Chapter 3
Fundamentals of Cost-Volume-Profit Analysis
Learning Objectives
Chapter Overview
I. COST-VOLUME-PROFIT ANALYSIS
• Profit Equation
• CVP Example
o Finding Break-Even and Target Volumes
▪ Break-Even Volume in Units
▪ Break-Even Volume in Sales Dollars
▪ Target Volume in Units
▪ Target Volume in Sales Dollars
• Graphic Presentation
Chapter Outline
LO 3-1 Use cost-volume-profit (CVP) analysis to analyze decisions.
COST-VOLUME-PROFIT ANALYSIS
• Cost-Volume-Profit (CVP) Analysis
o Cost-volume-profit (CVP) analysis is a study of the relations among revenues, costs, and
volume and their effect on profit.
o Managers make decisions on volume, pricing, or incurring a cost that will impact profit.
(See Business Application box “Cost-Volume-Profit Analysis and On-Demand Services.”)
• Profit equation
o Profit equation equals total revenues less total costs.
▪ Operating profit (also referred to as profit) = Total revenues – Total costs
Profit = TR – TC
▪ Total revenue (TR) = Price x Units produced and sold
TR = PX
▪ Total costs = (Variable costs per unit × Units of output) + Fixed costs
TC = VX + F
▪ Profit = (Price – Variable costs) × Units of output) + Fixed costs
o Contribution margin is the amount that units sold contribute toward (1) covering fixed
costs and (2) providing operating profits
▪ Unit contribution margin
• The difference between sales price and variable cost per unit
• Unit contribution margin = Price – Variable cost per unit = P – V
▪ Total contribution margin
• The difference between total revenues and total variable cost
• Total contribution margin
= (Price – Variable cost per unit) x Units of output = (P – V)X
▪ Alternatively, in CVP income statement format,
Total
Unit
Percentage
Sales revenue
PX
P
100%
- Variable costs
VX
V
V ÷ P
= Contribution margin
(P – V)X
P – V
(P – V) ÷ P
- Fixed costs
F
= Profit
(P – V)X – F
o Financial accounting classifies costs as either manufacturing or administrative; for
decision making, for decision making, costs are classified as fixed or variable.
▪ V represents the sum of variable manufacturing cost per unit and variable marketing
and administrative cost per unit
▪ F represents the sum of total fixed manufacturing costs and fixed marketing and
administrative costs
▪ X refers to the number of units produced and sold during the period
• CVP Example
o Exhibit 3.1 illustrates a contribution margin income statement; profit equals contribution
less fixed costs.
o Finding Break-Even and Target Volumes
▪ Break-even point is the volume level at which profits equal zero; if the company
makes many products, the volume is usually expressed in terms of sales dollars and if
the company makes only one product, the volume is usually expressed in terms of
volume.
• Break-even volume (in units) =
Fixed costs
Unit contribution margin
▪ Target volume is the level at which profits equal a target profit.
o Exhibit 3.4 (shown in a more generic form below) is a comparison of a CVP graph and a
LO 3-2 Understand the effect of cost structure on decisions.
• Use of CVP to Analyze the effect of Different Cost Structures
o An organization’s cost structure is the proportion of fixed and variable costs to total
costs; it has a significant effect on the sensitivity of its profits to changes in volume.
▪ A firm with a high proportion of fixed costs, such as electric utilities, is considered
capital intensive.
▪ A firm with a high proportion of variable costs, such as a grocery retailer, may be
considered labor intensive.
o Operating leverage describes the extent to which an organization’s cost structure is
made up of fixed costs.
▪ Operating leverage is high in firms with a high proportion of fixed costs and a low
proportion of variable costs and results in a high contribution margin per unit.
• The higher the firm’s fixed costs, the higher its break-even point.
• Once its break-even point has been reached, however, profit increases at a high
rate.
▪ Operating leverage is low in firms with a low proportion of fixed costs and a high
proportion of variable costs and results in a low contribution margin per unit.
• Firms with lower operating leverages are more flexible and better at withstanding
economic down times.
▪ Profit increase (decrease) as a result of improved (declining) sales can be calculated
as the product of operating leverage and sales increase (decrease) in percentage. (See
Business Application box “Effect of Cost Structure on Operating and Investing
Decisions.”)
▪ Exhibit 3.5 compares the cost structure of two companies.
• Lo-Lev Company has a low operating leverage, while Hi-Lev Company has a
high operating leverage.
• The graphs below use the data from this exhibit to illustrate the impact of an
increase in sales on these two companies.
