1. Cost-Volume-Profit Analysis and Planning
Module 16
Cost-Volume-Profit Analysis and Planning
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2. 1
Describe the uses and limitations of traditional cost-volume-profit analysis.
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3. Profitability Analysis
Involves examining the relationships among revenues, costs, and profits
Widely used in the economic evaluation of existing or proposed products or services
Performed before decisions are finalized
What you need to understand to perform profitability analysis
Selling prices
Behavior of activity cost drivers
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4. Cost-Volume-Profit Analysis
CVP
A technique to examine the relationships among total volume of an independent variable, total costs, total revenues, and profits for a time period.
Useful in the early stages of planning
Provides an easily understood framework for discussing planning issues and organizing relevant data
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5. CVP Use in For-Profit Companies
Provides answers to questions such as…
How many cappuccinos must Starbucks sell to earn total profit of $50,000?
At what sales volume will McDonald’s total revenues and total costs be equal?
What profit will Office Max earn at sales volume of $200 million?
What will happen to Disney’s profit if ticket selling prices are increased by 10% and fixed costs increase by 8%?
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6. CVP Use in Not-For-Profit Companies
Used by not-for-profit entities to…
Establish service levels
Plan fund-raising events
Determine funding requirements
Answers questions such as…
How many homeless people can the Homeless Center house with a budget of $400,000?
How much money must be raised from alumni at Princeton to provide 50 full scholarships?
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7. CVP Assumptions All costs are classified as fixed or variable.
The total cost function is linear within the relevant range.
The total revenue function is linear within the relevant range.
The analysis is for a single product, or the sales mix of multiple products is constant.
There is only one activity cost driver: unit or dollar sales volume.
Accuracy decreases as the scope of operations being analyzed increases.
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8.  = R – Y R = pX Y = a + bX The Profit Formula
Profit () of a product, service or event = Total revenues (R) minus total costs (Y):
 = R – Y
Revenues (R) are a function of unit sales volume (X) and unit selling price (p):
R = pX
Total costs for a time period (Y) are a function of fixed costs per period (a) and unit variable costs (b):
Y = a + bX
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9. Expanded Profit Formula
The expanded profit formula is:
π = pX – (a + bX)
Used to predict profit at any specified activity level, represented by X.
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10. Using the Profit Formula
To use the profit formula
Separate all the company’s costs into variable and fixed components
Nature of costs
Variable Costs
The cost of the primary raw materials converted into finished goods
Direct Materials
Wages earned by production employees converting raw materials into finished goods
Direct Labor
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11. Variable and Fixed Components
Variable Costs
All other variable costs associated with converting raw materials into finished goods
Variable manufacturing overhead
All variable costs not directly associated with converting raw materials into finished goods
Variable selling and administrative costs
Fixed Costs
All fixed costs associated with converting raw materials into finished goods
Fixed manufacturing overhead
All fixed costs not directly associated with converting raw materials into finished goods
Fixed selling and administrative costs
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12. Example Using the Profit Equation
Chillin’ Time produces and sells one product, ice cream bars, for $1.50 each. To ensure top quality, no inventories are maintained. Estimated costs are:
Variable Costs Per Ice Cream Bar
Fixed Costs Per Month
Manufacturing costs:
Manufacturing overhead
$1,200
Direct materials
$0.43
Selling and administrative
580
Direct labor
0.32
Total
$1,780
0.20
$0.95
0.15
$1.10
Profit Formula to earn $1,000
$1,000 = $1.50X - $1,780 - $1.10X
X = 6,950 ice cream bars
Chillin’ Time must sell 6,950 ice cream bars each month to result in $1,000 profit.
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13. Prepare and contrast contribution and functional income statements.2
Prepare and contrast contribution and functional income statements.
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14. Income Statement Formats
Contribution Income Statement
Functional Income Statement
Costs are classified according to behavior
Variable
Fixed
Contribution margin
Total revenues less total variable costs
Represents the amount that goes toward covering fixed costs and providing a profit
Costs are classified according to function
Manufacturing
Selling and administrative
Gross Margin
Total revenues less cost of goods sold
Represents the amount that goes toward covering other expenses and providing a profit
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15. Contribution Income Statement Example
CHILLIN’ TIME
Contribution Income Statement
For a Monthly Volume of 6,950 Ice Cream Bars
Sales (6,950 x $1.50)
$10,425.
