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					                   Managerial Accounting - 9.1


Chapter 22


Cost-Volume-Profit Analysis
and the Contribution Margin
Approach to Decision Making
                                   Managerial Accounting - 9.2


    Grand Canyon Railway

   “All aboard!”, shouts the conductor as the
    train departs from the depot in Williams,
    Arizona.
                                  Managerial Accounting - 9.3


    Grand Canyon Railway

 The restored turn-of-the century train
  features musicians in period costumes.
 Passengers can have breakfast on the trip to
  the canyon and appetizers on the afternoon
  trip back to Williams.
                                    Managerial Accounting - 9.4


    Grand Canyon Railway

   The railway offers three classes of service:
1   Coach, in restored 1923 cars
2   Club, with a mahogany bar
3   Chef, with an open-air rear platform
                                  Managerial Accounting - 9.5


    Grand Canyon Railway

 Restoration of the railway cost $20 million for
  the tracks, the locomotive and cars.
 Few of the railway’s costs vary with the
  number of guests because most are fixed.
 Food and beverage costs are variable.
                                 Managerial Accounting - 9.6


    Grand Canyon Railway

 Management must set ticket prices high
  enough to cover their costs and hopefully earn
  a profit, but low enough to fill the seats.
 Because most of the railway’s costs are fixed,
  the extra costs to serve each additional
  passenger are low.
                                Managerial Accounting - 9.7


    Grand Canyon Railway

 How do the railway’s managers ensure that
  revenues will cover costs and provide
  profits?
 How many seats must the railway fill to
  cover its costs?
 Managers perform cost-volume-profit
  analyses to answer these questions.
                                  Managerial Accounting - 9.8


    Chapter Objectives

1   Identify different cost behavior patterns.
2   Use a contribution margin income statement
    to make business decisions.
3   Compute breakeven sales.
                                   Managerial Accounting - 9.9


    Chapter Objectives

4   Compute the sales level needed to earn a
    target operating income.
5   Graph a set of cost-volume-profit
    relationships.
6   Compute a margin of safety.
                                Managerial Accounting - 9.10


    Chapter Objectives

7   Use the sales mix in CVP analysis.
8   Compute income using variable costing and
    absorption costing.
                                Managerial Accounting - 9.11


    Cost-Volume-Profit Analysis...

– expresses the relationship among costs, volume
  and profit or loss.
 It is a business tool for short-term decisions.
                    Managerial Accounting - 9.12


Objective 1

   Identify different cost
     behavior patterns.
                                 Managerial Accounting - 9.13


    Cost Driver...

– is any factor whose change makes a
  difference in a related total cost.
 Volume (units or dollars) is the most
  prominent cost driver.
                                  Managerial Accounting - 9.14


    Cost Behavior...

–   describes how costs change (if they change at
    all) as the cost driver changes.
                     Managerial Accounting - 9.15


    Types of Costs

 Variable
 Fixed

 Mixed
                                    Managerial Accounting - 9.16


    Variable Costs...

–   are costs that change in direct proportion to a
    change in the level of activity.
   Direct materials
   Direct labor
   Sales commissions
                                 Managerial Accounting - 9.17


    Variable Costs

 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.
                                 Managerial Accounting - 9.18


    Variable Costs

   Total                               Costs
    (thousands)
                  $6

                         2
                       Volume
            (thousands of passengers)
                                    Managerial Accounting - 9.19


    Fixed Costs...

–   are costs that do not change in total despite
    wide changes in volume.
   Rent
   Administrative salaries
   Depreciation
                               Managerial Accounting - 9.20


    Fixed Costs

 The train makes one round trip each day,
  regardless of the number of passengers on
  the train.
 Most of Grand Canyon Railway’s costs are
  fixed.
                                    Managerial Accounting - 9.21


    For Example:

–   depreciation and maintenance on the track
–   the locomotive
–   the Williams Depot museum
–   entertainment costs (salaries of the strolling
    musicians)
–   administrative expenses (salaries of general
    managers)
                             Managerial Accounting - 9.22


    Fixed Costs


    Administrative               Salaries


                         Volume
                     (passengers)
                                Managerial Accounting - 9.23


    Mixed Costs...

