C5 Cost-Volume-Profit Relationships Changes in Fixed Costs and Sales Volume
Basics of Cost-Volume-Profit Analysis • What is the profit impact if Racing Bicycle can increase unit
• The contribution income statement emphasizes on cost sales from 500 to 540 by increasing the monthly advertising
behavior. budget by $10,000?
• Contribution Margin (CM) is the amount remaining from New Profit = ($500 × 540) – ($300 × 540) – $80,000 – 10,000
sales revenue after variable expenses have been deducted. or 40% × ($500 × 540) – $80,000 – 10,000 = 18,000
• CM is used first to cover fixed expenses. Any remaining CM Change in profit = 18,000 – 20,000 = -2,000
contributes to net operating income. • A shortcut solution using incremental analysis
• It is helpful to managers in judging the impact on profits of
changes in selling price, cost, or volume.
ex. If Racing sells an additional bicycle, $200 additional CM
will be generated to cover fixed expenses and profit.
Change in Variable Costs and Sales Volume
CVP Relationships in Equation Form • What is the profit impact if Racing Bicycle can use higher
•The contribution format income statement can be expressed quality raw materials, thus increasing variable costs per unit
in the following equation: by $10, to generate an increase in unit sales from 500 to 580?
Profit = (sales – variable expenses) – fixed expenses New profit = ($500 × 580) – ($310 × 580) – $80,000 or
Profit = total contribution margin – fixed expenses New Profit = (190 / $500) × ($500 × 580) – $80,000 = 30,200
ex. Profit = ($500 × 500) – ($300 × 500) – $80,000 Change in profit = 30,200 – 20,000 = 10,200
Profit = $250,000 – $150,000 – $80,000 • A shortcut solution using incremental analysis
Change in profit = change in total CM
• For a company with only one product, = 190*580 – 200*500
Profit = (selling price per unit × quantity sold – = 10,200
variable expenses per unit × quantity sold )
– Fixed expenses, *In-class Exercise: P5-21A, Q1, 3, and 5
Profit = (P × Q – V × Q) – fixed expenses
Profit = unit contribution margin × Q – fixed expenses Target Profit Analysis
ex. Profit = $200 × 500 – $80,000 Determine unit sales to attain a target profit using either:
1. Equation method
Contribution Margin Ratio (CM Ratio) Profit = Unit CM × Q – Fixed expenses
• CM ratio = Total contribution margin/Total sales Solve for Q
Answers what % of each sales $ results in 2. Formula method
• For a company with only one product
CM ratio = Unit contribution margin/ Unit selling price
Profit = CM ratio × Sales – Fixed expenses • Suppose Racing Bicycle management wants to know how
many bikes must be sold to earn a target profit of $100,000.
• Equation method:
$100,000 = $200 X Q - $80,000
Q = 900
• Formula method
unit sales = ($100,000 + $80,000) / $200 = 900
• Determine sales dollars to attain a target profit using either:
Note: variable expense ratio = variable expenses/sales = 60% 1.Equation method
Profit = 40% × $250,000 – $80,000 Profit = CM ratio × Sales – Fixed expenses
Solve for Sales
Applications of CVP Analysis 2.Formula method
• It is a business tool for short-term decisions
• Effect on contribution margin and profit of
in: • Suppose RBC management wants to know the sales volume
• sales price or volume that must be generated to earn a target profit of $100,000.
• variable cost • Equation method:
• fixed costs $100,000 = 40% X Sales - $80,000
• Target profit analysis Sales = $450,000
• Break-even analysis • Formula method
Dollar sales = ($100,000 + $80,000) / 40% = $450,000
Break-even Analysis Operating Leverage: measure of how sensitive net operating
• Determine the unit sales and dollar sales needed to achieve income is to percentage changes in sales.
a target profit of zero. • at any given level of sales, of how a percentage
• Sales below the breakeven point result in a loss change in sales volume will affect profits
• Sales above the breakeven point provide a profit
• Equation method
0 = Unit CM × Q – Fixed expenses, solve for Q
0 = CM ratio × Sales – Fixed expenses, solve for Sales •Degree of Operating Leverage: $100,000/$20,000 = 5
• Formula method
Unit sales to break-even = fixed expenses / CM per unit
Dollar sales to break-even = fixed expenses / CM ratio
• Suppose RBC wants to know how many bikes must be sold
$0 = $200 X Q - $80,000, Q = 400; or • With an operating leverage of 5, if RBC increases its sales by
Q = $80,000 / $200 = 400 10%, net operating income would increase by 50%.
