1. Cost-Volume-Profit Relationships
Chapter 6: Cost-volume-profit relationships.
Cost-volume-profit (CVP) analysis helps managers understand the interrelationships among cost, volume, and profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.
Chapter 6
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Basics of Cost-Volume-Profit Analysis
Contribution margin is used first to cover fixed expenses. Any remaining contribution margin contributes to net operating income.
CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.
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3. The Contribution Approach
Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.
Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. For each additional unit Racing Bicycle Company sells, $200 more in contribution margin will help to cover fixed expenses and provide a profit.
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4. The Contribution Approach
Each month, RBC must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).
Each month Racing Bicycle must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).
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5. The Contribution Approach
If RBC sells 400 units in a month, it will be operating at the break-even point.
If Racing sells 400 units a month, it will be operating at the break-even point. Total sales will be 400 units times $500 each or $200,000, and total variable expenses will be 400 units times $300 each for $120,000. Contribution margin is exactly equal to total fixed expenses. Let’s see what happens if Racing sells one more bike or a total of 401 bikes.
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6. The Contribution Approach
If RBC sells one more bike (401 bikes), net
operating income will increase by $200.
You can see that the sale of one unit above the break-even point yields net operating income of $200, which is the contribution margin per unit sold.
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7. CVP Relationships in Equation Form
When a company has only one product we can further refine this equation as shown on this slide.
Profit = (Sales – Variable expenses) – Fixed expenses
Part I
If the company sells a single product, like Racing Bicycle Company, we can express the sales and variable expenses as shown in the blue and brown boxes. Sales are equal to the quantity sold (Q) times the selling price per unit sold (P), and variable expenses are equal to the quantity sold (Q) times the variable expenses per unit (V).
Part II
For the single product company we can refine the equation as shown on the screen. We can complete the calculations shown in the previous slides using the contribution income statement approach using this equation. Let’s see how we do this.
Profit = (P × Q – V × Q) – Fixed expenses
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8. CVP Relationships in Equation Form
It is often useful to express the simple profit equation in terms of the unit contribution margin (Unit CM) as follows:
Unit CM = Selling price per unit – Variable expenses per unit
Unit CM = P – V
Profit = (P × Q – V × Q) – Fixed expenses
Profit = (P – V) × Q – Fixed expenses
Profit = Unit CM × Q – Fixed expenses
Part I
Unit contribution margin is equal to the unit selling price less the unit variable expenses. Using the equations we have developed, we can express the Unit CM as P less V.
Part II
Now, let’s rearrange the basic profit equation for a single product company and we can see that profit is equal to the unit CM times the quantity sold less the fixed expenses. Let’s use this new profit equation to calculate net operating income when Racing Bicycle sells 401 units.
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9. Preparing the CVP Graph
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Preparing the CVP Graph
Break-even point (400 units or $200,000 in sales)
Profit Area
Dollars
Part I
The break-even point is where the total revenue and total expenses lines intersect. In the case of Racing Bicycle, break-even is 400 bikes sold, or sales revenue of $200,000.
Part II
The profit or loss at any given sales level is measured by the vertical distance between the total revenue and the total expenses lines.
Loss Area
Units
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10. Preparing the CVP Graph
Profit = Unit CM × Q – Fixed Costs
An even simpler form of the CVP graph is called the profit graph.
An even simpler form of the CVP graph is called the profit graph. The graph is based on the equation – profit equals Unit Contribution Margin times quantity sold less total fixed costs. To build the graph, plot two profit or loss points (in our case 300 units and 500 units sold) and connect them with a straight line.
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11. Preparing the CVP Graph
Break-even point, where profit is zero , is 400 units sold.
This is the profit graph for Racing Bicycle Company. As you can see, the break-even point, where profit is equal to zero, is at 400 bicycles sold.
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12. Contribution Margin Ratio (CM Ratio)
The CM ratio is calculated by dividing the total contribution margin by total sales.
The contribution margin ratio is calculated by dividing the total contribution margin by total sales. In the case of Racing Bicycle, the ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢.