– are part fixed and part variable.
 Part of the costs change with volume or usage,
  and part of the costs do not change.
                                 Managerial Accounting - 9.24


    Mixed Costs

 Utilities have a base charge plus additional
  charges depending on usage.
 Commissions may have a base salary plus
  additional compensation based on sales.
                      Managerial Accounting - 9.25


    Mixed Costs

   Commissions




                  Sales
                                  Managerial Accounting - 9.26


    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.
                                   Managerial Accounting - 9.27


    Relevant Range

   A fixed cost is fixed only within a given
    relevant range and a given time span.
                           Managerial Accounting - 9.28


    Relevant Range

   Fixed Costs
         $10,000
         $ 8,000

    $ 5,000


    0 100   300      500
      Volume in Units
                   Managerial Accounting - 9.29


Objective 2

 Use a contribution margin
 income statement to make
     business decisions.
                                Managerial Accounting - 9.30
    Two Approaches
    to Compute Profits
1   Conventional income statement
2   Contribution margin income statement
                                  Managerial Accounting - 9.31
    Conventional
    Income Statement
   In the conventional income statement,
    expenses are classified by functions.
                                Managerial Accounting - 9.32
    Conventional
    Income Statement
 It classifies expenses by value chain
  function.
 Sales - Cost of Goods Sold            =
  Gross Margin
 Gross Margin - Operating Expenses =
  Net Income
                                Managerial Accounting - 9.33
    Contribution Margin
    Income Statement
 This income statement format classifies
  expenses as either variable or fixed.
 It is useful in decision making and
  highlights the contribution margin.
                                  Managerial Accounting - 9.34


    Two Major Differences are:

1   Fixed manufacturing cost of goods sold is
    subtracted from sales to compute gross
    margin, but not to compute contribution
    margin.
                                   Managerial Accounting - 9.35


    Two Major Differences are:

2   Variable marketing expenses and other
    variable non-manufacturing expenses are
    subtracted from sales to calculate contribution
    margin, but not gross margin.
                                Managerial Accounting - 9.36


    Contribution Margin...

– measures the amount available to cover fixed
  expenses and provide operating income.
 It allows managers to determine the effect of
  proposed activities such as sales promotions
  or special orders.
                                 Managerial Accounting - 9.37


    Contribution Margin

   Luis and Cathy manufacture a small device
    that allow users to take a closer look at
    icebergs from a ship.
                                Managerial Accounting - 9.38


    Contribution Margin

 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.
                                  Managerial Accounting - 9.39


    Contribution Margin

 There is sufficient capacity to produce the
  order.
 How do we analyze this situation?

 Selling price - variable costs = contribution
  margin per unit
 $85 - $70 = $15 per unit
                               Managerial Accounting - 9.40


    Contribution Margin

 $15 x 20,000 units = $300,000 (total
  contribution margin)
 Sales (20,000 x $85)             $1,700,000
– Variable costs (20,000 x $70)   1,400,000
= Contribution margin              $ 300,000
                                 Managerial Accounting - 9.41


    Contribution Margin

 Should they accept the order?
 Yes

 Why?

 It increases the contribution margin by
  $300,000.
                  Managerial Accounting - 9.42


Objective 3

 Compute breakeven sales.
                                Managerial Accounting - 9.43
    Cost-Volume-Profit
    Analysis
   Accountants use two methods to perform
    CVP analysis.
1   Equation approach
2   Contribution margin approach
                                 Managerial Accounting - 9.44
    Cost-Volume-Profit
    Analysis
   Both methods use an equation or formula
    derived from the contribution margin
    income statement.

                              Sx-Vx-F = 0
                                 Managerial Accounting - 9.45


    Equation Approach

 With the equation approach, breakeven
  sales in units is calculated as follows:
 Unit sales price x Units sold

 Minus Variable unit cost x Units sold

 Minus fixed expenses

= Operating income
                                Managerial Accounting - 9.46


    Equation Approach

 At breakeven point:
 Sales -Variable expenses = Fixed expenses
                               Managerial Accounting - 9.47


    Breakeven Point

 Sales below the breakeven point result in
  a loss.
 Sales above the breakeven point provide a
  profit.
                                         Managerial Accounting - 9.48


    Breakeven Point

   Breakeven $                                              point
    Sales
        Total Expenses
                                                  Profit

                Fixed Expenses
      Loss

                                 Units
                                 Managerial Accounting - 9.49


    Breakeven Point

 Assume that fixed expenses amount to
  $90,000 and the variable costs per device is
  $70.
 How many devices must be sold at the
  regular price of $100 to break even?
 3,000
                                Managerial Accounting - 9.50


    Breakeven Point

 Sales - Variable expenses - Fixed expenses
  = Operating income
 ($100 x Units sold) - ($70 x Units sold) -
  $90,000 = 0
 $30 x Units sold = $90,000

 Units sold = $90,000/$30 = 3,000
                               Managerial Accounting - 9.51


    Breakeven Point

 What is the breakeven in dollars?
 $300,000

 $100 x 3,000 units = $300,000

 $300,000 - Variable expenses - Fixed
  expenses = 0
 $300,000 - $210,000 - $90,000 = 0
                                  Managerial Accounting - 9.52


    Contribution Margin Ratio...

