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									     ACCT 102
Management Accounting
    Lecture 3 & 4


       Cost-Volume-Profit
        (CVP) Analysis
                                                      2


               CVP Analysis
• Decision making and planning do not involve only
  the determination of relevant cost behavior
• They also involve a consideration of the combined
  effect on both cost and revenue functions of
  changes in the level of activity
• They are achieved by examining the relationship
  of costs, volume and revenues which in turn gives
  insight into the incremental impact on the
  profitability of the various choices open to
  management - CVP analysis.
                                                          3


             CVP Assumptions
 All costs are classified as fixed or variable with
  unit level activity cost drivers.
 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.
                        4


 The Profit Formula

   =R-Y
Where:
    = Profit
   R = Total revenues
   Y = Total costs
                             5


 The Profit Formula
   R = pX
   Y = a + bX
Where:
   p = Unit selling price
   a = Fixed costs
   b = Unit variable costs
  X = Unit sales
                          6


Detailed Profit Formula




      = pX - (a + bX)
                                                          7


         Break-even Point (BEP)
• Break-even Point
  • =0
  • Since  = pX - (a + bX) [Refer to previous slide]
     0 = pX - (a + bX)
     pX = (a + bX)
     TR = TC
  • Until break-even sales are reached, the object of
    interest operates at a loss
  • Beyond this point, increasing levels of profits are
    achieved
                                                      8


                       BEP
Example: Ace Pte Ltd
• Selling price (per unit)           $12
• Fixed costs per period             $50,000
• Semi-variable
   – Fixed component                 $30,000
   – Variable component (per unit)   $2
• Variable costs (per unit)          $5
• Relevant range of output (units)   6,000 – 50,000
                                            9


                       BEP
Break even point (BEP) using TR = TC
• At BEP,  = 0 and TR = TC
• Substituting the data,
  12x = 80,000 + 7x
   5x = 80,000
    x = 16,000 units
• Break even point in units = 16000 units
• Break even point in dollar sales
  = 16000 x 12 = $192,000
                                                       10


       Contribution Margin (CM)
• BEP output level for Ace Pte Ltd is 16,000 units
• What happens if it were to sell only 15,999 units?
      = Px – (a + bx)
      = (12 * 15,999) – (80,000 + (7 * 15,999))
       = (191,988) – (80,000 + 111,993)
       = 191,988 – 191,993 = – 5
                                                            11


                         CM
• If 16,001 units were sold, what would be the profit ?
      = Px – (a + bx)
      = (12 X 16,001) – (80,000 + (7 X 16,001)
       = 192,012 – (80,000 + 112,007)
       = 192,012 – 192,007 = 5
• Significance of the $5 loss and $5 profit respectively?
   • Each additional unit produced and sold generates an
     incremental profit of $5, which is given by the
     difference between the selling price of $12/unit and
     the variable cost of $7/unit
• Incremental profit termed “Contribution Margin” (CM)
                                                                  12


                            CM
• Contribution margin focuses on sales in relation to all
  variable costs
• Distinguish CM from Gross Margin (Sales – COGS)
• CM per unit = Selling price less variable costs per
                   unit
• CM ratio = CM per unit/Selling Price or
                Total CM/Sales or
                1 – VC-sales ratio
  Note: CM ratio is the portion of each dollar of sales revenue
  contributed towards covering fixed cost and earning a profit
                                                   13


      BEP (using CM approach)
• Break-even Point Formulas (using CM approach)

    Break-even
     unit sales              Fixed costs
                   =
      volume           Unit contribution margin


    Break-even                Fixed costs
                   =
    dollar sales       Contribution margin ratio
      volume
                                                14


      BEP (using CM approach)
• CM per unit    = SP – VC per unit
                 = $5
• BEP in units   = FC/CM per unit
                 = 16,000 units
• CM ratio = CM per unit/SP or Total CM/Sales
            = 0.417
• BEP in $ = FC / CM ratio
            = $192,000
                                                             15


