Chapter Nine CostVolumeProfit Analysis: A Managerial Planning Tool

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Chapter NineCost-Volume-Profit Analysis A
Managerial Planning Tool
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Learning Objectives
Learning Objectives

• Determine the number of units which must be sold
  to break even or to earn a targeted profit.
• Determine the amount of revenue required to break
  even or to earn a targeted profit.
• Apply cost-volume-profit analysis in a
  multiple-product setting.
• Prepare a profit-volume graph and a
  cost-volume-profit graph and explain the meaning
  of each.

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Learning Objectives (continued)

• Explain the impact of risk, uncertainty, and
  changing variables on cost-volume-profit
  analysis.
• Discuss the impact of activity-based costing on
  cost-volume-profit analysis.

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Cost-Volume-Profit Graph

• Revenue Total Revenues
• 
  Profit
• 
  Total Costs
• Y
• X
  Units sold
• X Break-even point in units
• Y Break-even point in sales revenue

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Simple CVP Example

• Fixed costs (F) 40,000
• Selling price per unit (P) 10
• Variable cost per unit (V) 6
• Tax rate 40
• 1. What is the break-even point in units?
• 2. What is the break-even point in dollars?

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Simple CVP Example(continued)

• Units Sold Approach
• 1. Let X break even point in units
• R TC
• PX F VX
• 10X 40,000 6X
• 10X - 6X 40,000
• 4X 40,000
• X 10,000 units

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Simple CVP Example(continued)

• Units Sold Approach (continued)
• 2. Break-even point in sales dollars is
• 10,000 x 10 100,000
• This can be shown with a variable-costing income
  statement
• Variable Costing Income Statement
• Sales (10,000 x 10) 100,000
• Less variable costs (10,000 x 6) 60,000
• Contribution margin 40,000
• Less fixed costs 40,000
• Profit before taxes 0
• Less income taxes 0
• Profit after taxes 0

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Simple CVP Example(continued)

• Sales Revenue Approach
• Alternative approach to solving break-even point
  in sales dollars
• Let X equal break-even sales in dollars
• R TC
• X F VX
• X 40,000 .6X
• X - .6X 40,000
• .4X 40,000
• X 100,000
• NOTE V is the variable cost percentage which
  equals
• Variable cost per unit/Selling price per unit
  6/10 60

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What sales in units and dollars are needed to
obtain a targeted profit before taxes of 20,000?

• Let X break-even point in units
• Sales
• Less variable costs ______
  
• Contribution margin 60,000 4X
• Less fixed costs 40,000
• Profit before taxes 20,000
• Therefore
• 60,000 4X
• 15,000units X
• Sales in dollars is (15,000 x 10) 150,000.

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What sales in units and dollars are needed to
obtain a targeted profit after taxes of 24,000?

• Let X break-even point in units
• Sales
• Less variable costs ________
• Contribution margin
• Less fixed costs 40,000
• Profit before taxes
• Less income taxes ________
• Profit after taxes 24,000

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What sales in units and dollars are needed to
obtain a targeted profit after taxes of
24,000?(continued)

• TRICK
• After Profit after taxes
• Before Profit before taxes
• After (1-tax rate) x Before
• 24,000 (1-.4) x Before
• 24,000/.6 Before
• 40,000 Before

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What sales in units and dollars are needed to
obtain a targeted profit after taxes of
24,000?(continued)

• Therefore,
• Sales 10X
• Less variable costs _______ 6X
• Contribution margin 80,000 4X
• Less fixed costs 40,000
• Profit before taxes 40,000
• Less income taxes 16,000 40
• Profit after taxes 24,000
• 4X 80,000
• X 80,000/4
• X 20,000 units
• Sales in dollars is (20,000 x 10) 200,000.

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What sales in units and dollars are needed to
obtain a targeted profit after taxes of
24,000?(continued)

• The income statement below illustrated that
  200,000 in sales will give you an after-tax
  profit of 24,000.
• Sales 200,000
• Less variable costs 120,000
• Contribution margin 80,000
• Less fixed costs 40,000
• Profit before taxes 40,000
• Less income taxes 16,000
• Profit after taxes 24,000

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Multiple-Product Analysis

• Product P - V CM x Mix Total CM
• A 10 - 6 4 x 3 12
• B 8 - 5 3 x 2 6
• Total CM per package 18
• Total fixed expenses 180,000
• Break-even point
• X F / total CM per package
• 180,000 / 18
• 10,000 packages to break-even

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Multiple-Product Analysis(continued)

• Each package contains 3 units of A and 2 units
  of B. Therefore, to break-even, we need to sell
  the following units of A and B
• A 3 x 10,000 30,000 units
• B 2 x 10,000 20,000 units

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A Multiple-Product Example

• Assume the following
• 
  Regular Deluxe Total Percent
• Unit of Sales
  400 200 600
  ----
• Sales Price per Unit 500
  750 ---- ----
• Sales Revenue 200,000
  150,000 350,000 100.0
• Less Variable Expenses 120,000
  60,000 180,000 51.4
• Contribution Margin 80,000
  90,000 170,000 48.6
• Less Fixed Expenses
  130,000
• Net Income
  40,000
• 1. What is the break-even point?
• 2. How much sales-revenue of each product must be
  generated to earn a before-tax profit 50,000?