– is the ratio of the contribution margin to the
  sales price.
 It is the contribution margin divided by
  sales.
 CM% = CM/Sales
                                Managerial Accounting - 9.53


    Contribution Margin Ratio

 The following computations pertain to Luis and
  Cathy’s business:
               Per Unit    Percent          Ratio
 Sales price   $100        100         1.00
– Variable                         expenses
  70          70        .70
= Contribution                        margin
  $ 30         30         .30
                                  Managerial Accounting - 9.54


    Contribution Margin Ratio

 $30/$100 = 30%
 This ratio shows what percentage of sales
  revenue is left after variable expenses are
  covered.
                                Managerial Accounting - 9.55


    Contribution Margin Formula

 Fixed expenses + Operating income
÷ Contribution margin per unit
= Units
 Luis and Cathy can use this formula to
  determine their breakeven in units.
 ($90,000 + 0)/$30 = 3,000 units
                                Managerial Accounting - 9.56
    Contribution Margin
    Ratio Formula
 Fixed expenses + Operating income
÷ Contribution margin ratio
= Sales (in dollars)
 Using the formula, Luis and Cathy’s
  breakeven point in sales dollars is:
 ($90,000 + 0)/0.30 = $300,000
                                Managerial Accounting - 9.57


    Change in Sales Price

 Suppose that the sales price per device is $106
  rather than $100.
 Variable expenses per device remains at $70
  and fixed expenses stay at $90,000.
 What is the revised breakeven sales in units?

 2,500
                                 Managerial Accounting - 9.58


    Change in Sales Price

 How did we obtain this number?
 New contribution margin: $106 - $70 = $36

 $90,000/$36 = 2,500 units

 What is the revised breakeven sales in dollars?

 2,500 units x $106 = $265,000
                                  Managerial Accounting - 9.59


    Change in Sales Price

   Observe that:
–   Sales price per unit increased.
–   Contribution margin per unit increased.
–   Breakeven sales decreased.
                               Managerial Accounting - 9.60


    Change in Sales Price

 Sales ($106 x 2,500)                   $265,000
– Variable expenses ($70 x 2,500)         175,000
– Fixed expenses                           90,000
= Operating income                              0
                                Managerial Accounting - 9.61


    Change in Variable Costs

 Suppose that variable expenses per device are
  $75 instead of $70.
 The sales price per device remains $100 and
  fixed expenses stay at $90,000.
 What are the new breakeven sales in units and
  in dollars?
                               Managerial Accounting - 9.62


    Change in Variable Costs

 Sales in units: 3,600
 Sales in dollars: $360,000

 How did we obtained these numbers?

 The new contribution margin drops to $25
  ($100 - $75) and the new contribution margin
  ratio drops to 0.25 ($25/$100).
                               Managerial Accounting - 9.63


    Change in Variable Costs

 (Fixed expenses + 0) divided by Contribution
  margin per unit = Sales in units
 $90,000/$25 = 3,600

 (Fixed expenses + 0) divided by Contribution
  margin ratio = Sales in dollars
 $90,000/0.25 = $360,000
                                Managerial Accounting - 9.64


    Change in Fixed Costs

 Suppose that rental costs increased by
  $30,000.
 What are the new fixed costs?

 $90,000 + $30,000 = $120,000

 Selling price and variable expenses per
  device remain at $100 and $70 respectively.
                                Managerial Accounting - 9.65


    Change in Fixed Costs

 What is the new breakeven point in units?
 $120,000/$30 = 4,000

 What is the new breakeven point in dollars?

