1. Prepared by Debby Bloom-Hill CMA, CFM

2. CHAPTER 4
Cost-Volume-Profit Analysis
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3. Common Cost Behavior Patterns
Variable Costs:
Costs which change directly in proportion to changes in quantity or activity.
Fixed Costs:
Costs which do not change when quantity or activity volume changes.
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4. Common Cost Behavior Patterns
Mixed Costs:
Costs that have both variable and fixed elements.
Step Costs:
Fixed for a range of output, but increase when upper bound of range is exceeded.
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5. Variable Costs
Total Variable Cost = $91 × Units produced
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6. Fixed Costs
Total fixed cost = $94,000
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7. Mixed Costs
Total cost = ($91 × Units produced) + $94,000
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8. Step Costs Total step costs =
$7,000 for relevant range 0 – 3,000 units produced
$14,000 for relevant range 3,001 – 6,000 units
$21,000 for relevant range 6,001 – 9,000 units
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9. Relevant Range
The relevant range is the range of activity for which assumptions as to how costs behave are reasonably valid.
If it is known that production is going to be within the relevant range, we can use assumptions about the fixed and variable costs.
Making assumptions about fixed and variable costs at production levels well above or below this range would not be valid.
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10. The Relevant Range
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11. Cost Estimation Methods
Account Analysis:
Classify costs into variable and fixed pools.
Scattergraphs:
Can see cost relationships visually.
High-Low Method:
Linear estimation connects high and low volume observations.
Regression Analysis:
Linear estimation is best fit to observed values - Covered in the Appendix to Ch. 4.
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12. Account Analysis Most common approach.
Requires professional judgment of management.
Management classifies costs as fixed, variable, or mixed.
Total variable costs divided by activity equals variable cost per unit.
Variable cost per unit and total fixed costs can be used in cost equation.
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13. Account Analysis
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14. Scattergraphs
Utilization of cost information from several previous periods.
Weekly, monthly, or quarterly cost reports are useful.
Plot the actual costs at the observed activity levels.
Look for relationship between cost and activity, linear is ideal.
Use relationship to predict future costs.
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15. Scattergraphs
Is there a relationship between units produced and production costs? Describe the relationship.
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16. High-Low Method Utilization of cost information from previous periods.
Fits a straight line from lowest activity level to highest activity level.
Slope of the line is the estimate of the unit variable cost.
The slope measures the change in cost per unit change in activity level.
Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost.
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17. High-Low Method Total cost at high activity level
Total cost at low activity level
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18. High-Low Method
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19. High-Low Method
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20. Cost-Volume-Profit Analysis
The Profit Equation:
Profit = SP(x) – VC(x) – TFC
Where:
x = Quantity of units produced and sold
SP = Selling price per unit
VC = Variable cost per unit
TFC = Total fixed cost
Fundamental to CVP analysis.
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21. Cost-Volume-Profit Analysis
Break-Even Point:
Number of units sold that allow the company to neither earn a profit nor incur a loss.
$0 = SP(x) – VC(x) – TFC
CodeConnect has the following cost structure:
Selling price $ per unit.
Variable cost $90.83 per unit.
Total fixed cost $160,285.
Find CodeConnect’s break-even point.
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22. Cost-Volume-Profit Analysis
Break-Even Point:
$0 = SP(x) – VC(x) – TFC
$0 = $ (x) – $90.83(x) – $160,285
$0 = $109.17(x) – $160,285
$109.17(x) = $160,285
x = $160,285 / $109.17
x = 1, units
Break-even point is 1,469 units (always round up).
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23. Break-Even Point
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24. Margin of Safety
The margin of safety is the difference between the expected level of sales and break-even sales.
If breakeven sales for Model DX375 is $293,600 and expected sales are $350,000, calculate the margin of safety.
The margin of safety is:
$350,000 - $293,600 = $56,400.
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25. Margin of Safety Ratio
The margin of safety can also be expressed as a ratio.
Called the margin of safety ratio.
Equal to the margin of safety divided by expected sales.
Shows what percentage sales would have to drop before the product shows a loss.
= = = 0.16
Margin of
safety ratio
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26. Contribution Margin Difference between revenue and variable costs:
Contribution margin = total revenue minus total variable costs.
