Cost-Volume-Profit Analysis

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Chapter 22

• Cost-Volume-Profit Analysis

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Objective 1

• Identify different
• cost behavior patterns.

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Types of Costs
Variable
Fixed
Mixed
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Variable Costs Example

• Consider Grand Canyon Railway.
• Assume that breakfast costs Grand Canyon Railway
  3 per person.
• If the railroad carries 2,000 passengers, it will
  spend 6,000 for breakfast services.

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Variable Costs Example
Total Variable Costs (thousands)
24 18 12 6

0 1 2 3 4 5
Volume (Thousands of passengers)
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Fixed Costs Example
400 300 200 100
Total Fixed Costs (thousands)

0 1 2 3 4 5
Volume (Thousands of passengers)
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Mixed Costs Example

• A mixed cost is part variable and part fixed.
• Assume a department of a company has fixed costs
  of 50 per month (600 per year).
• There are also variable costs of 3 per hour.

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Mixed Costs Example
2,850 2,100 1,350 600
Total Costs
Variable Cost

Fixed Cost
0 125 250 375 500 625
Volume (hours)
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Relevant Range...

• is a band of volume in which a specific
  relationship exists between cost and volume.
• Outside the relevant range, the cost either
  increases or decreases.
• A fixed cost is fixed only within a given
  relevant range and a given time span.

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Relevant Range
160,000 120,000 80,000 40,000

Fixed Costs
Relevant Range
0 5,000 10,000 15,000 20,000 25,000
Volume in Units
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Objective 2

• Use a contribution margin
• income statement to make
• business decisions.

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Two Approaches to Compute Profits
Conventional income statement
Contribution margin income statement
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Conventional Income Statement
Sales
Cost of Goods Sold
Gross Margin


Net Income
Gross Margin
Operating Expenses


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Contribution MarginIncome Statement
Sales
Variable Expenses
Contribution Margin


Net Income
Contribution Margin
Fixed Expenses


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Contribution Margin Example

• Luis and Tom manufacture a device that allows
  users to take a closer look at icebergs from a
  ship.
• The usual price for the device is 100.
• Variable costs are 70.
• They receive a proposal from a company in
  Newfoundland to sell 20,000 units at a price of
  85.

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Contribution Margin Example

• There is sufficient capacity to produce the
  order.
• How do we analyze this situation?
• 85 70 15 contribution margin.
• 15 20,000 units 300,000 (total increase in
  contribution margin)

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Objective 3

• Compute breakeven sales and
• perform sensitivity analyses.

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Cost-Volume-Profit Analysis
Sales Fixed Fixed Variable
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Cost-Volume-Profit Analysis

• Accountants use two methods to perform CVP
  analysis.
• Both methods use an equation or formula derived
  from the contribution margin income statement.

Sx Vx F 0
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Equation Approach
With the equation approach, breakeven sales in
units is calculated as follows
Unit sales price Units sold

Variable unit cost Units sold

Fixed expenses
Operating income

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Breakeven Point Example

• Assume that fixed expenses amount to 90,000.
• How many devices must be sold at the regular
  price of 100 to break even?
• (100 Units sold) (70 Units sold)
  90,000 0
• Units sold 90,000 30 3,000

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Contribution Margin
Per Unit Percent
Ratio Sales price 100 100 1.00 Variabl
e expenses 70 70 .70 Contribution
margin 30 30 .30
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Contribution Margin Formula
(Fixed expenses Operating income)
Contribution margin per unit Units
(90,000 0) 30 3,000 Units
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Contribution Margin Ratio Formula
(Fixed expenses Operating income)
Contribution margin ratio Sales
(90,000 0) .30 300,000
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Change in Sales Price Example

• Suppose that the sales price per device is 106
  rather than 100.
• What is the revised breakeven sales in units?
• New contribution margin 106 70 36
• 90,000 36 2,500 units

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Change in Variable Costs Example

• Suppose that variable expenses per device are 75
  instead of 70.
• Other factors remain unchanged.
• 90,000 25 3,600
• 90,000 0.25 360,000

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Change in Fixed Costs Example

• Suppose that rental costs increased by 30,000.
• What are the new fixed costs?
• 90,000 30,000 120,000
• What is the new breakeven point?
• 120,000 30 4,000 units
• 120,000 0.30 400,000

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Objective 4

• Compute the sales level needed to
• earn a target operating income.