 $120,000/0.30 = $400,000
                                 Managerial Accounting - 9.66


    Change in Fixed Costs

 The $120,000 in fixed costs is an increase of
  $30,000, or 33%, over the original fixed costs of
  $90,000.
 $120,000 - $90,000 = $30,000

 $30,000/90,000 = 33%
                                Managerial Accounting - 9.67


    Change in Fixed Costs

 Note that breakeven sales also increased by the
  same 33%.
 $400,000 - $300,000 = $100,000

 $100,000/300,000 = 33%

 The company must sell more devices to cover
  the higher fixed costs.
                   Managerial Accounting - 9.68


Objective 4

  Compute the sales level
  needed to earn a target
    operating income.
                                Managerial Accounting - 9.69


    Target Operating Income

 Suppose that a business would be content with
  operating income of $45,000.
 Assuming $100 per unit selling price price,
  variable expenses of $70 per unit and fixed
  expenses of $90,000, how many units must be
  sold?
 4,500
                                Managerial Accounting - 9.70


    Target Operating Income

 Fixed expenses + Operating income
÷ Contribution margin per unit
= Sales in units
 ($90,000 + $45,000)/$30 = 4,500

 What would be the sales in dollars?

 $135,000/0.30 = $450,000
                   Managerial Accounting - 9.71


Objective 5

Graph a set of cost-volume-
   profit relationships.
                                  Managerial Accounting - 9.72


    Various Sales Levels

   Remember that:
–   Sales price is $100 per unit.
–   Variable expenses are $70 per unit.
–   Fixed expenses are $90,000.
–   Contribution margin is $30.
                              Managerial Accounting - 9.73


    Various Sales Levels

 What operating income is expected when
  sales are 2,000 units?
 $30,000 Loss

 $30 x 2,000 = $60,000

 $60,000 - $90,000 = ($30,000)
                             Managerial Accounting - 9.74


    Various Sales Levels

 Sales (2,000 x $100)        $200,000
– Variable expenses       140,000
= Contribution margin           60,000
– Fixed expenses                90,000
= Operating loss         $ 30,000
                              Managerial Accounting - 9.75


    Various Sales Levels

 What operating income is expected when
  sales are 3,000 units?
 0 (breakeven point)

 $30 x 3,000 = $90,000

 $90,000 - $90,000 = 0
                            Managerial Accounting - 9.76


    Various Sales Levels

 Sales (3,000 x $100)       $300,000
– Variable expenses      210,000
= Contribution margin          90,000
– Fixed expenses               90,000
= Operating income           $      0
                              Managerial Accounting - 9.77


    Various Sales Levels

 What operating income is expected when
  sales are 4,500 units?
 $30 x 4,500 = $135,000

 $135,000 - $90,000 = $45,000
                            Managerial Accounting - 9.78


    Various Sales Levels

 Sales (4,500 x $100)       $450,000
– Variable expenses      315,000
= Contribution margin         135,000
– Fixed expenses               90,000
= Operating income           $ 45,000
                                             Managerial Accounting - 9.79
Operating Income at Various
Sales Levels

             600
             500
                                                      Sales
             400
   $ (000)




                                                      Fixed
             300
             200                                      Fixed +
                                                      Variable
             100
              0
                   0   1   2       3     4     5
                           Units (000)
                  Managerial Accounting - 9.80


Objective 6

     Compute a margin
        of safety.
                                   Managerial Accounting - 9.81


    Margin of Safety...

–   is the excess of expected sales over
    breakeven sales.
                                Managerial Accounting - 9.82


    Margin of Safety

 Luis and Cathy’s breakeven point is 3,000
  devices.
 Suppose they expect to sell 4,000 during the
  period.
 What is the margin of safety in units?

 1,000
                                 Managerial Accounting - 9.83


    Margin of Safety

 Expected sales in units
– Breakeven sales in units
= Margin of safety in units
 4,000 - 3,000 = 1,000 units

 What is the margin of safety in dollars?

 $100,000
                                Managerial Accounting - 9.84


    Margin of Safety

 Margin of safety in units
x Sales price per unit
= Margin of safety in dollars
 1,000 x $100 = $100,000

 Sales can drop by 1,000 units, or $100,000,
  before Luis and Cathy incur a loss.
                                Managerial Accounting - 9.85


    Margin of Safety

 For any level of sales, managers can
  compute the margin of safety as a
  percentage.
 Margin of safety in units

÷ Sales in units
= Margin of safety %
 1,000/4,000 = 25%
                                Managerial Accounting - 9.86


    Margin of Safety

 What is the margin of safety percentage in
  dollars?
 25%

 Margin of safety in dollars

÷ Sales dollars
= Margin of safety %
 $100,000/$400,000 = 25%
                                   Managerial Accounting - 9.87


