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					                               CHAPTER 3
                  PROFITABILITY ANALYSIS AND PLANNING

REVIEW QUESTIONS

1. Cost-volume-profit analysis is a technique used to examine the relationships among the total
volume of some independent variable, total costs, total revenues, and profits during a time
period. It is particularly useful in the early stages of planning when it provides a framework for
discussing planning issues.

2. The important assumptions that underlie cost-volume-profit analysis are:
       1. All costs are classified as fixed or variable with unit level activity cost drivers.
       2. The total cost function is linear within the relevant range.
       3. The total revenue function is linear within the relevant range.
       4. The analysis is for a single product, or the sales mix of multiple products is constant.
       5. There is only one activity cost driver: unit or dollar sales volume.

3. The use of a single variable in cost-volume-profit analysis is most reasonable when analyzing
the profitability of a specific event or the profitability of an organization that produces a single
product or service on a continuous basis.

4. In a contribution income statement, costs are classified according to behavior as variable or
fixed, and the contribution margin (the difference between total revenues and total variable costs)
that goes toward covering fixed costs and providing a profit is emphasized. In a functional
income statement costs, are classified according to function (rather than behavior), such as
manufacturing and selling and administrative. This is the type of income statement typically
included in corporate annual reports.

5. The unit contribution margin is equal to the difference between the unit selling price and the
unit variable costs. In computing the unit break-even point, the fixed costs are divided by the
unit contribution margin.

6. The contribution margin ratio is the portion of each dollar of sales revenue contributed toward
covering fixed costs and earning a profit. It is especially useful in situations involving several
products or when unit sales information is not available.

7. The desired profit is added to the fixed costs, increasing the sales volume required to cover
both.

8. A profit-volume graph contains only one line showing the relationship between volume and
profits, while a cost-volume-profit graph contains two lines – one for total revenues and one for
total costs. A profit-volume graph is most likely to be used when management is primarily


                                                 59
60 Chapter 3

interested in the impact on profits of changes in sales volume and less interested in the related
revenues and costs.

9. Income taxes increase the sales volume required to earn a desired after-tax profit.

10. Other things being equal, the higher the degree of operating leverage, the greater the
opportunity for profit with increases in sales. Conversely, a higher degree of operating leverage
magnifies the risk of large losses with a decrease in sales.

11. In a multi-level contribution income statement, costs are separated using a cost hierarchy.
There are several contribution margins, one for each level of costs that responds to a short-run
change in activity.

12. Using a manufacturing cost hierarchy, the batch-level break-even point is determined as the
batch level costs divided by the unit contribution margin.
                                                           Profitability Analysis and Planning 61


EXERCISES

Exercise 3-1
a.
                              Alberta Company
                        Contribution Income Statement
                         For the Month of May 2004

Sales (6,000  $50)                                                 $300,000
Less variable costs:
  Direct materials (6,000  $8)                     $ 48,000
  Direct labor (6,000  $12)                          72,000
  Factory overhead (6,000  $10)                      60,000
 Selling and administrative (6,000  $5)              30,000        (210,000)
Contribution margin                                                 $ 90,000
Less fixed costs:
 Factory overhead                                   $ 40,000
 Selling and administrative                           20,000         (60,000)
Profit                                                              $ 30,000

b.
                                                                            Profit =
                   $350,000        Fixed costs =                            $30,000
                                     $60,000
                   $300,000
                   $250,000
         Total    $200,000
     revenues and
                                                                          Variable costs =
      Total costs $150,000                                                   $210,000
                   $100,000
                    $50,000
                          $0
                               0       2,000       4,000    6,000   8,000 10,000
                                                    Unit sales



Note: The instructor might extend this assignment in class, computing the break-
even point, the margin of safety, and the impact on profits of a change in sales.
62 Chapter 3