Less variable costs:
Direct materials (6,950 x $0.43)
$2,988
Direct labor (6,950 x $0.32)
2,224
Manufacturing overhead (6,950 x $0.20)
1,390
Selling and administrative (6,950 x $0.15)
1,043
(7,645)
Contribution margin
2,780.
Less fixed costs:
Manufacturing
1,200
Selling and administrative
580
(1,780)
Profit
$ 1,000.
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16. Functional Income Statement Example
CHILLIN’ TIME
Functional Income Statement
For a Monthly Volume of 6,950 Ice Cream Bars
Sales (6,950 x $1.50)
$10,425.
Less cost of goods sold:
Direct materials (6,950 x $0.43)
$2,988
Direct labor (6,950 x $0.32)
2,224
Variable manufacturing overhead (6,950 x $0.20)
1,390
Fixed manufacturing overhead
1,200
(7,802)
Gross margin
2,623.
Less other expenses:
Variable selling and administrative (6,950 x $0.15)
1,043
Fixed selling and administrative
580
(1,623)
Profit
$ 1,000.
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17. Analysis Using Contribution Margin Ratio
Sensitivity analysis
How a model responds to changes in one or more independent variables
Unit contribution margin
Indicates how sensitive and income model is to a change in unit sales
Contribution margin
The portion of every sales dollar contributed toward covering fixed costs and earning a profit
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18. Contribution Margin Example
Chillin’ Time’s contribution income appears below:
Total
Per Unit
Sales (6,950 units)
$ 10,425
$ 1.50
Variable costs
(7,645)
(1.10)
Contribution margin
2,780
Fixed costs
(1,780)
Profit
$ 1,000
Contribution margin per unit
$1.50 – $1.10 = $0.40
Contribution margin ratio
[$1.50 – $1.10] / $1.50 =
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19. Sensitivity Analysis Example
Total
Per Unit
Ratio to Sales
Sales (6,950 units)
$10,425.
$ 1.50
1.000
Variable costs
(7,645)
(1.10)
(0.733)
Contribution margin
2,780.
$ 0.40
0.267
Fixed costs
(1,780)
Profit
$ 1,000.
If sales increase by 100 ice cream bars per month, by how much will net income increase?
100 x $0.40 = $40
If sales increase by $1,050 per month, by how much will net income increase?
$1,050 x = $280
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20. 3
Apply cost-volume-profit analysis to find a break-even point and for preliminary profit planning.
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21. Break-Even Point Occurs when total revenues equal total costs
Can be unit sales volume, or
Dollar sales volume
Operating below break-even
Company operates at a loss
Operating above break-even
Company operates at a profit
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22. Break-even unit sales volume
Break-Even Point
Break-even unit sales volume
Fixed costs
Selling price per unit – Variable costs per unit =
Fixed costs
Unit contribution margin =
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23. Break-Even Point Example
Chillin’ Time sells ice cream bars with a $1.10 unit variable cost for $1.50 each. How many bars must it sell to break even?
Fixed costs
Unit contribution margin =
$1,780
$ $1.10 =
= 4,450 units
Chillin’ Time’s Break-Even Unit Sales Volume
When Chillin’ Time sells 4,450 ice cream bars per month, it will break even.
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24. Profit Planning—Target Profit
If Chillin’ Time wants to earn a monthly profit of $800, how many ice cream bars must it sell?
Fixed costs + Desired profit
Unit contribution margin =
Target unit sales volume
$1,780 + $800
$ $1.10 =
= 6,450 units
Chillin’ Time’s Target Unit Sales Volume
When Chillin’ Time sells 6,450 ice cream bars per month, it will generate profit of $800.
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25. Cost-Volume-Profit Graph
$12,000 -
$10,000 -
$8,000 -
$6,000 -
$4,000 -
$2,000 -
$0 -
, , , ,000
Unit Sales
Variable costs line $1.10 per unit
Fixed costs $1,780
Loss area
Profit area
Total Revenues and Total Costs
Total revenue line $1.50 per unit
Break-even point 4,450 units
Total costs line $1,780 + $1.10 per unit
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26. Total profit or loss line
Profit-Volume Graph
Total Revenues
Break-even point $6,675
Profit area
Loss area
$900 -
$600 -
$300 -
$0 -
($300) -
($600) -
($900) -
$4, $8, $12,000
Total Profit or (Loss)
Total profit or loss line
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27. Impact of Income Taxes
Determining the unit sales volume required to earn a desired after-tax profit:
After-tax profit
(1 – Tax rate) =
Before-tax profit
Determine the required before-tax profit.
