1. Determine the break-even point in number of units and in
total sales dollars.
2. Determine the number of units that must be sold, and the amount
of revenue required, to earn a targeted profit.
3. Prepare a profit-volume graph and a cost-volume-profit graph and
explain the meaning of each.
4. Apply cost-volume-profit analysis in a multiple-product setting.
5. Explain the impact of risk, uncertainty, and changing variables
on cost-volume-profit analysis.
Cost-volume-profit analysis (CVP analysis) is a tool for planning and decision making. It enables a firm to determine the sales (in units or dollars) necessary to attain a desired level of profit. CVP analysis is useful in assessing the effect of operating changes (such as changes in selling price or operating costs) upon profit.
1. BREAK-EVEN POINT IN UNITS AND SALES
- The break-even point is the point where total revenue equal total cost, the point of zero profit.
A. Using Operating Income in CVP Analysis
- A functional income statement was used that classified expenses by function as:
1. manufacturing costs (both fixed and variable)
2. selling and administrative costs (both fixed and variable)
The format used when costs are classified by function for absorption costing is:
Sales
– Cost of goods sold (Manufacturing costs)
= Gross margin
– Selling and administrative expenses
= Net income
- For CVP analysis, a contribution margin income statement is used that classifies costs by behavior as:
1. variable costs
variable manufacturing
variable selling and administrative
2. fixed costs
- fixed manufacturing
- fixed selling and administrative
- The format used for a contribution margin income statement follows:
Sales
– Variable expenses:
Variable cost of goods sold
Variable selling and administrative
= Contribution margin
– Fixed expenses:
Fixed overhead
Fixed selling and administrative
= Net income
- Contribution margin equals sales less all variable expenses. It is the amount left after variable expenses are covered, the amount that contributes to covering fixed expenses and operating income.
Cornerstone 4-1: How to Prepare a Contribution Margin Income Statement
- See Mowen and Hansen text afor in-class, demo problems.
B. Break-Even Point in Units
- If the contribution margin income statement is recast as an equation, the operating-income equation is:
- Operating income = Sales – Total variable expenses – Total fixed expenses
OR
Operating income = (Price × Units sold) – (Variable cost per unit × Units sold) – Total fixed expenses
- At breakeven, this can also be expressed as:
Total revenue – Total variable cost – Total fixed cost = $0
or
Total revenue = Total variable cost + Total fixed cost
C. Shortcut to Calculating Break-Even Units
- To determine how many units must be sold in order to break even, solve for X (the number of units) in the following equation:
Total revenue = Variable cost + Fixed cost
(Selling price per unit)( X) = (Variable cost per unit)( X) + Fixed cost
X = 
X = 
- Contribution margin per unit is calculated as:
Contribution margin per unit = Selling price per unit – Variable cost per unit
Cornerstone 4-2: How to Solve for the Break-Even Point in Units
- See Mowen and Hansen text for in-class, demo problems.
D. Break-Even Point in Sales Dollars
- Break-even in units can be converted to break-even in sales revenue as follows:
Break-even sales = (Selling price per unit × Unit sales at break-even)
- Also, break-even in sales dollars can be calculated using the following equation:
Break-even sales = 
Cornerstone 4-3: How to Calculate the Variable Cost Ratio and the Contribution Margin Ratio
- See Mowen and Hansen text for in-class, demo problems.
Cornerstone 4-4: How to Solve for the Break-Even Point in Sales Dollars
- See Mowen and Hansen text for in-class, demo problems.
2. UNITS AND SALES DOLLARS NEEDED TO ACHIEVE A TARGET PROFIT
- In order to earn a desired profit, total revenues must equal variable costs, fixed costs and desired profit.
Total revenue = Total variable cost + Total fixed cost + Desired profit
A. Units to Be Sold to Achieve a Target Income
To determine how many units must be sold in order to earn a desired profit, solve for X (the number of units) in the following equation:
Total revenue = Total variable cost + Total fixed cost + Desired profit
(Selling price per unit)( X) = (Variable cost per unit)( X) + Total fixed cost + Desired profit
X = 
X = 
After fixed costs are covered, the contribution margin per unit above break-even volume is profit per unit.