Exercise 3-2
a.   Break-even point = $120,000/(1  0.25) = $160,000

b.    Margin of safety = $200,000  $160,000 = $40,000

c.    Sales volume for desired profit = ($120,000 + $60,000) = $240,000
                                            (1  0.25)
                                                     Profitability Analysis and Planning 63


Exercise 3-3
a. Sales                                              $800,000
  Variable costs                                      (380,000)
  Contribution margin                                 $420,000

  Contribution margin ratio = $420,000/$800,000 = 0.525
  Annual break-even dollar sales volume = $210,000/0.525 = $400,000

b. Annual margin of safety in dollars:
       Sales                                                  $800,000
       Break-even sales dollars                               (400,000)
       Margin of safety                                       $400,000

c. To determine the variable and total costs lines, it is necessary to compute the
variable cost ratio:

  Variable = variable costs = $380,000 = 0.475
  cost ratio  sales          $800,000

At a volume of $1,000,000 sales dollars, variable costs are $475,000.

                $1,000,000
                                                                          Profit =
                                                                          $210,000
   Total          $750,000
                                     Fixed costs =
 Revenues                            $210,000
   and            $500,000
   Total                                                                  Variable costs =
                                                                          $380,000
  Costs           $250,000

                           $0
                                $0       $250, $500, $750, $1,00
                                          000   000   000 0,000
                                           Total Revenues

d. Revised annual break-even dollar sales:

  ($210,000 + $52,500)/0.525 = $500,000
64 Chapter 3


Exercise 3-4
a. 1. Total variable costs
   2. Total revenue
   3. Total costs
   4. Variable costs
   5. Fixed costs
   6. Total costs
   7. Contribution margin
   8. Break-even unit sales volume
   9. Loss area
   10. Profit area

b. Line CC                      Line OR              Break-Even Point
   1. Shift downward            No change            Shift left (decrease)
   2. No change                 Increase slope       Shift left (decrease)
   3. Increase slope            No change            Shift right (increase)
   4. Shift upward              Decrease slope       Shift right (increase)
   5. Shift downward and        No change            Shift left (decrease)
     decrease slope

Exercise 3-5

a. 1.   Loss area
   2.   Profit area
   3.   Break-even point
   4.   Axis on which profit and loss are measured
   5.   Fixed costs
   6.   Profit at volume E

b.     Line CF                  Break-Even Point
     1. Increase slope          Shift left (decrease)
     2. Decrease slope          Shift right (increase)
     3. Shift upward            Shift left (decrease)
     4. Shift downward and      Shift right (increase)
        decrease slope
     5. Shift upward and        Can't tell; the two changes
        decrease slope          have opposite effects.
                                                  Profitability Analysis and Planning 65


Exercise 3-6
a.


                    $18,000
              $15,000
       Total
     revenues $12,000
        and    $9,000
       Total   $6,000
       costs
               $3,000
                           $0
                                0         1,000       2,000         3,000
                                             Unit sales


b.

                 $6,000
                 $3,000
       Total
      Profit            $0
        or
                ($3,000) 0           1,00 2,00 3,00 4,00
      (Loss)
                                       0    0    0    0
                ($6,000)
                ($9,000)
                                          Total units



c. It is most appropriate to use a profit-volume graph when management is
primarily interested in the impact on profits of changes in sales volume and less
interested in the related revenues and costs.
66 Chapter 3


Exercise 3-7
a.

      Selling price                          $3.50 per hot dog
      Variable costs                         3.20 per hot dog
      Contribution margin                    $0.30

      Break-even point = $150,000/$0.30
                       = 500,000 hot dogs

b.


               $3,500
        Total  $3,000
      revenues $2,500
         and   $2,000
        Total  $1,500
        costs  $1,000
        (000)    $500
                   $0
                              0      250    500     750     1,000
                                      Unit sales (000)
                                                   Profitability Analysis and Planning 67


Exercise 3-7 (cont.)

c.


                 $200
      Total  $100
      Profit
        or     $0
     (Loss)        0                  250        500         750        1,000
      (000) ($100)

                ($200)
                                        Total units (000)



d.