    Assumptions of CVP Analysis

1   Expenses can be classified as either variable
    or fixed.
2   CVP relationships are linear over a wide
    range of production and sales.
3   Sales prices, unit variable cost and total
    fixed expenses will not vary within the
    relevant range.
                                 Managerial Accounting - 9.88


    Assumptions of CVP Analysis

4   Volume is the only cost driver.
5   The relevant range of volume is specified.
6   Inventory levels will be unchanged.
7   The sales mix remains unchanged during the
    period.
                    Managerial Accounting - 9.89


Objective 7

     Use the sales mix
     in CVP analysis.
                               Managerial Accounting - 9.90


    Sales Mix

 Companies that sell more than one product
  use a weighted average contribution margin
  for CVP analysis.
 Suppose that Luis and Cathy plan to sell
  two types of devices instead of one.
                                  Managerial Accounting - 9.91


    Sales Mix

 Recall that the regular device variable cost
  is $70 and sells for $100.
 Its contribution margin is $30.

 The second larger device costs $100 and
  sells for $154.
 Its contribution margin is $54.
                                 Managerial Accounting - 9.92


    Sales Mix

 They estimate that sales will be 3,000
  regular devices and 1,000 large devices.
 This is a 3:1 sales mix.

 For every 3 regular devices, they expect to
  sell 1 large device.
                                 Managerial Accounting - 9.93


    Sales Mix

 They expect 3/4 of the devices sold to be
  regular devices and 1/4 to be a large device.
 To determine the breakeven sales, the
  weighted average contribution margin must
  be computed.
                             Managerial Accounting - 9.94


    Sales Mix

                   Regular Large
 Sales price             $100     $154
– Variable expenses    70      100
= Contribution margin       30       54
x Sales mix (units)          3        1
                         $ 90     $ 54
 The total is $144
                                 Managerial Accounting - 9.95


    Sales Mix

 What is the weighted average contribution
  margin?
 $144/(3 + 1) = $36

 What is the breakeven sales in total units?

 $90,000/$36 = 2,500
                               Managerial Accounting - 9.96


    Sales Mix

 How many regular devices are in this mix?
 2,500 x 3/4 = 1,875

 How many large devices?

 2,500 x 1/4 = 625
                                Managerial Accounting - 9.97


    Sales Mix

 What is the overall breakeven point in
  dollar sales?
 1,875 regular x $100 = $187,500

 625 large     x $154 = 96,250
                        $283,750
                               Managerial Accounting - 9.98


    Sales Mix

 How many packages of 3 regular and 1
  large device are in this mix?
 $90,000/$144 (contribution margin per
  package) = 625
                               Managerial Accounting - 9.99


    Sales Mix

 How many regular devices are in these
  packages?
 625 x 3 = 1,875

 How many large devices?

 625 x 1 = 625
                  Managerial Accounting - 9.100


Objective 8

   Compute income using
    variable costing and
    absorption costing.
                             Managerial Accounting - 9.101


    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.
                               Managerial Accounting - 9.102


    Product Costing

 Under variable costing, fixed manufacturing
  costs are considered period costs and are
  expensed in the period when they are
  incurred.
 Variable costing is for internal use only.
                              Managerial Accounting - 9.103


    Product Costing

 The only difference between absorption
  costing and variable costing is that
  absorption costing considers fixed
  manufacturing costs as inventoriable
  product costs.
 Variable costing does not.
                               Managerial Accounting - 9.104


    Product Costing

 Assume the following costs:
 Direct material unit cost $6.00

 Direct labor unit cost         $3.00
 Variable mfg. overhead         $2.00
 Variable marketing        $2.50
 Fixed manufacturing            overhead per
  unit                 $5.00
 What is the product cost/unit?
                              Managerial Accounting - 9.105


    Product Costing

              Absorption costing
 Direct materials                       $ 6.00
 Direct labor                             3.00
 Variable manufacturing overhead          2.00
 Fixed manufacturing overhead          5.00
 Total                                  $16.00
                              Managerial Accounting - 9.106


    Product Costing

           Variable costing
 Direct materials                       $ 6.00
 Direct labor                             3.00
 Variable manufacturing overhead          2.00
 Fixed manufacturing overhead             0
 Total                                  $11.00
                    Managerial Accounting - 9.107




End of Chapter 22

				
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