200000
400000
600000
800000
1000000
1200000
1400000
$
LO-LEV
TR
TC
• Margin of Safety
LO 3-3 Use Microsoft Excel to perform CVP analysis.
CVP ANALYSIS WITH SPREADSHEETS
• Spreadsheet programs such as Microsoft Excel® are ideally suited to doing CVP routinely.
LO 3-4 Incorporate taxes, multiple products, and alternative cost structures
into the CVP analysis.
EXTENSIONS OF THE CVP MODEL
• Income Taxes
o Assuming that operating profits before taxes and taxable income are the same, income
taxes may be incorporated into the basic model as follows (where t is the tax rate):
After-tax profit = [(P – V)X – F] × (1 – t)
o Target volume (in units) =
Fixed costs + [Target profit/(1 – t)]
Unit contribution margin
See Demonstration Problem 2
• Multiproduct CVP Analysis
o Without some assumptions, there is an infinite number of combinations of services or
products that would achieve a given level of profit.
o To simplify matters, managers often assume a particular product mix and compute break-
even or target volumes using either of two methods, a fixed product mix or weighted-
average contribution margin, both of which give the same result.
o Fixed Product Mix
▪ Using the fixed product mix method, managers define a package or bundle of
LO 3-5 Understand the assumptions and limitations of CVP analysis.
ASSUMPTIONS AND LIMITATIONS OF CVP ANALYSIS
• CVP analysis relies on certain assumptions that may limit the applicability of the results for
decision making.
o The limitations are due to the assumptions made; they are not inherent to the method of
CVP analysis itself.
o It is usually assumed that unit variable cost and unit price are constant for all levels of
volume.
o Simplifying assumptions are easier to deal with, but can be relaxed to incorporate more
realistic situations.
o The more important the decision, the more the manager will want to ensure that the
assumptions made are suitable.
o The degree of sensitivity of the decisions to the assumptions made dictates caution about
the results and the need for considering alternative assumptions.
Matching
Matching Answers
11. F
Multiple Choice
4. If variable cost per unit is increased by 15%, fixed cost is increased to $15,120, and the unit
6. The excess of actual or projected sales over the break-even sales is known as:
7. A company produces key chains. The data include price $1, unit variable cost $0.40, monthly
9. A start-up company manufactures two products: X is sold for $5 with variable cost of $3
each; Y is sold for $8 with variable cost of $4 each. An annual fixed cost of $10,000 is
11. In October, Fashionable Clothing manufactured 2,000 items with the following financial
statement amounts: direct materials $12,000, sales $48,000, direct labor $16,000,
depreciation $3,600, rent $1,500, and variable overhead $9,000. What is contribution margin
12. Which of the following statements regarding margin of safety is correct?
Multiple Choice Answers
1. a (LO1)
2. d (LO1)
3. c (LO1)
−
4. d (LO2)
Variable cost = $0.80 × (1 + 15%) = $0.92.
7. b (LO4)
12. a (LO2)
Demonstration Problem 1
6. Number of units sold that would produce an operating profit of 15% of sales dollars.
Demonstration Problem 1 – Solution
CM = Contribution margin
F = Fixed costs
P = Price
V – Variable costs per unit
X = Units of output
Part 1
Operating profit = (P – V)X + F = ($150 – $90) × 1,200 – $48,000 = $24,000
Part 2
Break-even volume (in units) =
F
=
$48,000
= 800 units
P – V
$150 – $90
Part 3
$22.50X = $60X – $48,000
$48,000 = $60X – $22.50X
$48,000 = $37.50X
X = 1,280 units
Demonstration Problem 2
(Same background information as in Demonstration Problem 1.)
The Power Tool Division of ABC Hardware sells one product, Jig Saw, and has the following
data for the second quarter:
Units of output
1,200 units
Price per unit
$ 150
Variable cost per unit
90
Total fixed costs
48,000
Required:
Assume that the Power Tool Division of ABC Hardware now faces a tax rate of 30 percent.
Determine the number of Jig Saws required to generate the after-tax operating profit of $16,800.
Demonstration Problem 2 – Solution
Demonstration Problem 3
2. Weighted-average contribution margin method
Demonstration Problem 3 – Solution
CM = Contribution margin
F = Fixed costs
P = Price
V – Variable costs per unit
Part 1
2) must be sold to break even.
Part 2
The produce mix consists of 60 % (or 3 ÷ 5) Jig Saws and 40% (or 2 ÷ 5) Circular Saws.
Weighted-average contribution margin per unit = (0.60 × $60) + (0.40 × $80) = $68