It is easier to determine profit or loss at any volume with a profit-volume graph
than with a cost-volume-profit graph. This is especially true in situations, such as
this, where the unit contribution margin is small and the scale of activity is large.
Although a profit-volume graph provides a clear illustration of profits, it does not
illustrate revenues and costs. Hence, a manager using a profit-volume graph does
not see the relationship between revenues, costs, and profits.
68 Chapter 3


Exercise 3-8

a. Contribution margin                            $380,000
   Sales                                          950,000
   Contribution margin ratio                          0.40

   Break-even point in sales dollars = $190,000/0.40
                                     = $475,000

b. Current sales                                  $950,000
   Break-even sales                               (475,000)
   Margin of safety                               $475,000

c. Current fixed costs                            $190,000
   Impact of increase                               50,000
   New fixed costs                                $240,000

  Revised break-even point = $240,000/0.40
                           = $600,000

d. Required before-tax income = $200,000/(1  0.36)
                             = $312,500

   Sales volume required to provide an after-tax income of $200,000:
   ($190,000 + $312,500)/0.40 = $1,256,250

e. Sales                                               $1,256,250
   Variable costs (60% of sales)                        (753,750)
   Contribution margin (40% of sales)                  $ 502,500
   Fixed costs                                           (190,000)
   Net income before taxes                             $ 312,500
   Income taxes (36%)                                    (112,500)
   Net income after taxes                              $ 200,000
                                              Profitability Analysis and Planning 69


Exercise 3-9

a. Fixed costs                                          $5,000,000
  Contribution
   [($4,000  $1,000)  1,500]        $4,500,000
  Endowments and grants                  250,000        (4,750,000)
  Required from other sources                           $ 250,000

b. Break-even price ($30,000/5,000) = $6.00

  Revenues (4,250  $6)                                    $25,500
  Fixed costs                                              (30,000)
  Deficit                                                  $(4,500)

c. Cost to city ($20  10,000) = $200,000

d. Contribution [($1.25  $0.75)  5,000]                    $2,500
   Fixed costs                                                (500)
   Amount raised                                             $2,000

e. Available funds                                          $20,000
   Fixed costs                                               (5,000)
   Available for variable costs                             $15,000
   Variable costs per present                                $10
   Number of presents                                          1,500
70 Chapter 3


Exercise 3-10

a.                              Capital-                    Labor-
                               Intensive                  Intensive
Fixed costs:
  Factory overhead          $2,440,000                  $1,320,000
  Selling                      500,000                     500,000
  Total                     $2,940,000                  $1,820,000

Selling price                    $35.00                     $35.00
Variable costs:
  Direct materials $5.00                        $5.60
  Direct labor     10.00                        11.20
  Factory overhead 4.00                          5.80
  Selling           2.00         (21.00)         2.00       (24.60)
  Unit cont. margin              $14.00                     $10.40

Fixed costs                 $2,940,000                  $1,820,000
Unit cont. margin            $14.00                     $10.40
Unit break-even point          210,000                     175,000

b. Paper Mate would be indifferent between the two methods at the unit volume,
X, where total costs are equal.

$21X + $2,940,000 = $24.60X + $1,820,000
           $3.60X = $1,120,000
                X = 311,111 units

Identical results are obtained if profit, rather than cost, equations are used.

($35  $21)X + $2,940,000 = ($35  $24.60)X + $1,820,000
                       X = 311,111 units

Paper Mate should use the labor-intensive method if sales are less than 311,111
units and use the capital-extensive method if sales are above 311,111 units.
                                                  Profitability Analysis and Planning 71


Exercise 3-10 (cont.)

c.

1. Operating leverage is a measure of the responsiveness of income to changes in
sales. The higher a firm's operating leverage, the more sensitive are its profits to
changes in sales volume. It is also an indication of an organization's cost
structure. The higher the portion of an organization's fixed costs (in comparison
with variable costs), the higher its operating leverage.

