Cost-Volume-Profit Analysis
Cost-Volume-Profit Analysis
Learning Objective 1
Learning Objective 1
Understand the assumptions
underlying cost-volume-profit
Cost-Volume-Profit Assumptions
and Terminology
Cost-Volume-Profit Assumptions
and Terminology
1. Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold.
Cost-Volume-Profit Assumptions
and Terminology
Cost-Volume-Profit Assumptions
and Terminology
3. When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range
(and time period).
Cost-Volume-Profit Assumptions
and Terminology
Cost-Volume-Profit Assumptions
and Terminology
5. The analysis either covers a single product or assumes that the sales mix when multiple
products are sold will remain constant as the level of total units sold changes.
6. All revenues and costs can be added and
Cost-Volume-Profit Assumptions
and Terminology
Cost-Volume-Profit Assumptions
and Terminology
Operating income
= Total revenues from operations
– Cost of goods sold and operating costs (excluding income taxes)
Learning Objective 2
Learning Objective 2
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Assume that the Pants Shop can purchase pants for $32 from a local factory; other variable costs
amount to $10 per unit.
The local factory allows the Pants Shop to return all unsold pants and receive a full $32
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
How much revenue will the business receive if 2,500 units are sold?
2,500 × $70 = $175,000
How much variable costs will the business incur? 2,500 × $42 = $105,000
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
What is the contribution margin per unit? $70 – $42 = $28 contribution margin per unit
What is the total contribution margin when 2,500 pairs of pants are sold?
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Contribution margin percentage (contribution margin ratio) is the contribution margin per
unit divided by the selling price.
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Essentials of Cost-Volume-Profit
(CVP) Analysis Example
If the business sells 3,000 pairs of pants, revenues will be $210,000 and contribution margin would equal 40% × $210,000 = $84,000.
FEDER AL RE SE RVE NOTE
THE UNITED STAT ES OF AMERICA
THE UNITED STATES OF AMERICA
L70744 629F
Learning Objective 3
Learning Objective 3
Determine the breakeven point
and output level needed to achieve
a target operating income using
the equation, contribution margin,
Breakeven Point
Breakeven Point
Sales
–
expensesVariable=
expensesFixedAbbreviations
Abbreviations
SP = Selling price
VCU = Variable cost per unit
CMU = Contribution margin per unit CM% = Contribution margin percentage
Abbreviations
Abbreviations
Q = Quantity of output units sold (and manufactured)
OI = Operating income
Equation Method
Equation Method
$70Q – $42Q – $84,000 = 0 $28Q = $84,000
Q = $84,000 ÷ $28 = 3,000 units
Let Q = number of units to be sold to break even (Selling price × Quantity sold) – (Variable unit cost
Contribution Margin Method
Contribution Margin Method
$84,000 ÷ $28 = 3,000 units
Graph Method
Graph Method
0 42 84 126 168 210 252 294 336 3780 1000 2000 3000 4000 5000
Units
$(
00
0) Rev
enue
Total costs
Breakeven
Target Operating Income
Target Operating Income
Target Operating Income
Target Operating Income
Assume that management wants to have an operating income of $14,000.
How many pairs of pants must be sold? ($84,000 + $14,000) ÷ $28 = 3,500
Learning Objective 4
Learning Objective 4
Target Net Income
and Income Taxes Example
Target Net Income
and Income Taxes Example
Management would like to earn an after tax income of $35,711.
The tax rate is 30%.
What is the target operating income? Target operating income
Target Net Income
and Income Taxes Example
Target Net Income
and Income Taxes Example
How many units must be sold?
Revenues – Variable costs – Fixed costs = Target net income ÷ (1 – tax rate)
Target Net Income
and Income Taxes Example
Target Net Income
and Income Taxes Example
Proof:
Revenues: 4,822 × $70 $337,540 Variable costs: 4,822 × $42 202,524 Contribution margin $135,016 Fixed costs 84,000 Operating income 51,016 Income taxes: $51,016 × 30% 15,305
Learning Objective 5
Learning Objective 5
Explain CVP analysis
in decision making and
Using CVP Analysis Example
Using CVP Analysis Example
Suppose the management anticipates selling 3,200 pairs of pants.
Management is considering an advertising campaign that would cost $10,000.
It is anticipated that the advertising will increase sales to 4,000 units.
Using CVP Analysis Example
Using CVP Analysis Example
3,200 pairs of pants sold with no advertising: Contribution margin $89,600
Fixed costs 84,000
Operating income $ 5,600 4,000 pairs of pants sold with advertising:
Using CVP Analysis Example
Using CVP Analysis Example
Instead of advertising, management is considering reducing the selling price
to $61 per pair of pants.
It is anticipated that this will increase sales to 4,500 units.
Using CVP Analysis Example
Using CVP Analysis Example
3,200 pairs of pants sold with no change in the selling price:
Operating income = $5,600
Sensitivity Analysis and
Uncertainty Example
Sensitivity Analysis and
Uncertainty Example
Assume that the Pants Shop can sell 4,000 pairs of pants.
Fixed costs are $84,000.