Step 1:
Substitute the required before-tax profit into the profit formula.
Step 2:
Solve for the required unit sales volume.
Step 3:
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28. Impact of Income Taxes Example
Chillin’ Time sells ice cream bars with a $1.10 unit variable cost for $1.50 each. It is subject to a 30 percent income tax rate. How many ice cream bars must Chillin’ Time sell to earn a desired monthly after-tax profit of $840?
After-tax profit
(1 – Tax rate) =
Before-tax profit
$840
(1 – 0.30)
= $1,200
$1,780 + $1,200
$ $1.10 =
Target unit sales volume
= 7,450 ice cream bars
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29. Contribution Income Statement with Income Taxes
Sales (7,450 x $1.50)
$11,175
Less variable costs:
Direct materials (7,450 x $0.43)
$3,204
Direct labor (7,450 x $0.32)
2,384
Variable manufacturing overhead (7,450 x $0.20)
1,490
Variable selling and administrative (7,450 x $0.15)
1,118
8,195
Contribution margin
2,980
Less fixed costs:
Fixed manufacturing overhead
1,200
Fixed selling and administrative
580
1,780
Before-tax profit
Income taxes ($1,200 × 30%)
360
After-tax profit
$ 840
100%
30%
70%
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30. Analyze the profitability and sales mix of a multiple-product firm.4
Analyze the profitability and sales mix of a multiple-product firm.
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31. Multiple Product Break-Even Point
Applicable when unit information is not available or when a company sells more than one product.
Fixed costs
Contribution margin ratio =
Dollar break-even point
Fixed costs + Desired profit
Contribution margin ratio =
Target dollar sales volume
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32. Sales Mix Analysis Sales mix
The relative portion of unit or dollar sales that are derived from each product
When sales mix is constant, the basic cost- volume-profit model can be used effectively
When sales mix is not constant, must determine average unit contribution margin or average contribution margin ratio for each alternative mix
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33. Unit Sales Analysis
It is now 2018 and Chillin’ Time has two products – ice cream bars and popsicles, with the following information:
Ice Cream Bars
Popsicles
Total
Unit sales
5,000
10,000
Selling price per unit
$2.00
$0.80
Variable cost per unit
$1.10
$0.40
Fixed costs per month
$ 3,400
Sales revenue
$10,000
$4,000
$14,000
Variable costs
5,500
2,000
7,500
Contribution margin
$ 4,500
$2,000
$ 6,500
Contribution margin ratio
0.450
0.500
Current sales mix based on units: 5,000 to 5,000 or 1 to 1. Chillin’ Time sells 1 ice cream bar for every popsicle sold.
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34. Unit Multi-Product Break-Even Example
Average contribution margin per unit = [($0.90 x 1) + ($0.40 x 1)] / 2 units = $0.65
Fixed costs
Unit contribution margin =
Unit break-even point
$3,400
$0.65 =
= 5, ≈ 5,231 units
Ice cream bars: 5,231 x 1/2 = 2,616* and Popsicles: 5,231 x 1/2 = 2,616*
*rounded
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35. Unit Multi-Product Break-Even Example
If the sales mix changes to 4:1, how much will the unit break-even sales volume be?
Average contribution margin per unit = [($0.90 x 4) + ($0.40 x 1)] / 5 units = $0.80
Unit break-even point with new sales mix:
Fixed costs
Unit contribution margin =
$3,400
$0.80
4,250 units
Ice cream bars: 4,250 x 4/5 = 3,400 and Popsicles: 4,250 x 1/5 = 850
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36. Comparing Break-Even Example
Break-even units
Sales Mix 1 to 1
Ice cream bars: 5,231 x 1/2 = 2,616*
and
Popsicles: 5,231 x 1/2 = 2,616*
*rounded
Sales Mix 4 to 1
Ice cream bars: 4,250 x 4/5 = 3,400
and
Popsicles: 4,250 x 1/5 = 850
The change in sales mix causes the total number of units needed to break even to change because of the different contribution margins for the two products.
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37. Dollar Multi-Product Break-Even Example
Current sales mix in dollars is $10,000 to $4,000 or about 71% to 29%. How much is the break-even sales volume in dollars?