2.                           Capital-                     Labor-
                            Intensive                   Intensive
Unit contribution margin $ 14.00                      $ 10.40
Unit sales volume          250,000                    250,000
Contribution margin      $3,500,000                  $2,600,000
Fixed costs              (2,940,000)                 (1,820,000)
Net income               $ 560,000                   $ 780,000

Contribution margin        $3,500,000                 $2,600,000
Net income                  560,000                   780,000
Operating leverage               6.25                       3.33

3. The capital-intensive method has a higher operating leverage because of the
greater use of fixed assets.
72 Chapter 3


Exercise 3-11

a.
                            Alabama Berry Basket
                       Contribution Income Statement
                    For the Year Ended December 31, 2004

Sales (40,000  $90)                                    $3,600,000
Variable costs (40,000  $80)                           3,200,000
Contribution margin                                     $ 400,000
Fixed costs                                               (275,000)
Net income                                              $ 125,000

b. Operating leverage = Contribution margin/Net income
                      = $400,000/$125,000
                      = 3.2

c. Percentage change = Percentage decrease  Operating
   in profits          in sales                leverage
                     =   10                     3.2
                     =   32 percent decrease

Profits should decrease by 32 percent to $85,000, computed as: [$125,000 
($125,000  0.32)].

d. Contribution margin [40,000  ($90  $77.50)]        $500,000
   Fixed costs                                          (375,000)
   Net income                                           $125,000
   Operating leverage ($500,000/$125,000)                      4

The acquisition of the berry-picking machines will reduce variable costs, thereby
increasing the contribution margin. It will also increase fixed costs, thereby
increasing the difference between the contribution margin and net income. The net
effect would be an increase in operating leverage.
                                                   Profitability Analysis and Planning 73


Exercise 3-12

Weekly contribution per average customer:

      $15 sales per visit  (1 - 0.80) contribution ratio  1.5 visits = $4.50

Annual contribution per customer = $4.50  52 weeks = $234

Customers required for desired profit = ($80,000 + $40,000)/$234 = 513

Required population = 513 customers/0.04 customers in population = 12,825

Exercise 3-13

a.    Minimum order size         =      $200       = $2,500
      to break even on order         (0.10 – 0.02)

b.    Annual sales to break- = ($200  4 orders) + $500 = $16,250
      even on average customer       (0.10 – 0.02)

c.    Average order size = $16,250/4 = $4,062.50

d.    Order level costs ($200  4 orders  100 customers)          $   80,000
      Customer level costs ($500  100 customers)                      50,000
      Facility level costs                                             60,000
      Total costs                                                  $ 190,000
      Contribution margin ratio                                         0.08
      Minimum annual sales to break even                           $2,375,000

e.    Average order size = $2,375,000/(4 orders  100 customers) = $5,937.50

f.    Part (a) considers only order level costs while part (c) also considers
      customer level costs, and part (e) adds facility level costs. In order for a
      company to break even on an order, it need only cover order level costs. To
      break even on a customer, the company must cover order level and customer
      level costs. Finally, to achieve true break-even, all costs must be covered.
74 Chapter 3


Exercise 3-14
                  Unit              Sales
                  Contribution      Mix
      Product     Margin            (units)*             Weight
       A           $1                 6            $1  6/10 = $0.60
       B            2                 3             2  3/10 = 0.60
       C            3                 1             3  1/10 = 0.30
                                     10                        $1.50

      *B = 3C and A = 2B, so A = 3  2 = 6

      Average unit contribution margin = $1.50

      Break-even unit sales volume = $90,000/$1.50 = 60,000 units

      Units of A at break-even = 60,000  6/10 = 36,000

Exercise 3-15

a.              Unit           Sales
              Selling           Mix
     Product     Price         (units)         Weight
     Standard    $ 50  1,750/2500               $35
     Multiform 125              500/2,500        25
     Complex      250           250/2500         25
     Average unit selling price                  $85

                  Unit                Sales
              Contribution             Mix
      Product     Margin              (units)*         Weight
      Standard    $ 20              1,750/2500         $14
      Multiform     50                500/2,500         10
      Complex      100                250/2500          10
      Average unit contribution margin                  $34

      Contribution margin ratio     =        $34/$85      =     0.40

      Break-even sales volume       =        $30,000/0.40       =      $75,000
                                             Profitability Analysis and Planning 75



b.