Contribution margin ratio is 40%.
Sensitivity Analysis and
Uncertainty Example
Sensitivity Analysis and
Uncertainty Example
To satisfy a demand for 4,000 pairs, management must acquire additional space for $6,000.
Should the additional space be acquired?
Sensitivity Analysis and
Uncertainty Example
Sensitivity Analysis and
Uncertainty Example
Operating income at $245,000 revenues with existing space = ($245,000 × .40)
– $84,000 = $14,000.
Sensitivity Analysis and
Uncertainty Example
Sensitivity Analysis and
Uncertainty Example
Operating income at $280,000 revenues with additional space = ($280,000 × .40) – $90,000
= $22,000.
Learning Objective 6
Learning Objective 6
Alternative Fixed/Variable Cost
Structures Example
Alternative Fixed/Variable Cost
Structures Example
What is the new contribution margin?
Decrease the price they charge from $32 to $25 and charge an annual administrative fee of $30,000. Suppose that the factory the Pants Shop is using to
Alternative Fixed/Variable Cost
Structures Example
Alternative Fixed/Variable Cost
Structures Example
$70 – ($25 + $10) = $35
Contribution margin increases from $28 to $35. What is the contribution margin percentage?
$35 ÷ $70 = 50%
Alternative Fixed/Variable Cost
Structures Example
Alternative Fixed/Variable Cost
Structures Example
Management questions what sales volume would yield an identical operating income
regardless of the arrangement. 28x – 84,000 = 35x – 114,000 114,000 – 84,000 = 35x – 28x
Alternative Fixed/Variable Cost
Structures Example
Alternative Fixed/Variable Cost
Structures Example
Cost with existing arrangement = Cost with new arrangement .60x + 84,000 = .50x + 114,000
.10x = $30,000 x = $300,000
Operating Leverage
Operating Leverage
Operating leverage describes the effects that fixed costs have on changes in operating
income as changes occur in units sold.
Operating Leverage Example
Operating Leverage Example
Degree of operating leverage
= Contribution margin ÷ Operating income What is the degree of operating leverage of the Pants Shop at the 3,500 sales level
under both arrangements? Existing arrangement:
Operating Leverage Example
Operating Leverage Example
$98,000 contribution margin – $84,000 fixed costs = $14,000 operating income
$98,000 ÷ $14,000 = 7.0 New arrangement:
Operating Leverage Example
Operating Leverage Example
$122,500 contribution margin – $114,000 fixed costs = $8,500
$122,500 ÷ $8,500 = 14.4
The degree of operating leverage at a given level of sales helps managers calculate the effect of
Learning Objective 7
Learning Objective 7
Effects of Sales Mix on Income
Effects of Sales Mix on Income
Pants Shop Example
Management expects to sell 2 shirts at $20 each for every pair of pants it sells.
Effects of Sales Mix on Income
Effects of Sales Mix on Income
What is the contribution margin of the mix? Contribution margin per shirt: $20 – $9 = $11
Effects of Sales Mix on Income
Effects of Sales Mix on Income
$84,000 fixed costs ÷ $50 = 1,680 packages 1,680 × 2 = 3,360 shirts
Effects of Sales Mix on Income
Effects of Sales Mix on Income
What is the breakeven in dollars?
Effects of Sales Mix on Income
Effects of Sales Mix on Income
What is the weighted-average budgeted contribution margin?
Effects of Sales Mix on Income
Effects of Sales Mix on Income
The breakeven point for the two products is: $84,000 ÷ $16.667 = 5,040 units
Effects of Sales Mix on Income
Effects of Sales Mix on Income
Sales mix can be stated in sales dollars: Pants Shirts Sales price $70 $40 Variable costs 42 18
Effects of Sales Mix on Income
Effects of Sales Mix on Income
Assume the sales mix in dollars is 63.6% pants and 36.4% shirts. Weighted contribution would be:
40% × 63.6% = 25.44% pants 55% × 36.4% = 20.02% shirts
Effects of Sales Mix on Income
Effects of Sales Mix on Income
Breakeven sales dollars is $84,000 ÷ 45.46% = $184,778 (rounding).
Learning Objective 8
Learning Objective 8
Adapt CVP analysis to situations
in which a product has more
Multiple Cost Drivers Example
Multiple Cost Drivers Example
Suppose that the business will incur an additional cost of $10 for preparing documents associated
with the sale of pants to various customers. Assume that the business sells 3,500
pants to 100 different customers.
Multiple Cost Drivers Example
Multiple Cost Drivers Example
Revenues: 3,500 × $70 $245,000 Variable costs:
Pants: 3,500 × $42 147,000 Documents: 100 × $10 1,000
Total 148,000
Multiple Cost Drivers
Multiple Cost Drivers
Would the operating income of the Pants Shop be lower or higher if the business sells pants
to more customers?
The cost structure depends on two cost drivers: 1. Number of units
Learning Objective 9
Learning Objective 9
Distinguish between
contribution margin
Contribution Margin versus
Gross Margin
Contribution Margin versus
Gross Margin
Contribution income statement emphasizes contribution margin.
End of Chapter 3