1. Cornerstones of Managerial Accounting 2e Chapter Four
Cost-Volume-Profit Analysis: A Managerial Planning Tool
Mowen/Hansen
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2. Cost-Volume-Profit Analysis
A powerful tool for planning and decision making. It can be used to calculate:
The number of units that must be sold to break-even
The impact of an increase in price on profit.
The impact of a given reduction in fixed costs on the break-even point.

3. Or to put it another way:
Break-Even Point
Total Revenue =
Total Cost
Or to put it another way:
Total Revenue
– Total Cost
Zero Profit

4. Using Operating Income in Cost-Volume-Profit Analysis
Contribution Margin
Variable Expense
Contribution Margin
Sales - =
Contribution Margin is then used to cover Fixed Costs and Operating Income.

5. Contribution Margin Income Statement
Divides costs based on behavior
Costs are divided into variable and fixed components
Important subtotal is contribution margin
Sales revenue minus variable expenses

6. Break-even point is when Operating Income is zero.
Contribution Margin
Variable Expense
Contribution Margin
Sales - =
Contribution Margin
Fixed Costs
Operating Income - =
Break-even point is when Operating Income is zero.

7. Units to Be Sold to Achieve a Target Income
Two ways:
Using Operating Income equation
Using the Basic Break-even equation
Cornerstone 4-5 will walk us through these computations

8. Units to Be Sold to Achieve a Target Income
Number of units to earn target income
Fixed Cost + Target Income =
Price – Variable Cost per unit
Number of units to earn target income
$45,000 + $37,500 =
$400 - $325
Number of units to earn target income
1,100 =

9. Sales Revenue to Achieve a Target Income
Sales dollars to earn target income
Fixed Cost + Target Income =
Contribution margin ratio
Sales dollars to earn target income
$45,000 + $37,500 =
0.1875
Sales dollars to earn target income
$440,000 =

10. Profit-Volume Graph
Visually portrays the relationship between profits and units sold
Operating Income is the dependent variable
Units sold is the independent variable

11. Cost-Volume-Profit Graph
Depicts the relationship among cost, volume, and profits
To obtain the more detailed relationships, it is necessary to graph two separate lines:
Total revenue
Total cost
The vertical axis is measured in dollars
The horizontal axis is measured in units sold

12. Assumptions of Cost-Volume-Profit Analysis
Revenue and cost functions are linear
Price, total fixed costs, and unit variable costs can be identified and remain constant over relevant range
All units produced are sold-there are no change in inventory levels
Sales mix is constant
Selling prices and costs are known with certainty

13. Linear Cost and Revenue Functions
Cost-Volume-Profit assumes that cost and revenue functions are linear. In other words they are straight lines.

14. Production Equal to Sales
Cost-Volume-Profit assumes that what is produced is actually sold
Inventory levels do not change over the period
CVP focuses on current costs by excluding inventory costs of previous periods

15. Constant Sales Mix
Multiple product break-even analysis requires a constant sales mix.
Relative combination of products being sold by a firm
Sales mix is difficult to predict with certainty

16. Certainty of Prices and Costs
In actuality, firms seldom know prices, variable costs, and fixed costs with certainty. There are formal ways of explicitly building uncertainty into the Cost-Volume-Profit model.

17. Multiple-Product Analysis
Cost-Volume-Profit analysis becomes more complex with multiple products.
We need to adapt the single-product formulas.

18. Direct Fixed Expenses
Those fixed costs that can be traced to each segment and would be avoided if the segment did not exist.

19. Common Fixed Expenses
The fixed costs that are not traceable to the segments and would remain even if one of the segments was eliminated.

20. Multiple-Product Analysis
Break-even point in units
Key is to identify the expected sales mix.
Sales mix is the relative combination of products being sold by a firm.

21. Sales Mix Measured in units sold
Reduced to the smallest possible whole numbers
Required in order to determine break even point in units

22. CVP Analysis: Risk and Uncertainty
The break-even point can be affected by changes in:
Price
Unit contribution margin
Fixed cost
Changes in any of the above will
affect the sales mix.

23. Risk and Uncertainty Effects on Managers
Management must realize the uncertain nature of future prices, costs, and quantities.
Managers move from consideration of a break-even point to what might be called a “break-even band”.
Managers may engage in sensitivity or what-if analysis.

24. Margin of Safety
The units sold or the revenue earned above the break-even volume.
Can be viewed as a crude measure of risk.
When there is a downturn in sales, the risk of suffering losses will be less if the firm’s margin of safety is large than if the margin of safety is small.

25. Margin of Safety 400 1,000 600 Margin of Safety in units
Sales in units
Break-even units = -
Margin of Safety in units =
1,000 -
600
Margin of Safety in units
400 =

26. Margin of Safety $160,000 Margin of Safety in sales revenue
Break-even sales =
Sales -
Margin of Safety in sales revenue =
$400(1,000) -
$400(600)
Margin of Safety in sales revenue
$160,000 =

27. Degree of Operating Leverage
The relative mix of fixed costs to variable costs in a company
Higher proportions of fixed costs to the amount of variable costs create higher operating leverage
The greater the degree of operating leverage, the larger the effect on operating income when sales change
Degree of Operating Leverage
Contribution Margin =
Operating Income

28. Operating Leverage
The degree of operating leverage (DOL) can be measured for a given level of sales.
Degree of operating leverage
Contribution Margin =
Operating Income
Degree of operating leverage
($400 – $325)(1,000 units) =
$30,000
Degree of operating leverage
2.5 =

29. Percentage Change in Operating Leverage=
DOL x
% change in sales
% change in operating leverage
2.5
20% = x
% change in operating leverage
50% =

30. Expected Operating Income
Original operating income =
(% change x Orig. operating income) +
Expected Operating Income =
$30,000
+ (0.50 x $30,000)
Expected Operating Income
$45,000 =