     Actual sales volume = 2,500  $85   =    $212,500
     Break-even sales volume                   75,000
     Margin of safety                         $137,500

c.

               $75
               $50
     Total
     Profit    $25
       or       $0
     (Loss)
              ($25) $0              $50          $100             $150
     (000)
              ($50)
              ($75)
                                  Total sales ($000)
76 Chapter 3


PROBLEMS

Problem 3-16

Once the following, or a similar, format is established, each case is solved by
filling in the given information and working toward the unknowns.

                           Case 1      Case 2     Case 3       Case 4
Unit sales                  1,000       800        4,300?*      3,000?*

Sales revenue             $20,000     $ 1,600? $137,600?       $60,000
Variable costs:
  Unit                  $     10        $ 1       $    12        $    5?
  Unit sales             1,000         800      4,300        3,000?
  Total                ( 10,000)         (800)    (51,600       15,000 ?
Contribution margin     $10,000 ?      $ 800     $ 86,000 ?    $45,000 ?
Fixed costs            (8,000)           (400)? (80,000)      (30,000) ?
Net income              $ 2,000 ?      $ 400      $ 6,000?#    $15,000?#

Unit cont. margin:
  Cont. margin            $10,000 ?    $ 800      $86,000 ?    $45,000 ?
  Unit sales               1,000       800       4,300 ?     3,000 ?
  Unit contribution       $    10 ?    $   1?      $ 20 ?       $ 15

Break-even point:
  Fixed costs           $8,000         $ 400      $ 80,000     $30,000 ?
  Unit cont. margin      $10 ?         $1 ?        $20 ?     $15
  Unit break-even point    800 ?         400 ?       4,000       2,000

Margin of safety (unit
 sales less unit break-
 even point)                  200 ?       400 ?        300        1,000

*Solved as the unit break-even point plus the margin of safety.
#Solved as the unit contribution margin times margin of safety.
                                                 Profitability Analysis and Planning 77


Problem 3-17

Once the following or similar format is established, each case can be solved by
filling in the knowns and working toward the unknowns.

                       Case 1         Case 2       Case 3        Case 4
Sales revenue       $100,000        $80,000      $50,000       $40,000*
Cont. margin ratio     0.60 ?        0.75        0.40         0.80 ?
Contribution margin $ 60,000        $60,000 ?    $20,000       $32,000 ?
Fixed costs          (30,000)       (45,000) ?   (10,000) ?    (20,000) ?
Net income          $ 30,000 ?      $15,000      $10,000       $12,000 ?

Variable cost ratio       0.40 ?        0.25         0.60 ?        0.20
Contribution margin ratio 0.60 ?        0.75 ?       0.40          0.80 ?
Total                     1.00          1.00         1.00          1.00

Break-even point:
  Fixed costs         $ 30,000      $45,000      $10,000 ?     $20,000 ?
  Cont. marg. ratio    0.60 ?       0.75 ?      0.40         0.80
  Dollar
   break-even point   $ 50,000 ?    $60,000 ?    $25,000 ?     $25,000

Margin of safety (dollar
 sales less dollar
 break-even point) $ 50,000 ?       $20,000 ?    $25,000 ?     $15,000

