21–1
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,
21-2, 21-3,
21-4
21-1, 21-3,
21-5, 21-7
C2. Describe several applications of
cost-volume-profit analysis.
4, 9, 11, 21
21-7, 21-10
21-5, 21-12,
21-13, 21-14,
21-15, 21–16
22–4, 22-6
Analytical objectives:
A1. Compute contribution margin
and describe what it reveals
about a company’s cost
structure.
6, 7, 8
21-5, 21-14
21-1, 21-4,
21-5, 21-6
21-7
A2. Analyze changes in sales using
the degree of operating
leverage.
17, 18
21-11
21-9, 21-21
21-2
Procedural objectives:
P1. Determine cost estimates using
the scatter diagram, high-low,
and regression methods of
estimating costs.
13
21-3, 21-4
21-1, 21-6
21-7, 21-8
21-3
P2. Compute break-even point for a
single product company.
14, 20
21-6, 21-8,
21-9
21-10
21-2, 21-4,
21-6
21-2
P3. Graph costs and sales for a
single product company.
15, 16
21-13
21-11
21-2
P4. Compute break-even point for a
multiproduct company.
20
21-12
21-17, 21-18,
21-19, 21-20
21-5, 21-7
22-8, 21-9
21–2
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 21-2A 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. It is most readily solved
manually if you use the working papers that accompany text.
Narrated PowerPoint Correlation Guide
Learning Objective
Slides
C1
3-7
P1
8-13
A1
14-16
P2
17-19
P3
20-22
C2
23-30
P4
31-37
A2
39-40
Synopsis of Chapter Revision
• Leather Head Sports: NEW opener with new entrepreneurial assignment
• Was Chapter 22 in prior edition
Chapter Outline
I. Identifying Cost Behavior (CVP analysis) ⎯Cost-volume-profit
analysis is a tool to predict how changes in costs and sales levels affect
income; 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.
A. Fixed Costs
1. A total fixed cost remains unchanged in amount when volume
product are usually plotted on the horizontal axis and dollars
of cost are plotted on the vertical axis. (Exhibit 21.1)
(cost remains constant at all levels of volume within the
relevant range).
b. Intersection point of line on cost (vertical) axis is at fixed
cost amount.
4. Likely that amount of fixed cost will change when outside of
variable cost changes with the level of production. (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.
C. Mixed Costs
1. Include both fixed and variable cost components.
2. When volume and cost are graphed, (Exhibit 21-1)
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
components when included in a CVP analysis.
Notes
Chapter Outline
D. 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
E. Curvilinear (or Nonlinear) Costs
1. Increase at a non-constant rate as volume increases.
as a curved line that starts at intersection point of cost axis and
volume axis (total cost is zero when volume is zero) and
II. Measuring Cost Behavior⎯After establishing that cost data are
reliable and useful in predicting future costs, three methods are
commonly used to analyze past cost behavior.
“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
Notes
21–5
Chapter Outline
B. High-low Method
1. Estimate the cost equation by graphically connecting the two
cost amounts at the highest and lowest unit volumes.
(Exhibit 21-5)
b. Variable cost per unit is the slope of the line⎯is computed
as the change in cost divided by the change in units:
Variable cost = high volume costs – low volume costs
the highest and lowest resulting in less precision.
C. Least-Squares Regression⎯computation details covered in
advanced cost accounting courses.
5. Statistical method of identifying cost behavior.
6. Cost equation readily calculated using most spreadsheet
due to use of all data points available.
III. Break-Even Analysis⎯special case of CVP analysis.
A. Contribution Margin
1. Requires separating costs and expenses by behavior (fixed or
per unit basis).
3. Contribution margin per unit (CM per unit) is computed as:
Selling price per unit minus Variable cost per unit
4. Contribution margin ratio—the proportion of a unit’s selling
unit variable costs).
5. Contribution margin ratio (CM %) is computed as:
contribution margin per unit divided by sales price per unit.
Notes
Chapter Outline
B. Computing Break-Even Point
a loss.
b. Can be expressed either in units or dollars of sales.
CM per unit
b. Break-even sales dollars = Fixed costs
CM%
c. Contribution Margin Income Statement
Margin of safety (units) Margin of Safety (dollars)
D. Preparing a Cost-Volume-Profit Chart (also called a break-even graph
or chart)
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.
Notes
Chapter Outline
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.
a. Volume levels to left of break-even point⎯vertical 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 point⎯vertical distance
is amount of profit expected because the total sales line is
above the total costs line.
2. If expected cost and revenue behavior is different from three
assumptions stated above, CVP analysis may still be useful.
can offset each other. The same can be said for fixed costs.
b. Relevant range of operations⎯Assumes 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.)
Notes
Chapter Outline
IV. Applying Cost-Volume-Profit Analysis ⎯Useful in helping managers
evaluate likely effects of strategies considered in planning business
– Variable Costs (# units sold x unit variable cost)
Contribution Margin
– Fixed Costs
fixed costs + target pretax income
CM%
fixed costs + target pretax income
CM
compute sales for a target income (exhibit 21.24)
C. Sensitivity Analysis⎯Knowing 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
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
Notes
Chapter Outline
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 _
CM per composite unit
c. Compute the contribution margin per unit of each product.
(sales price per unit less variable cost per unit).
d. Multiply the contribution margin per unit for each unit x the
f. Divide fixed costs by the weighted average contribution
margin to compute the break-even point in units.
V. Decision Analysis—Degree of Operating Leverage⎯Useful tool in assessing
the effect of changes in the level of sales on income.
Notes
21–10
Alternate Demo Problem Twenty-One
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:
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.
21–11
Solution: Alternate Demo Problem Twenty-One
(a)
Break-even point (in units) = Fixed costs/CM per unit
$32,000/($40 per unit – $24 per unit) = 2,000 units
2,000 units x $40 per unit = $80,000 dollars
(or)
Break-even point (in dollars) = Fixed costs/CM ratio
$32,000/[($40 per unit –$16 per unit)/$40 per unit] = $80,000
$80,000 dollars/$40 per unit = 2,000 units
(b)
Net income = (CM per unit x number of units sold) – Fixed costs
New fixed costs = $32,000 + $4,000 = $36,000
New CM = $40 per unit – $23 per unit = $17 per unit
($17 per unit x 3,200 units) – $36,000 = $18,400
(c)
Break-even point (in units) = Fixed costs/CM per unit
New fixed costs = $32,000 + $8,000 = $40,000
New CM = $44 per unit – $24 per unit = $20 per unit
$40,000/$20 per unit = 2,000 units
2,000 units x $44 per unit = $88,000
(d)
Break–even point (in units) = Fixed costs/CM per unit
New fixed costs = $32,000 – $8,000 = $24,000
New CM = $40 per unit – $26.40 per unit = $13.60 per unit
$24,000/$13.60 per unit = 1,765 units
1,765 units x $40 per unit = $70,600
(e)
Required sales (in units) = (Fixed costs + Target NI)/CM per unit
($24,000 + $23,600)/$13.60 per unit = 3,500 units