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A Multiple-Product BEP

• BEP Fixed Costs Net Income/ Composite CM
  ratio
• 130,000 /0.486
• 267,490 for the firm
• BEP for Regular Model (How does one allocate?)
• (200/350) x 267,490 152,851
• BEP for Deluxe Model
• (150/350) x 267,490 114,639

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A Multiple-Product Targeted Revenue

• BEP Fixed Costs Net Income/ Composite CM
  ratio
• (130,000 50,000) / 0.486
• 370,370 for the firm
• BEP for Regular Model
• (200/350) x 370,370 211,640
• BEP for Deluxe Model
• (150/350) x 370,370 158,730

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Three Methods of Using the CVP Model

• Operating Income Approach
• Contribution Approach
• Graphical Approach

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Graphical Approach - 1

• Profit
  I (P-V)X-F
• 
  Slope P-V
• 
  Profit
• loss break-even point
  UNITS
• in units
• -

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The Graphical Approach - 2
Profit
300,000 200,000 100,000
Total Revenue
BEP
Total Costs
Loss
Variable Costs
Fixed Costs
0 100 200 400
600 800
Number of Ovens Sold
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The Operating Income Approach for BEP

• Sales - Variable costs - Fixed Costs Net Income
• Sales-Revenue Method
• 100(Sales)- 60(Sales) - 70,000 0 (at BEP)
• .4
  (Sales) 70,000
• 
  Sales 175,000
• Units-Sold Method
• Let x Number of microwaves at the break-even
  point
• 500(x) - 300(x) - 70,000 0 (at BEP)
• 200 (x) 70,000
• x 350
  microwaves

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The Contribution Approach for BEP

• Sales-Revenue Method
• BEP (Revenue) (Fixed Costs Net Income)/
  Contribution Ratio
• 70,000 / 0.40
• 175,000
• Units-Sold Method
• BEP (Revenue Units) (Fixed Costs Net
  Income)/Contribution per
• 
  microwave
• 
  70,000/200 per microwave
• 350 units
  

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CVP A Short-Term Planning and Analysis Tool
Assists in...

• ...establishing prices
• ...analyzing the impact of volume on profits
• ...focusing on the impact of costs on profits
• ...analyzing the impact of mix of products on
  profits

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Discuss the Limitations of CVP Analysis

• A number of limitation are commonly mentioned
  with respect to CVP analysis
• 1. The analysis assumes a linear revenue
  function and a linear cost function.
• 2. The analysis assumes that price, total fixed
  costs, and unit variable costs can be accurately
  identified, and remain constant over the relevant
  range.
• 3. The analysis assumes that what is produced is
  sold.
• 4. For multiple-product analysis, the sales mix
  is assumed to be known.
• 5. The selling prices and costs are assumed to
  be known with certainty.

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Margin of Safety

• Assume that a company has the following projected
  income statement
• Revenues 100,000
• Variable expenses (60,000)
• Contribution margin 40,000
• Fixed expenses (30,000)
• Income before taxes 10,000
• Break-even point in dollars (R)
• R 30,000 / .4 75,000
• Safety margin 100,000 - 75,000
• Safety margin 25,000

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Degree of Operating Leverage(DOL)

• DOL 40,000 / 10,000 4.0
• Now suppose that sales are 25 higher than
  projected. What is the percentage change in
  profits?
• Percentage change in profits
• DOL x percentage change in sales
• 4.0 x 25 100
• Proof
• Revenues 125,000
• Less variable expenses (75,000)
• Contribution margin 50,000
• Less fixed expenses (30,000)
• Income before taxes 20,000

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Operating Leverage and Margin of Safety

• Assume the following
• Total
  Per unit of Sales
• Sales (400 Microwaves) 200,000
  500 100
• Less Variable Expenses 120,000
  300 60
• Contribution Margin 80,000
  200 40
• Less Fixed Expenses 70,000
• Net Income
  10,000
• 1. What is the Operating Leverage?
• 2. What is the Margin of Safety?

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Operating Leverage and Margin of Safety

• Operating Leverage Contribution margin/Net
  Income
• 
  80,000/10,000
• 8 (an
  indication of operating risk)
• change in profits Operating leverage x Change
  in sales
• 8 x 10
  increase in sales
• 80 increase
  in profits
• Margin of Safety Targeted Revenue -
  Break-even Point
• 200,000 -
  175,000
• 25,000

Operating Leverage Contribution Margin / Net
Income
80,000 / 10,000
8 (an indication of operating risk) change
in profits Operating leverage x Change in
sales 8 x
10 increase in sales
80 increase in profits Margin of
Safety Targeted Revenue - Break-even
Point
200,000 - 175,000
25,000
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C-V-P and ABC

• Assume the following
• Sales price per unit 15
• Variable cost 5
• Fixed costs (conventional)-180,000
• Fixed costs (ABC)-80,000
• Other Data
• Cost Driver Unit Variable Costs Level of Cost
  Driver
• Set-ups 500 100
• Inspections 50 600
• 1. What is the BEP under conventional analysis?
• 2. What is the BEP under ABC analysis?
• 3. What is the BEP if set-up cost could be
  reduced to 450 and inspection cost
• reduced to 40?

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C-V-P and ABC (Continued)

• 1. Break-even units (conventional analysis)
• BEP 180,000/10
• 18,000 units
• 2. Break-even units (ABC analysis)
• BEP 100,000 (100 x 500)
  (600 x 50)/10
• 18,000 units
• 3. BEP 100,000 (100 x 450) (600
  x 40)/10
• 16,900 units
• What implications does ABC have for improving
  performance?

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Numerical Questions from the Back of Chapter 8
and 9

• E8-1, E8-5, E8-15, P8-5
• E9-1, E9-5, E9-11, E9-13

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Question E8-5

• Please go to your textbook to read the question.

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Question E8-15

• Please go to your textbook to read the question.

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Question P8-5

• Please go to your textbook to read the question.

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Question E9-1

• Please go to your textbook to read the question.

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Question E9-5

• Please go to your textbook to read the question.

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Question E9-11

• Please go to your textbook to read the question.

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Question E9-13

• Please go to your textbook to read the question.

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The End