*Computed as the break-even point plus the margin of safety.
78 Chapter 3


Problem 3-18

a. Unit contribution margin: $35  $25 = $10

Total contribution (20,000  $10)                             $200,000
Fixed costs                                                   110,000
Net income before taxes                                       $ 90,000
Net income after taxes                                         49,500
Income taxes                                                 $ 40,500
Net income before taxes                                       $90,000
Tax rate                                                          0.45

b. Required before-tax income = $88,000/(1  0.45)
                             = $160,000

Volume required to provide an after-tax income of $88,000:

  ($110,000 + $160,000)/$10 = 27,000 units

c. Contribution margin
     Current                                                   $10.00
     Impact of reduction in variable costs                       2.50
     New                                                       $12.50
   Fixed costs:
     Current                                                 $110,000
     Impact of increase in fixed costs                         20,000
     New                                                     $130,000

Volume required to provide an after-tax income of $88,000:

  ($130,000 + $160,000)/$12.50 = 23,200 units

The reduction in variable costs was more than enough to offset the increase in
fixed costs. Consequently, the volume required to achieve an after-tax profit of
$88,000 declined from 27,000 units to 23,200 units.

d. Requirements (a) through (c) assume that taxable income and accounting
income are equal and that the tax rate is constant.
                                                   Profitability Analysis and Planning 79


Problem 3-19

a. Prior to solving this problem it is necessary to determine the variable costs per
unit, the fixed costs per year, and the unit selling price.

      Using the high-low method:

      Variable costs
      per unit    = ($90,000  $75,000)/(8,000  5,000) = $5

      Fixed costs = $90,000  $5(8,000) = $50,000
      or          = $75,000  $5(5,000) = $50,000

      Unit selling price = $65,000/5,000 = $104,000/8,000 = $13

      Unit contribution margin = $13  $5 = $8

      Break-even point = $50,000/$8 = 6,250 units

b. Sales volume required to earn a profit of $10,000:

      ($50,000 + $10,000)/$8 = 7,500 units
80 Chapter 3


Problem 3-20

a.

Contribution ratio = 1.0  0.60 = 0.40

Break-even point = $1,300,000/0.40 = $3,250,000

b.

Before-tax profit = $500,000/(1  0.34) = $757,576 (rounded)

Required sales volume = ($1,300,000 + $757,576)/0.40 = $5,143,940

c.

                  Profits of automation = Profits of outsourcing
 (1  0.54)X - ($1,300,000 + $300,000) = (1  0.65)X - ($1,300,000  $300,000)
                    0.46X  $1,600,000 = 0.35X  $1,000,000
                                  0.11X = $600,000
                                      X = $5,454,545 (rounded)

d.
               Automation                             Outsourcing
Strength:                                Strength:
 It will provide higher profits if       This alternative has less risk and
   sales increase                           a lower break-even point.
 It may provide new opportunities        It is preferred at the current sales
 May enhance quality                       volume.
                                          It allows focusing on core
                                            competencies.
Weakness:                                Weakness
 This alternative has higher risk        This alternative will not have as
  and a higher break-even point.            great a potential for high profits.
                                          It has less control of operations.
                                                 Profitability Analysis and Planning 81


Problem 3-21

a. The break-even point in patient-days equals total fixed costs divided by the
contribution margin per patient-day.

      Fixed costs:
        Melford Hospital Charges                                 $2,900,000
        Salaries                                                    480,000
        Total                                                    $3,380,000
      Unit contribution margin:
        Revenues per patient-day                                        $300
        Variable costs per patient-day                                  (100)*
        Contribution margin per patient-day                             $200

      *$6,000,000 total 2004 revenues/$300 revenue per patient-day equals
      20,000 patient-days for 2004.