Cornerstone 4-5: How to Solve for the Number of Units to Be Sold to Earn a Target Operating Income
- See Mowen and Hansen text for in-class, demo problems.
B. Sales Revenue to Achieve a Target Income
- Sales dollars necessary to earn a desired profit can be calculated as:
Sales revenue = 
Cornerstone 4-6: How to Solve for the Sales Needed to Earn a Target Operating Income
- See Mowen and Hansen text for in-class, demo problems.
3. GRAPHs of CVP RELATIONSHIPS
This section discusses the cost-volume-profit graph.
A. The Profit-Volume Graph
- The profit-volume graph portrays the relationship between profits and sales volume.
B. The Cost-Volume-Profit Graph
- The cost-volume-profit graph depicts the relationships among cost, volume, and profits.
- The point where the total revenue line and the total cost line intersect is the break-even point.
C. Assumptions of Cost-Volume-Profit Analysis
- Limitations of CVP analysis include:
- The analysis assumes a linear revenue function and a linear cost function.
- The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range.
- The analysis assumes that units produced are sold.
- For multiple-product analysis, the sales mix is assumed to be known.
- The selling prices and costs are assumed to be known with certainty.
4. MULTIPLE-PRODUCT ANALYSIS
A. Break-Even Point in Units
- When CVP analysis is used for a multiple-product firm, the product is defined as a package of products. For example, if the sales mix is 3:1 for Products A and B, the package would consist of 3 units of Product A and 1 unit of Product B.
- The contribution margin per package is calculated as:
(Contribution margin per unit of A × Sales mix for A)
+ (Contribution margin per unit of B × Sales mix for B)
= Package contribution margin
- Break-even in packages for a multiple-product firm is then calculated as:
Break-even packages = 
- Direct fixed expenses are fixed costs that can be traced to each segment (or product) and would be avoided if the segment did not exist.
- Common fixed expenses are the fixed costs that are not traceable to the segments and would remain even if one of the segments was eliminated.
- The contribution margin income statement format used for multiple products is:
Sales
Less: Variable expenses
Contribution margin
Less: Direct fixed expenses
Product margin
Less: Common fixed expenses
Operating income
Cornerstone 4-7: How to Calculate the Break-Even Units for a Multiple-Product Firm
- See Mowen and Hansen text for in-class, demo problems.
B. Break-Even Point in Sales Dollars
- Break-even in sales dollars for a multiple-product firm is calculated as:
Break-even sales = 
- The contribution margin ratio is calculated as:
Contribution margin ratio = Total contribution margin/Total sales
Cornerstone 4-8: How to Calculate the Break-Even Sales Dollars for a Multiple-Product Firm
- See Mowen and Hansen text for in-class, demo problems.
5. CVP ANALYSIS AND RISK AND UNCERTAINTY
A. Margin of Safety
- Margin of safety is a measure of how far sales can drop until the break-even point is reached. It is a crude measure of risk.
- The margin of safety expressed in dollars is the difference between budgeted sales and break-even sales.
Margin of safety = Expected sales – Sales at break-even
Cornerstone 4-9: How to Compute the Margin of Safety
- See Mowen and Hansen text for in-class, demo problems.
B. Operating Leverage
- Operating leverage is concerned with the mix of fixed costs and variable costs. For example, if a firm chooses to automate its operations, fixed costs increase, variable costs (direct labor) decrease, and operating leverage increases.
- The degree of operating leverage (DOL) is a measure of the sensitivity of profit changes to changes in sales volume. DOL measures the percentage of change in profit that results from a percentage of change in sales.
Degree of operating leverage = Contribution margin/Operating income
- The higher the degree of operating leverage, the greater the change in profit when sales change.
Percentage change in profit = DOL × Percentage change in sales
Cornerstone 4-10: How to Compute the Degree of Operating Leverage
- See Mowen and Hansen text for in-class, demo problems.
Cornerstone 4-11: How to Compute the Impact of Increased Sales on Operating Income Using the Degree of Operating Leverage
- See Mowen and Hansen text for in-class, demo problems.
C. Sensitivity Analysis and CVP
- Sensitivity analysis is a “what if” technique that examines the impact of changes on an answer. For example, computer spreadsheets are used to analyze changes in prices, variable costs, and fixed costs on expected profits.