Contribution margin per unit = selling price minus variable cost per unit.
For CodeConnect’s Model DX375, the contribution margin per unit is the $ selling price less the variable cost of $90.83 =$ – $90.83 = $
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27. Contribution Margin
The contribution margin per unit measures the amount of incremental profit generated by selling 1 additional unit.
For CodeConnect, how much incremental profit would be generated by selling 100 more units?
Incremental profit = number of units sold * contribution margin per unit
Incremental profit = 100 * $ = $10,917.
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28. Contribution Margin
The profit equation in terms of the contribution margin:
Profit = SP(x) – VC(x) – TFC
Profit = (SP – VC)(x) – TFC
Profit = Contribution margin per unit(x) - TFC
At the Breakeven point (Profit = 0):
Contribution margin per unit (x) = TFC.
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29. Units Needed for Target Profit
Solve the profit equation for the sales quantity in units.
Unit sales (x) needed to attain a specified profit = =
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30. Contribution Margin Ratio
The unit contribution margin ratio measures the amount of incremental profit generated by an additional dollar of sales.
Two methods to calculate the contribution margin ratio:
Contribution margin divided by sales revenue (Sales – TVC) / Sales.
Unit contribution margin divided by selling price (SP – VC) / SP.
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31. Contribution Margin Ratio
For the Model DX375 bar code reader, the contribution margin ratio is: =
This indicates that the company earns an incremental $ for every dollar of sales.
If sales increase $10,000 the incremental profit is * $10,000 = $5,
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32. Multiproduct Analysis
Contribution margin approach:
Used if the items sold are similar.
Calculate a weighted average contribution margin per unit.
Use the weighted average contribution margin in the profit formula to calculate breakeven point and target sales.
The relative product mix is then used to calculate the required sales of individual items.
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33. Multiproduct Analysis
The company has fixed costs of $3,500,000.
Assume 2 units of Model A are sold for every 1 unit of Model B.
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34. Multiproduct Analysis:
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35. Multiproduct Analysis
Break-even sales in units:
The 2,500 units is made up of the 2:1 mix, so Rohr must sell 1,667 Model A (2/3 of 2,500) and 833 Model B units (1/3 of 2,500)
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36. Multiproduct Analysis
Contribution Margin Ratio Approach:
Products are substantially different.
Calculate total company contribution margin ratio.
Use total company contribution margin ratio to compute required sales in dollars.
Total company fixed costs (common costs) are not included for contribution margin approach but used for contribution margin ratio approach.
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37. Multiproduct Analysis
A company with 4 divisions has the following information available:
Total sales $6,450,000
Total variable costs $4,706,000
Total direct fixed costs $484,000
Total common fixed costs $1,120,000
Calculate total contribution margin ratio.
($6,450,000 – $4,706,000) / $6,450,000 = .2704
Calculate total company break-even sales in dollars.
($484,000 + $1,120,000) / = $5,931,953
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38. Assumptions in CVP Analysis
Assumptions can affect the validity of the analysis.
Costs can be separated into fixed and variable components.
Total fixed cost and unit variable cost do not change over the levels of interest.
Multiproduct analysis assumes the product mix does not change.
Despite assumptions, CVP is useful.
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39. Operating Leverage Level of fixed versus variable costs in a company.
A company with a high level of fixed costs has a high operating leverage.
Companies with high operating leverage have large fluctuations in profit when sales increase or decrease.
These companies are seen as more risky.
High operating leverage is better when sales are expected to increase.
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40. Constraints
Due to shortages of space, equipment or labor there can be constraints on how many items can be produced.
Utilize contribution margin per unit to analyze situations.
Calculate contribution margin per unit of constraint.
Produce product with highest contribution margin per unit of constraint.
Linear programming can solve multiple constraints.
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41. Constraints
A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available.
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42. Constraints With the 1,000 available machine hours,
Product A generates $20,000 of contribution margin.
Product B generates $50,000 of contribution margin.
Although Product A has the higher contribution margin per unit, Product B has the higher contribution margin per unit of constraint.
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43. Copyright
© 2010 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.
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