$100,000 ÷ $250,000 = 40%
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13. The formula uses the following equation.
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The Formula Method
The formula uses the following equation.
Target profit + Fixed expenses CM per unit =
Unit sales to attain the target profit
Target profit expressed in units sold. For this equation we divide the sum of the desired target profit plus total fixed expenses by the contribution margin per unit.
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14. Target Profit Analysis in Terms of Unit Sales
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Target Profit Analysis in Terms of Unit Sales
Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of $100,000.
Target profit + Fixed expenses CM per unit =
Unit sales to attain the target profit
$100,000 + $80,000
$200
Unit sales =
Part I
Suppose Racing Bicycle Company wants to earn net operating income of $100,000. How many bikes must the company sell to achieve this profit level? Let’s use the formula method.
Part II
Unit sales to attain the target profit level is equal the sum of $100,000 (the target profit) plus $80,000 (total fixed expenses) divided by the unit contribution margin of $200. We arrive at 900 units sold to earn net operating income of $100,000.
Unit sales = 900
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15. 3-15
Formula Method
We can calculate the dollar sales needed to attain a target profit (net operating profit) of $100,000 at Racing Bicycle.
Target profit + Fixed expenses
CM ratio =
Dollar sales to attain the target profit
$100,000 + $80,000
40%
Dollar sales =
Part I
The formula method is summarized on this slide. It can also be used to compute the dollar sales needed to attain a target profit. Study the equation in the box on your screen.
Part II
Suppose RBC wants to compute the dollar sales required to earn a target profit of $100,000. The formula method can be used to determine that sales must be $450,000 to earn the desired target profit.
Dollar sales = $450,000
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16. Break-even in Unit Sales: Equation Method
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Break-even in Unit Sales: Equation Method
Profits = Unit CM × Q – Fixed expenses
Suppose RBC wants to know how many bikes must be sold to break-even (earn a target profit of $0).
$0 = $200 × Q + $80,000
Profits are zero at the break-even point.
Part I
To find the break-even point, we set profits equal to zero, and solve for the unknown quantity, Q. Suppose RBC wants to know how many bikes must be sold to break-even (earn a target profit of $0).
Part II
Racing Bicycle has a unit contribution margin of $200, and total fixed expenses of $80,000. Take a second and solve this equation.
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17. Break-even in Dollar Sales: Formula Method
Now, let’s use the formula method to calculate the dollar sales at the break-even point.
Fixed expenses
CM ratio =
Dollar sales to break even
$80,000
40%
Dollar sales =
Part I
You can see that if we elect to use the formula method.
Part II
We calculate the same $200,000 sales at the break-even point.
Dollar sales = $200,000
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18. The Margin of Safety in Dollars
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The Margin of Safety in Dollars
The margin of safety in dollars is the excess of budgeted (or actual) sales over the break-even volume of sales.
Margin of safety in dollars = Total sales - Break-even sales
Let’s look at Racing Bicycle Company and determine the margin of safety.
The margin of safety helps management assess how far above or below the break-even point the company is currently operating. To calculate the margin of safety in dollars, we take total current sales and subtract break-even sales. Let’s calculate the margin of safety for RBC.
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19. Operating Leverage = Contribution margin Net operating income
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Operating Leverage
Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. It is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits.
Contribution margin
Net operating income
Degree of
operating leverage =
Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. The degree of operating leverage is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. It is computed by dividing contribution margin by net operating income. Let’s look at Racing Bicycle.
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20. Key Assumptions of CVP Analysis
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Key Assumptions of CVP Analysis
Selling price is constant.
Costs are linear and can be accurately divided into variable (constant per unit) and fixed (constant in total) elements.
In multiproduct companies, the sales mix is constant.
In manufacturing companies, inventories do not change (units produced = units sold).
Here are the four key assumptions of cost-volume-profit analysis. You are probably familiar with the first three by now. The forth assumption tells us that there can be no change in inventory levels. That is, all units produced are sold in the current period.
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21. End of Chapter 6
End of chapter 6.
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