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Target Operating Income Example

• Suppose that a business would be content with
  operating income of 45,000.
• Assuming 100 per unit selling price, variable
  expenses of 70 per unit, and fixed expenses of
  90,000, how many units must be sold?
• (90,000 45,000) 30 4,500

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Objective 5

• Graph a set of cost-volume-profit
• relationships.

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Various Sales Levels Example

• Assume selling price is 35 per unit.
• Variable expense is 21 per unit.
• Fixed cost is 7,000.
• What is the breakeven point?
• 500 units or 17,500

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Cost-Volume-Profit Graph
Breakeven sales point 500 units or 17,500
Sales revenue line
Total expense line
Fixed expense line
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Various Sales Levels Example

• What operating income is expected when sales are
  300 units?
• 14 300 4,200

4,200 7,000 (2,800)
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Various Sales Levels Example

• What operating income is expected when sales are
  1,000 units?
• 14 1,000 14,000

14,000 7,000 7,000
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Objective 6

• Compute a margin of safety.

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Margin of Safety Example

• Margin of safety is the excess of expected sales
  over breakeven sales.
• Assume Luis and Toms breakeven point is 3,000
  devices.
• Suppose they expect to sell 4,000 during the
  period.
• What is the margin of safety?

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Margin of Safety Example
4,000 3,000 1,000 units
1,000 100 100,000
1,000 4,000 25
100,000 400,000 25
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Assumptions of CVP Analysis

• Expenses can be classified as either variable or
  fixed.
• CVP relationships are linear over a wide range of
  production and sales.
• Sales prices, unit variable cost, and total fixed
  expenses will not vary within the relevant range.

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Assumptions of CVP Analysis

• Volume is the only cost driver.
• The relevant range of volume is specified.
• Inventory levels will be unchanged.
• The sales mix remains unchanged during the
  period.

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Objective 7

• Use the sales mix in CVP analysis.

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Sales Mix Example

• Suppose that Luis and Tom plan to sell two types
  of devices instead of one.
• They estimate that sales will be 3,000 regular
  devices and 1,000 large devices.
• This is a 31 sales mix.
• They expect 3/4 of the devices sold to be regular
  devices and 1/4 to be large devices.

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Sales Mix Example
Regular
Large Sales price 100
154 Variable expenses 70
100 Contribution margin 30
54 Sales mix (units) 3 1
90 54
The total is 144.
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Sales Mix Example
Weighted-average contribution margin 144 (3
1) 36
Breakeven sales 90,000 36 2,500
2,500 3/4 1,875 regular devices
2,500 1/4 625 large devices
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Sales Mix Example
1,875 regular 100 187,500 625 large
154 96,250 Breakeven 283,750
90,000 144 625 packages in the mix
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Objective 8

• Compute income using variable
• costing and absorption costing.

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Product Costing
Absorption costing assigns all manufacturing
costs to products. Financial statements prepared
under GAAP use absorption costing.
Variable costing assigns only variable
manufacturing costs to products. Variable costing
is for internal use only.
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Product Costing Example
Assume the following costs Direct material unit
cost 6.00 Direct labor unit
cost 3.00 Variable manufacturing
overhead 2.00 Variable marketing 2.50 Fixe
d manufacturing overhead per unit 5.00
What is the product cost/unit?
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Product Costing Example

Absorption Costing
Direct materials 6.00 Direct
labor 3.00 Variable
manufacturing overhead 2.00 Fixed
manufacturing overhead 5.00
Total 16.00
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Product Costing Example

Variable Costing
Direct materials 6.00 Direct
labor 3.00 Variable
manufacturing overhead 2.00 Fixed
manufacturing overhead -0-
Total 11.00
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End of Chapter 22