Cost-Volume-Profit Analysis. Chapter 3

1. Cost-Volume-Profit Analysis

Chapter 3
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2. Learning Objective 1

Understand the assumptions
underlying cost-volume-profit
(CVP) analysis.
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3. Cost-Volume-Profit Assumptions and Terminology

1. Changes in the level of revenues and costs arise
only because of changes in the number of product
(or service) units produced and sold.
2. Total costs can be divided into a fixed component
and a component that is variable with respect to
the level of output.
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4. Cost-Volume-Profit Assumptions and Terminology

3. When graphed, the behavior of total revenues
and total costs is linear (straight-line) in relation
to output units within the relevant range
(and time period).
4. The unit selling price, unit variable costs, and
fixed costs are known and constant.
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5. Cost-Volume-Profit Assumptions and Terminology

5. The analysis either covers a single product or
assumes that the sales mix when multiple
products are sold will remain constant as the
level of total units sold changes.
6. All revenues and costs can be added and
compared without taking into account the time
value of money.
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6. Cost-Volume-Profit Assumptions and Terminology

Operating income
= Total revenues from operations
– Cost of goods sold and operating costs
(excluding income taxes)
Net income = Operating income – Income taxes
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7. Learning Objective 2

Explain the features
of CVP analysis.
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8. Essentials of Cost-Volume-Profit (CVP) Analysis Example

Assume that the Shirts Shop can purchase a shirt
for $32 from a local factory; other variable costs
amount to $10 per unit.
The local factory allows the shirts Shop to
return all unsold shirts and receive a full $32
refund per shirt within one year.
The average selling price per shirt is $70
and total fixed costs amount to $84,000.
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9. Essentials of Cost-Volume-Profit (CVP) Analysis Example

How much revenue will the business receive if
2,500 units are sold?
2,500 × $70 = $175,000
How much variable costs will the business incur?
2,500 × $42 = $105,000
$175,000 – 105,000 – 84,000 = ($14,000)
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10. Essentials of Cost-Volume-Profit (CVP) Analysis Example

What is the contribution margin per unit?
$70 – $42 = $28 contribution margin per unit
What is the total contribution margin when
2,500 shirts are sold?
2,500 × $28 = $70,000
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11. Essentials of Cost-Volume-Profit (CVP) Analysis Example

Contribution margin percentage (contribution
margin ratio) is the contribution margin per
unit divided by the selling price.
What is the contribution margin percentage?
$28 ÷ $70 = 40%
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12. Essentials of Cost-Volume-Profit (CVP) Analysis Example

If the business sells 3,000 shirts,
revenues will be $210,000 and contribution
margin would equal 40% × $210,000 = $84,000.
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13. Learning Objective 3

Determine the breakeven point
and output level needed to achieve
a target operating income using
the equation, contribution margin,
and graph methods.
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14. Breakeven Point

Sales
–
Variable
expenses
=
Fixed
expenses
Sales = Variable costs + Fixed costs
Total revenues = Total costs
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15. Abbreviations

SP = Selling price
VCU = Variable cost per unit
CMU = Contribution margin per unit
CM% = Contribution margin percentage
FC = Fixed costs
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16. Abbreviations

Q = Quantity of output units sold
(and manufactured)
OI = Operating income
TOI = Target operating income
TNI = Target net income
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17. Equation Method

(Selling price × Quantity sold) – (Variable unit cost
× Quantity sold) – Fixed costs = Operating income
Let Q = number of units to be sold to break even
$70Q – $42Q – $84,000 = 0
$28Q = $84,000
Q = $84,000 ÷ $28 = 3,000 units
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18. Contribution Margin Method

$84,000 ÷ $28 = 3,000 units
$84,000 ÷ 40% = $210,000
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19. Graph Method

$(000)
Graph Method
Breakeven
378
336
294
252
210
168
126
84
42
0
Fixed costs
0
1000
2000
3000
4000
5000
Units
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20. Target Operating Income

(Fixed costs + Target operating income)
divided either by Contribution margin
percentage or Contribution margin per unit
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21. Target Operating Income

Assume that management wants to have an
operating income of $14,000.
How many shirts must be sold?
($84,000 + $14,000) ÷ $28 = 3,500
What dollar sales are needed to achieve this income?
($84,000 + $14,000) ÷ 40% = $245,000
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22. Learning Objective 5

Explain CVP analysis
in decision making and
how sensitivity analysis helps
managers cope with uncertainty.
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23. Using CVP Analysis Example