• How about sales dollars to break-even
$0 = 40% X Sales - $80,000, Sales = $200,000, or
Dollar sales = $80,000 / 40% = $200,000
Margin of Safety
• The excess of sales over the break-even volume of sales
• Margin of safety in dollars = Total sales - Break-even sales
• Margin of safety percentage = Margin of safety in dollars /
• Can be viewed as a crude measure of risk.
• When there is a downturn in sales, the risk of • 10% increase in sales from $250,000 to $275,000 results in
suffering losses will be less if the firm’s margin of safety is a 50% increase in income from $20,000 to $30,000.
large than if the margin of safety is small.
*In-class Exercises: E5-16, E5-9
•If we assume that RBC has actual sales of $250,000, given
that the break-even sales are $200,000, the margin of safety
is $50,000 or 20% of sales.
Cost Structure and Profit Stability
• Cost structure refers to the relative proportion of fixed and
variable costs in an organization.
• Managers often have some latitude in determining their
organization’s cost structure.
• An advantage of a high fixed cost structure is that income
will be higher in good years compared to companies with
lower proportion of fixed costs.
• A disadvantage of a high fixed cost structure is that income
will be lower in bad years compared to companies with lower
proportion of fixed costs.
• Companies with low fixed cost structures enjoy greater
stability in income across good and bad years
Cost-volume-profit (CVP) analysis helps managers Target profit analysis
understand the interrelationships among cost, volume, and We can compute the number of units that must be
profit by focusing their attention on the interactions among sold to attain a target profit using either the equation
the prices of products, volume of activity, per unit variable method or the formula method. How to do that?
costs, and total fixed costs. It is a vital tool used in many We can also compute the target profit in sales
business decisions such as deciding what products to dollars using either the equation method or the formula
manufacture or sell, what pricing policy to follow, what method. How to do that?
marketing strategy to employ, and what type of productive
facilities to acquire. Break-even analysis
The equation and formula methods can be used to
The contribution income statement and contribution margin determine the unit sales and dollar sales needed to achieve a
The contribution income statement is helpful to target profit of zero. How to do that?
managers in judging the impact on profits of changes in
selling price, cost, or volume. The emphasis is on cost Margin of safety
behavior. Variable costs are separate from fixed costs. The The margin of safety in dollars is the excess of
contribution margin is defined as the amount remaining from budgeted (or actual) sales over the break-even volume of
sales revenue after variable expenses have been deducted. sales. It is a useful tool if a firm is worried about declining
Contribution margin is used first to cover fixed expenses. Any sales (e.g., new competition, economic downturn, weather
remaining contribution margin contributes to net operating disappointments).
income. How to compute margin of safety in dollars and percentage?
Contribution margin can also be expressed on a per
unit basis—Sales price for one unit less variable cost for one CVP considerations in choosing a cost structure
unit. Contribution margin can also be expressed as Cost structure refers to the relative proportion of
contribution margin ratio—Contribution margin/Sales, which fixed and variable costs in an organization. Managers often
indicates the percentage of sales dollars available to cover have some latitude in determining their organization's cost
fixed costs. structure. What are the advantages and disadvantages of
having a high fixed cost or a low fixed cost structure?
Basics of Cost-Volume-Profit Analysis
The relationships among revenue, cost, profit, and Operating leverage
volume can be expressed in equation form for those who How to compute the degree of operating leverage at
prefer an algebraic approach to solving problems. a particular level of sales? Also, explain how it can be used to
Profit = (sales – total variable expenses) – fixed expenses predict changes in net operating income.
Can you refine this equation if the company has only one Note: Skip structuring sales commissions and sales mix (pp.
This equation can also be expressed using unit
contribution margin. How?
This equation can also be expressed using
contribution margin ratio. How?
Note: The CVP relationships expressed graphically is not
required (skip pages 192-194).
Applications of CVP concepts
You can also use above approaches to “play-with”
your costs. For example, you could show the effects on
contribution margin and profit of changes in variable costs,
fixed costs, selling price, and volume.