21-5, 21-7
C2. Describe several applications of
cost-volume-profit analysis.
4, 9, 11, 21 21-7, 21-13 21-11, 21-12,
21-13, 21-14,
21-15, 21-16,
21-17, 21-18,
21-19, 21-20,
21-21
21-4, 21-5,
21-4, 21-6
Analytical objectives:
A1. Compute contribution margin
6, 7, 8 21-5, 21-17 21-8 21-1, 21-4,
21-7
A2. Analyze changes in sales using
17, 18 21-16 21-9, 21-24,
21-2
P1. Determine cost estimates using
the scatter diagram, high-low,
and regression methods of
estimating costs.
13 21-3, 21-4 21-4, 21-5,
21-6, 21-7
21-2
P2. Compute break-even point for a
single product company.
14, 20 21-6, 21-8,
21-9, 21-10,
21-11, 21-12
21-9, 21-16 21-3, 21-4,
21-6
21-2
P3. Graph costs and sales for a
single product company.
15, 16 21-15 21-10 21-3
21-1
Chapter 21 – Cost-Volume-Profit Analysis
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 21-3A and 21-6A 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
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
Added several new end of chapter assignments
21-2
Chapter 21 – Cost-Volume-Profit Analysis
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
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 21.1) 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
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 21.1)
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
3. Mixed costs are often separated into fixed and variable
components when included in a CVP analysis.
Notes
21-3
Chapter 21 – Cost-Volume-Profit Analysis
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
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 21-4)
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
Notes
21-4
Chapter 21 – Cost-Volume-Profit Analysis
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 21A 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
sales price per unit.
Notes
21-5
Chapter 21 – Cost-Volume-Profit Analysis
Chapter Outline
C. Computing Break-Even Point
1. Break-even point
2. Computation of break-even point
a. Break-even units = Fixed costs
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 21.15)
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
21-6
Chapter 21 – Cost-Volume-Profit Analysis
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
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 21.24)
Notes
21-7
Chapter 21 – Cost-Volume-Profit Analysis
Chapter Outline
C. Sensitivity Analysisknowing the effects of changing some estimates
used in CVP analysis by substituting new estimated amounts (in total
or per unit as appropriate) in the related formula can be helpful in
making predictions. Can also use the contribution margin income
statement.
D. Multiproduct Break-Even PointModify basic CVP analysis when
company produces and sells several products.
1. Important assumptionSales mix of the different products is
known and remains constant.
2. Sales mix is the ratio (proportion) of the sales volumes for
various products.
3. To apply multiproduct CVP analysis, estimate break-even point
by using a composite unit.
a. Determine sales mix of various products.
b. Composite Unit—a specific number of units of each product
in proportion to their expected sales mix. Multi-product CVP
treats this composite unit as a single product
c. Using sales mix, determine the selling price of a composite
unit by multiplying the sales mix ratio times the selling price
of each product and then adding the totals for all of the
products.
d. Compute the variable cost of a composite unit in the same
manner.
e. Determine the CM per composite unit by subtracting the total
variable price from the total selling price of the composite
unit
f. In break-even analysis, a composite unit is treated as a unit
of a single product.
g. Break-even point in composite units is computed as:
Fixed Costs _ = Composite Units to break-even
CM per composite unit
h. To determine how many units of each product must be sold to
break even, multiply the number of units of each product in
the composite (sales mix) by the break-even point in
composite units.
Notes
21-8
1. Usefulness depends on validity of three assumptions.
a. Constant selling price per unit.
b. Constant variable costs per unit.
c. Constant total fixed costs.
2. If expected cost and revenue behavior is different from three
assumptions stated above, CVP analysis may still be useful.
a. Summing of costs can offset individual deviationsIndividual
variable cost items may not be perfectly variable, but when
summed, individual deviations can offset each other. The
same can be said for fixed costs.
b. Relevant range of operationsAssumes a specific cost is
variable or fixed is more likely valid when operations are
within the relevant range. (If normal range of activity
changes, some costs may need reclassification.)
c. Estimates from CVP analysisManagers need to understand
that CVP analysis provides approximate estimates about
future, not precise answers, and that other qualitative factors
should also be considered.
V. Decision Analysis–Degree of Operating Leverage
A. Useful tool in assessing the effect of changes in the level of sales on
income is the degree of operating leverage computation.
B. Operating leverage is the extent, or relative size, of fixed costs in the
total cost structure.
C. Degree of operating leverage (DOL) is computed as:
Total Contribution margin (dollars)
pretax income
D. Use DOL to measure the effect of changes in the level of sales on
pretax income by multiplying DOL by the percentage change in sales.
Alternate Demo Problem Twenty-One
Problem #1
Trimble Company sells an electronic toy for $40. The variable cost is $24
per unit and the fixed cost is $32,000 per year. Management is considering
the following changes:
21-9
Chapter 21 – Cost-Volume-Profit Analysis
Alternative #1
Lease a new packaging machine for $4,000 per year, which will reduce
variable cost by $1 per unit.
Alternative #2
Increase selling price 10 percent to counteract an expected 25 percent
increase in fixed cost.
Alternative #3
Reduce fixed cost by 25 percent by moving to a lower rent location. This
would have the effect of increasing variable costs by 10 percent.
Required:
Consider and answer each of the following questions independently:
Round calculations to the nearest unit
(a) Determine the current break-even point in units and dollars.
(b)Determine the expected profit assuming alternative #1 and sales of
3,200 units.
(c) Determine the break-even point in units and dollars assuming
alternative #2.
(d)Determine the break-even point required in units and dollars
assuming alternative #3.
(e) Determine the volume of sales required to earn $23,600 assuming
alternative #3.
Alternative Demo Problem Twenty-one
Multi-product breakeven point
Problem #2
Handy Home sells window and doors in the ratio of 8:2 (windows:doors).
The selling price of each window is $200 and of each door is $500. The
variable cost of a window is $125 and of a door is $350. Fixed costs are
$900,000.
Required:
1. Determine the contribution margin for one composite unit
21-10
2. Compute the break-even point in composite units
3. Compute the number of units of each product that will be sold at the
Break-even point.
4. Compute the number of units of each product that need to be sold to
achieve a net income of $180,000.
21-11