1. Cornerstones of Managerial Accounting, 5e
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2. Chapter 4: Cost-Volume-Profit Analysis: A Managerial Planning Tool
Cornerstones of Managerial Accounting, 5e
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3. Break-Even Point in Units and in Sales Dollars
Companies use CVP analysis to help them reach important benchmarks, like breakeven point.
The break-even point is the point where total revenue equals total cost (i.e., the point of zero profit).
Also the level of sales at which contribution margin just covers fixed costs and when operating income is equal to zero.
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4. Break-Even Point in Units and in Sales Dollars (cont.)
Since new companies typically experience losses (negative operating income), they view their first break-even period as a significant milestone.
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5. Using Operating Income in Cost-Volume-Profit Analysis
For CVP analysis, it is useful to organize costs into fixed and variable components.
Below is the income statement format that is based on the separation of costs into fixed and variable components is called the contribution margin income statement.
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6. Using Operating Income in Cost-Volume-Profit Analysis (cont.)
Direct materials
Variable selling and administrative costs
Direct labor
Variable overhead
Fixed selling and administrative costs
Fixed overhead
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7. Using Operating Income in Cost-Volume-Profit Analysis
Contribution margin is the difference between sales and variable expense.
The amount of sales revenue left over after all the variable expenses are covered that can be used to contribute to fixed expense and operating income.
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8. Using Operating Income in Cost-Volume-Profit Analysis
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9. Break-Even Point in Units
If the contribution margin income statement is recast as an equation, it becomes more
useful for solving CVP problems.
Basic CVP Equation
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10. Break-Even Point in Units (cont.)
Break-even units are equal to the fixed cost divided by the contribution margin per unit.
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11. Break-Even Point in Sales Dollars
Managers using CVP analysis may use sales revenue as the measure of sales activity instead of units sold. A units sold measure can be converted to a sales revenue measure by multiplying the unit selling price by the units sold:
For example, the break-even point for Whittier is 600 mowers; the selling cost is $400 per mower.
Breakeven in Sales $’s = 600 x $400 = $240,000
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12. Variable Cost Ratio and Contribution Margin Ratio
Any answer expressed in units sold can be easily converted to one expressed in sales revenues.
Variable Cost Ratio
Contribution Margin Ratio
Alternatively:
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13. Fixed Cost’s Relationship with Variable Cost Contribution & Margin Ratios
Since the total contribution margin is the revenue remaining after total variable costs are covered, it must be the revenue available to cover fixed costs and contribute to profit.
How does the relationship of fixed cost to contribution margin affect operating income?
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14. Fixed Cost’s Relationship with Variable Cost Contribution & Margin Ratios
There are three possibilities:
Fixed cost equals contribution margin; operating income is zero; the company breaks even.
Fixed cost is less than contribution margin; operating income is greater than zero; the company makes a profit.
Fixed cost is greater than contribution margin; operating income is less than zero; the company makes a loss.
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15. Units to Be Sold to Achieve a Target Income
While the break-even point is useful information and an important benchmark for relatively young companies, most companies would like to earn operating income greater than $0.
CVP allows us to do this by adding the target income amount to the fixed cost.
First, let’s look in terms of units that must be sold.
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16. Sales Revenue to Achieve a Target Income
How much sales revenue must Whittier generate to earn an operating income of $37,500?
This question is similar to the one we asked earlier in terms of units but phrases the question directly in terms of sales revenue.
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17. Sales Revenue to Achieve a Target Income
To answer the question, add the targeted operating income of $37,500 to the $45,000 of fixed cost and divide by the contribution margin ratio. This equation is:
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18. Impact of Change in Revenue on Change in Profit
Assuming that fixed costs remain unchanged, the contribution margin ratio can find the profit impact of a change in sales revenue.
To obtain the total change in profits from a change in revenues, multiply the contribution margin ratio times the change in sales:
Change in
Profits
Contribution
Margin
Ratio
Change in
Sales = x
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19. Graphs of Cost-Volume-Profit Relationships: The Profit-Volume Graph
A profit-volume graph visually portrays the relationship between profits (operating income) and units sold.
The profit-volume graph is the graph of the operating income equation:
Operating income = (Price x Units) –
(Unit variable cost x Units) – Total fixed cost
In the following graph, operating income is the dependent variable, and units is the independent variable.
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20. Graphs of Cost-Volume-Profit Relationships: The Profit-Volume Graph
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21. The Cost-Volume-Profit Graph
The cost-volume-profit graph depicts the relationships among cost, volume, and profits (operating income).
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22. The Cost-Volume-Profit Graph (cont.)
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23. CVP Analysis Assumptions
Major assumptions of CVP analysis include: 1 2
Linear revenue and cost functions remain constant over the relevant range.
Selling prices and costs are known with certainty. 3 4
All units produced are sold; no finished goods inventories remain.
Sales mix is known with certainty for multiple-product break-even settings.
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24. Multiple-Product Analysis
Cost-volume-profit analysis is simple in the single-product setting. However, most firms produce and sell a number of products or services.
How do we adapt the formulas used in a single-product setting to a multiple-product setting?
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25. Multiple-Product Analysis (cont.)
One important distinction is to separate direct fixed expenses from common fixed expenses.
Direct fixed expenses are those fixed costs that can be traced to each segment 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.
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26. Break-Even Calculations for Multiple Products
When more than one product is produced and sold, managers must estimate the sales mix and calculate a package contribution margin.
Sales mix is the relative combination of products being sold by a firm.
Fixed Costs
Package Contribution Margin
Break-Even Packages =
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27. Cost-Volume-Profit Analysis and Risk and Uncertainty
Managers must be aware of so many factors in our dynamic world. CVP analysis is a tool that managers use to handle risk and uncertainty.
Risks??
Changes in prices??
Fixed costs??
Uncertainty??
Variable costs??
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28. Methods to Deal with Uncertainty and Risk
1. Management must realize the uncertain nature of future prices, costs, and quantities.
2. Management must assume a breakeven “band” rather than a breakeven point.
3. Managers should use sensitivity or “what- if” analyses.
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29. Sales - Break-even units = 500 – 200 = 300 units
Margin of Safety
The margin of safety is the units sold or the revenue earned above the break-even volume.
Example: If the break-even volume for a company is 200 units and the company is currently selling 500 units, the margin of safety in units is:
Sales - Break-even units = 500 – 200 = 300 units
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30. Margin of Safety (cont.)
If the break-even volume for a company is $200,000 and the current revenues are $500,000, the margin of safety in sales revenue is:
Revenue - Break-even volume = $500,000 – 200,000 = $300,000
The margin of safety as a percentage of total sales dollars can then be expressed as:
Margin of safety ÷ Revenues = $300,000 ÷ $500,000 = 60%
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31. Operating Leverage
Operating leverage is the use of fixed costs to extract higher percentage changes in profits as sales activity changes.
Measure of the proportion of fixed costs in a company’s cost structure.
Used as an indicator of how sensitive profit is to changes in sales volume.
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32. Operating Leverage (cont.)
The degree of operating leverage (DOL) can be measured for a given level of sales by taking the ratio of contribution margin to operating income or:
Contribution margin ÷ Operating income
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33. Summary of Operating Leverage
HIGH
LOW
% profit increase with sales increase
Large
Small
% loss increase with sales decrease
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34. Sensitivity Analysis LO-5
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