           Incremental Analysis
• Focuses on changes occurring in revenues, costs,
  and/or volume. Looks at
   • what if price per unit were to increase or decrease,
   • what if variable cost per unit or fixed costs were to
     increase or decrease, and
   • what if sales volume were to increase decrease and
     so on.
                                                          16


           Incremental Analysis
Question
• Using the previous example, if Ace Pte Ltd current
  sales is 25,000 units and it is confident that it can
  increase its sales by another 10,000 units through a
  promotion program that will cost $30,000, should the
  company carry out the promotion program?
                                                           17


           Incremental Analysis
Answer
• Since every dollar of contribution margin after the
  BEP is profit, Ace should carry out the promotion
  program if the additional contribution margin from the
  additional sales is in excess of the additional cost.
• Increase in contribution      $50,000
• Increase in fixed cost        $30,000
• Incremental profit            $20,000
                                                              18


            Incremental Analysis
Question
• Ace estimates that if the selling price is reduced by $1,
  it can generate additional sales of 5,000 units over its
  current sales of 25,000 units. Should Ace proceed with
  the price reduction?
                                                            19


             Incremental Analysis
Answer
• If the sales price is reduced by $1, total contribution
  from the current sales will reduce by $25,000.
• Contribution from the additional sales will amount to
  $20,000.
• Net loss as a result of reducing sales price by $1 will
  be $5,000.
                                                        20

     Contribution and Functional
         Income Statements
• Contribution income statement: Costs are classified
  according to behavior as variable or fixed
• Functional income statement: Costs are classified
  according to function, e.g. COGS, selling expenses,
  administrative expenses
• Contribution income statements provides better
  information to internal decision makers.
                                                       21

   Contribution and Functional
       Income Statements
              Variable Costs per Carton
Manufacturing:
    Direct materials                 $1.00
    Direct labor                      0.25
    Manufacturing overhead            1.25    $2.50
Selling and administrative                     0.50
Total                                         $3.00
                Fixed Costs per Month

Manufacturing overhead                       $ 5,000
Selling and administrative                    10,000
Total                                        $15,000
                                                               22


  Contribution Income Statement
                   Benchmark Paper Company
                 Contribution Income Statement
             for a Monthly Volume of 5,400 Cartons
Sales (5,400 x $8)                                   $43,200
Less variable costs:
  Direct materials (5,400 x $1.00)           $ 5,400
  Direct labor (5,400 x $0.25)                 1,350
  Manufacturing overhead (5,400 x $1.25)       6,750
  Selling and administrative (5,400 x $0.50)   2,700 -16,200
Contribution margin                                  $27,000
Less fixed costs:
  Manufacturing                              $ 5,000
  Selling and administrative                  10,000 -15,000
Profit                                               $12,000
                                                                23


    Functional Income Statement
                   Benchmark Paper Company
                  Functional Income Statement
             for a Monthly Volume of 5,400 Cartons
Sales (5,400 x $8)                                    $43,200
Less cost of goods sold:
  Direct materials (5,400 x $1.00)            $ 5,400
  Direct labor (5,400 x $0.25)                  1,350
  Variable Mfg. overhead (5,400 x $1.25)        6,750
  Fixed manufacturing overhead                  5,000 -18,500
Gross margin                                          $24,700
Less other expenses:
  Variable selling and admin. (5,400 x $0.50) $ 2,700
  Fixed selling and administrative             10,000
Profit                                                $12,000
                                                             24


 Contribution Income Statement
                                                Ratio to
                           Total    Per Unit     Sales
Sales (5,400 units)       $43,200      $8         1.000
Variable costs            -16,200       -3       -0.375
Contribution margin       $27,000      $5         0.625
Fixed costs               -15,000
                                       Contribution Margin
Profit                    $12,000             Ratio
If sales increase by 100 cartons
  per month, what will be the
     increase in net income?        100 x $5 = $500
                                                         25