Average contribution margin ratio = $6,500 / $14,000 = 0.464
Dollar break-even point with new sales mix:
Fixed costs
Contribution margin per unit =
$3,400
0.464
= $7,328
Ice cream bars: $7,328 x 0.71 = $5,203 and Popsicles: $7,328 x 0.29 = $2,125
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38. Dollar Multi-Product Break-Even Example
Current sales mix in dollars is $10,000 to $4,000 or about 71% to 29%. If the sales mix changes to a 60% to 40% ratio, how much will the break-even sales volume in dollars be?
Average contribution margin ratio = [(0.45 x 0.60) + (0.50 x 0.40)] = 0.47
Dollar break-even point with new sales mix:
Fixed costs
Contribution margin per unit =
$3,400
0.47
= $7,234
Ice cream bars: $7,234 x 0.60 = $4,340 and Popsicles: $7,234 x 0.40 = $2,894
© Cambridge Business Publishers, 2015

39. Comparing Break-Even Example
Break-even sales dollars
Sales Mix 71% to 29%
Ice cream bars: $7,328 x 0.71 = $5,203
and
Popsicles: $7,328 x 0.29 = $2,125
Sales Mix 60% to 40%
Ice cream bars: $7,234 x 0.60 = $4,340
and
Popsicles: $7,234 x 0.40 = $2,894
The change in sales mix causes the sales dollars needed to break even to change because of the different contribution margins for the two products.
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40. 5
Apply operating leverage ratio to assess opportunities for profit and the risks of loss.
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41. Degree of operating leverage
What is operating leverage?
A measure of the extent that an organization’s costs are fixed
Contribution margin
Income before taxes =
Degree of operating leverage
High degree of operating leverage
Signals the existence of a high portion of fixed costs
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42. Operating Leverage Risk and Opportunity
Sales Increase
Sales Decrease
High operating leverage
High opportunity for profit increases
High risk
of loss
Low operating leverage
Low opportunity for profit increases
Low risk
The higher the degree of operating leverage…
The greater the opportunity for profit with increases in sales, AND
The greater the risk of large losses when sales decrease
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43. Measuring Expected Change in Profit
Taco Express and Mia’s Cantina are competitors and reported the same sales revenue and before-tax profit during May:
Taco Express
Mia’s Cantina
Sales
$40,000
$40,000.
Variable costs
(22,000)
(8,000)
Contribution margin
18,000
32,000.
Fixed costs
Before-tax profit
$10,000
$10,000.
Taco Express
Mia’s Cantina
Degree of operating leverage
$18,000
= 1.8
$32,000
= 3.2
$10,000
If sales drop by 20% for both, which company suffers more?
Decrease in profit
1.8 x 20%
= 36%
3.2 x 20%
= 64%
Decline in Profit
Mia’s Cantina's higher operating leverage results in a larger profit decline.
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44. Perform profitability analysis with unit and nonunit cost drivers.6
Appendix 16A
Perform profitability analysis with unit and nonunit cost drivers.
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45. Profitability Analysis Considerations
Limitation
Only one activity cost driver used
Unit-level approach based on the assumption that units sold or sales dollars is the only cost driver
Solution
Use a cost hierarchy approach that incorporates non-unit as well as unit-level activity cost drivers
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46. Multi-Level Contribution Income Statement with Income Taxes
Sales $ 3,000,000.
Less unit-level costs:
Cost of goods sold ($3,000,000 x 0.80) (2,400,000)
Unit level contribution margin 600,000.
Cost of processing order (3,200 orders x $20) (64,000)
Order-level contribution margin 536,000.
Less customer-level costs:
Mail, phone, sales visits, recordkeeping, etc.
(400 customers x $200) (80,000)
Customer-level contribution margin 456,000.
Less facility-level costs:
Depreciation, manager salaries, insurance, etc (120,000)
Before-tax profit 336,000.
Income taxes ($336,000 x 0.40) ,400.
After-tax profit $ ,600.
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47. Unit-Level Break-Even Example
The following costs have been determined based on the multi-level break-even contribution income statement:
Type of Activity
Cost
Unit-level
$0.80 per sales dollar
Order-level
$64,000
Customer-level
$80,000
Facility-level
$120,000
Assuming no changes in other costs, what is the unit-level break-even dollar sales volume?
Order- level costs
Customer-level costs
Facility-level costs +
Contribution margin ratio
[$64,000 + $80,000 + $120,000] ÷ [1 ‒ 0.8] = $1,320,000
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