Suppose the management anticipates
selling 3,200 shirts.
Management is considering an advertising
campaign that would cost $10,000.
It is anticipated that the advertising will
increase sales to 4,000 units.
Should the business advertise?
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24. Using CVP Analysis Example

3,200 shirts sold with no advertising:
Contribution margin (3200 unit x 28 =70-42contribution) 89600
Fixed costs
(84,000)
Operating income
$ 5,600
4,000 pairs of shirts sold with advertising:
Contribution margin (units 4000 x 28 contribution) $112,00
Fixed costs (84000 + 10 000 advertising)
(94,000
Operating income
$ 18,000
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25. Using CVP Analysis Example

Instead of advertising, management is
considering reducing the selling price
(from 70) to $61 per shirt.
It is anticipated that this will increase
sales to 4,500 units.
Should management decrease the selling
price per shirt to $61?
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26. Using CVP Analysis Example

3,200 shirts sold with no change
in the selling price:
Operating income = $5,600 {(70-42) 3200 – 84000}
4,500 shirts sold at a reduced selling price:
Contribution margin: (4,500 × $19 i.e 61price-42v.cost) $85,5
Fixed costs
(84,000)
Operating income
$ 1,500
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27. Sensitivity Analysis and Uncertainty Example

Assume that the shirts Shop can sell
4,000 shirts.
Fixed costs are $84,000.
Contribution margin ratio is 40%.
At the present time the business cannot
handle more than 3,500 shirts.
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28. Sensitivity Analysis and Uncertainty Example

Operating income at $245,000 revenues with
existing space = ($245,000 × .40)
– $84,000 = $14,000.
(3,500 shirts × $28) – $84,000 = $14,000
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29. Sensitivity Analysis and Uncertainty Example

Operating income at $280,000 revenues with
additional space = ($280,000 × .40) – $90,000
= $22,000.
(4,000 shirts × $28 contribution margin)
– $90,000 = $22,000
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30. Learning Objective 6

Use CVP analysis to plan
fixed and variable costs.
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31. Alternative Fixed/Variable Cost Structures Example

Suppose that the factory the shirts Shop is using to
obtain the merchandise offers the following:
Decrease the price they charge from $32 to $25 and
charge an annual administrative fee of $30,000.
What is the new contribution margin?
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32. Alternative Fixed/Variable Cost Structures Example

$70 – ($25 + $10) = $35
Contribution margin increases from $28 to $35.
What is the contribution margin percentage?
$35 ÷ $70 = 50%
What are the new fixed costs?
$84,000 + new fees $30,000 = $114,000
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33. Alternative Fixed/Variable Cost Structures Example

Management questions what sales volume
would yield an identical operating income
regardless of the arrangement.
contribution28x – 84,000 = new contribution 35x – 11
114,000 – 84,000 = 35x – 28x
7x = 30,000
x = 4,286 shirts
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34. Alternative Fixed/Variable Cost Structures Example

Cost with existing arrangement
= Cost with new arrangement
.60x + 84,000 = .50x + 114,000
.10x = $30,000 x = $300,000
($300,000 × .40) – $ 84,000 = $36,000
($300,000 × .50) – $114,000 = $36,000
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35. Learning Objective 7

Apply CVP analysis to a company
producing different products.
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36. Effects of Sales Mix on Income

shirts Shop Example
Management expects to sell sports cap at $20
each in addition to the shirts.
This will not require any additional fixed costs.
Variable cost per cap = $ 8
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37. Effects of Sales Mix on Income

Contribution margin per cap: $20 – $8 = $12
What is the contribution margin of the mix?
= $28 + $12 = $40
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38. Effects of Sales Mix on Income

$84,000 fixed costs ÷ $40 = 2,100 packages
2,100 × 1 = 2,100 caps
2,100 × 1 = 2,100 shirts
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39. Effects of Sales Mix on Income

What is the breakeven in dollars?
2,100 caps × $20
2,100 shirts × $70
= $ 42,000
= 147,000
$198,000
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40. Effects of Sales Mix on Income

What is the weighted-average budgeted
contribution margin?
shirts: 1 × $28 + caps: 1 × $12
= $40 ÷ 3 = $ 13.3
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41. Effects of Sales Mix on Income

The breakeven point for the two products is:
$84,000 ÷ $13.333 = 6,300 units
6,300 × 1/3 = 2,100 unites of caps
6,300 × 2/3 = 4,200 unites of shirts
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42. Effects of Sales Mix on Income

Sales mix can be stated in sales dollars:
Sales price
Variable costs
Contribution margin
Contribution margin ratio
shirts caps
$70
$ 20
42
8
$28
$12
40% %60
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43. End of Chapter 3

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