Contribution Income Statement
 Break-even                 Fixed costs
  unit sales   =    Selling price - Variable costs
   volume              per unit        per unit
 Break-even
  unit sales               Fixed costs
               =
   volume            Unit contribution margin

 Break-even
  unit sales       $15,000
               =               = 3,000 units per month
   volume             $5
                                                         26


                Profit Planning
Assume Benchmark’s management desires to
   know the unit sales volume required to
    achieve a monthly profit of $18,000.
  Target unit
 sales volume         Fixed costs + Desired Profit
                 =
                       Unit contribution margin
  Target unit
                     $15,000 + $18,000
 sales volume    =                       = 6,600 units
                            $5
                                                         27


             Profit Planning
        Benchmark desires a profit of $12,000.

Target dollar sales       Fixed costs + Desired profit
                      =
     volume                Contribution margin ratio

Target dollar sales           $15,000 + $12,000
     volume           =
                                    0.625

Target dollar sales
    volume            = $43,200
                                                             28


               Margin of safety
• Margin of safety is the excess of a company’s
    actual sales above its BEP point (in units or dollars)
•   It is the amount that sales can drop before it starts
    to make a loss.
•   It can be expressed as:
     • Units (actual units less break-even units)
     • Dollars (actual sales in dollars less break-even
        sales in dollars), or
     • Percentage (excess of units/sales dollar over
        breakeven units/sales dollar as a % of budgeted
        or actual units/sales dollar).
                                                     29


            Margin of safety
• Using data from Benchmark, assume that the sales
  for Benchmark is projected to be 4000 units. The
  margin of safety for Benchmark is:
   • in units:     4,000 – 3,000 = 1,000 units
   • in sales $: 32,000 – 24,000 = $8,000
   • in %:         1000/4,000 = 25% or
                   8,000/32,000 = 25%
                                                                                                       30


                                        Graphs relating to CVP
                                 $60,000 -                                   Profit area
Total Revenues and Total Costs




                                 $50,000 -
                                             Break-even point
                                 $40,000 -      3,000 units                           Total revenues
                                                                                       $8 per unit
                                 $30,000 - Loss area
                                                                     Fixed costs
                                 $20,000 -                            $15,000
                                 $10,000 -                                         Variable costs
                                                                                   $3X
                                     $0 -                |              |            |          |
                                        0              2000           4000         6000       8000
                                                              Unit Sales
                                                          CVP Graph
                                                                                       31


                                  Graphs relating to CVP
                                              Total profit
                          $20,000 -
                                                or loss
                          $15,000 - Break-even point
Total Profit or (Loss)




                           $5,000 -     $24,000                      Profit area

                               $0 -             |              |                   |
                                       Loss
                          ($5,000) -
                                   0          20,000         40,000          60,000
                                       area
                         ($10,000) -

                         ($15,000) -
                                                    Total Revenues

                                              Profit-Volume Graph
                                                     32


          Operating Leverage
• Operating leverage provides information
  concerning the relationship between a company’s
  variable and fixed costs.
• Generally, companies that are highly labor
  intensive tend to have higher variable costs and
  lower fixed costs, and thus, low operating
  leverage. The reverse is also true for capital
  intensive companies.
                                                                  33


           Operating Leverage
• Characteristics of a highly leveraged company
   – Generally have high contribution margin since their
     variable costs tend to be lower. However, the higher fixed
     costs would mean that the BEP would also be high.
   – If selling price is relatively stable, the volume of sales
     would have high impact on profit/loss. A small increase in
     sales volume can have a major impact on profit/loss within
     a given relevant range.
   – It is important to reduce operational leverage during
     periods of economic distress
                                                                    34


              Operating Leverage

          Degree of          Total Contribution margin
                           =
      operating leverage              Income

                                       $20,000
                        4 =
                                        $5,000

Degree of operating leverage measures how a percentage change
 in sales from the current level will impact company profit/loss.

        If Benchmark’s sales increase 12.5 percent,
            how much should profits increase?
                                              35


         Operating Leverage


Increase in sales                    12.5%
Degree of operating leverage          x 4.0
Increase in profits                  50.0%


Current profit                       $5,000
Increase in profits ($5,000 x 50%)    2,500
New profit                           $7,500
                                                          36


        Multiple Product CVP
• Assumptions required:
  • Sales mix is constant
  • Fixed costs is not directly related to a particular
    product. If fixed costs are directly related to a
    particular product, then the fixed costs should
    be regarded as fixed costs of the product and
    included in the separate analysis related to it
    => 2 separate CVPs
                                                              37


         Multiple Product CVP
• CM may be used to determine the break-even
  units volume or the units required to achieve a
  desired profit

                                      Fixed costs
   Break-even point (units) =
                              Weighted-average contribution
                                        margin

   Target sales (units)      Fixed costs + Desired profit
                          =
                            Weighted-average contribution
                                       margin
                                                           38


        Multiple Product CVP
• CM ratio may be used to determine the break-even
  dollar sales volume or the dollar sales volume
  required to achieve a desired profit

                                   Fixed costs
    Break-even point ($) =
                           Weighted-average contribution
                                   margin ratio

    Target sales ($)      Fixed costs + Desired profit
                       =
                         Weighted-average contribution
                                 margin ratio
                       39


Multiple Product CVP
                       40


Multiple Product CVP
                                                               41


              Multi-Level CVP
• Major limitation of traditional CVP
   – Exclusive use of unit level activity cost drivers, i.e.
     does not consider other categories of cost drivers
   – High probability of significant errors in cost
     estimation and prediction (Refer to Lecture 2
     notes)
• Expansion of CVP to incorporate non-unit activity
  cost drivers
   – Difficult to develop graphical relationships
   – Good way to begin is to make use of a contribution
     statement that incorporates a hierarchy of cost
     drivers
                                                                        42


                 Multi-Level CVP
• Example: General Distribution
   –   Sales (Multiple products)           $3,000,000
   –   Number of sales orders              3,200
   –   Number of customers                 400
   –   Cost hierarchy
        • Unit level activities:
            – COGS                         $0.80 per sales dollar
        • Order level activities
            – Cost of processing order     $20 per order
        • Customer level activities
            – Mail, phone, sales visits…   $200 per customer per year
        • Facility level costs
            – Depreciation, insurance…     $120,000 per year
                                                                     43


               Multi-Level CVP
                      General Distribution
           Multi-Level Contribution Income Statement
                        for the Year 2002
Sales                                                  $3,000,000
Less unit level costs:
  Cost of goods sold ($5,000,000 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, and
  so forth (400 customers x $200)                        - 80,000
Customer level contribution margin                      $456,000
                                                                  44


               Multi-Level CVP
                      General Distribution
           Multi-Level Contribution Income Statement
                        for the Year 2002
Customer level contribution margin                     $456,000
Less facility level costs:
  Depreciation, manager salaries, insurance,
  and so forth                                         -120,000
Profit                                                 $336,000
                                                              45


               Multi-Level CVP
                   Current      Current
Unit level break-  order- + customer- + Facility
  even point in     level         level             level
 dollars with no = costs         costs              costs
changes in other
   costs (in $)            Contribution margin ratio

                = ($64,000 + $80,000 + $120,000)/(1 - 0.80)

                = $1,320,000
                                                                 46


                Multi-Level CVP

Break-even order                 Cost of each order
   size (in $)   =
                              Contribution margin ratio
                 = ($20)/(1 - 0.80)

                 = $100

 •   To break even, each order must have be for $100 of goods.
 •   Discourage smaller orders
                                                                  47


                  Multi-Level CVP
                   Cost of each order x Average orders per customer
  Break-even               + Cost of customer level activity
 on an average    =
customer (in $)                Contribution margin ratio
                  = ($20 x 8 + $200)/(1 - 0.80)

                  = $1,800

•    To break even, each customer must purchase $1,800 of goods
•    Discontinue relations with customers with annual purchases of
     less than this amount or try to serve such customers in a less
     costly manner

								
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