      $2,000,000 total 2004 variable costs/20,000 patient-days equals $100
      variable costs per patient-day

            Break-even point in patient-days = $3,380,000/$200
                                             = 16,900 patient-days

b.
                                Pediatrics
     Schedule of Change in Earnings From Rental of 20 Additional Beds
                    For the Year Ending June 30, 2005

Increase in revenues (20 beds  90 days  $300/ day)      $ 540,000
Increase in expenses:
  Fixed charges by Melford Hospital:
    Annual charge per bed ($2,900,000/60) $ 48,333
    Number of additional beds                    20
    Total increase in fixed charges        $966,660
  Variable charges by Melford Hospital
    ($100/patient-day  90 days  20 beds) 180,000         (1,146,660)
Net decrease in earnings                                  $ (606,660)
82 Chapter 3


Problem 3-22

a. Contribution margin
  ratio of Touring model = ($80.00  $52.80)/$80.00 = 0.34

b. Required before-tax profit = $24,000/(1  0.40)
                              = $40,000
     Required sales
     of touring model = ($316,800 + $40,000)/($80.00  $52.80)
                       = 13,118 pairs

c.    Profit of Mountaineering model = Profit of Touring model
      Let X = unit sales
       $88.00X  ($369,600 + $52.80X) = $80.00X  ($316,800 + $52.80X)
                     $35.2X  $369,600 = $27.2X  $316,800
                                  $8X = $52,800
                                    X = $52,800/$8
                                    X = 6,600 pairs

Before-tax profit or (loss): Mountaineering:
 ($88.00  $52.80)6,600  $369,600 = $(137,280)
Before-tax profit or (loss): Touring:
 ($80.00  $52.80)6,600  $316,800 = $(137,280)

d.
Contribution margin ratio
of Mountaineering model = ($88.00  $52.80)/$88.00 = 0.40
Contribution margin ratio
of Touring model          = ($80.00  $52.80)/$80.00 = 0.34

Profit of Mountaineering model = Profit of Touring model
             0.40X  $369,600 = 0.34X  $316,800
                          0.06X = $52,800
                              X = $52,800/0.06
                              X = $880,000
Before-tax profit or (loss):
 Mountaineering: 0.40($880,000)  $369,600 = $(17,600)
Before-tax profit or (loss):
 Touring:      0.34($880,000)  $316,800 = $(17,600)
                                                 Profitability Analysis and Planning 83


Problem 3-22 (cont.)

e. The Siberian Ski Company should produce the Mountaineering model. This
model is shown, below, to have a higher profit at a sales volume of 12,000 pairs.
Because it has a higher unit contribution margin, this profit advantage will
increase beyond 12,000 pairs.

Minimum profit of
Mountaineering model = ($88.00  $52.80)12,000  $369,600
                     = $52,800
Minimum profit of
Touring model        = ($80.00  $52.80)12,000  $316,800
                     = $9,600

f. Break-even point of
   Mountaineering model = $369,600/($88.00  $52.80)
                        = 10,500 pairs

The problem is to find the variable costs for the Touring model that will produce
the same break-even point. Let b represent this cost. Then:

$316,800/($80.00  b) = 10,500
($80.00  b)/$316,800 = 1/10,500
              $80  b = $316,800/10,500
              $80  b = $30.17
                    b = $80  $30.17
                    b = $49.83

Current variable costs                                    $52.80
Variable cost to produce desired break-even point         (49.83)
Decrease in variable costs per pair                       $ 2.97

g.
New variable costs: $52.80  0.90 = $47.52
New fixed costs: $316,800  1.10 =$348,480

New break-even point = $348,480/($80.00  $47.52)
of touring ski
                     = 10,729 pairs
84 Chapter 3


Problem 3-23
a. Delta Air Lines cost estimating equation:
        Variable cost ratio = $15,104 - $13,566 = 0.827772
                              $16,741 - $14,883
        Annual fixed costs = $15,104 – ($16,741 x 0.827772) = $1,246.272
        Total costs (in millions) = $1,246.272 + 0.827772X
     Southwest Airlines cost estimating equation:
        Variable cost ratio = $4,628.415 - $3,954.001 = 0.737893
                              $5,649.56 - $4,735.578
        Annual fixed costs = $4,628.415 – ($5,649.56 x 0.737893) = $459.646
        Total costs (in millions) = $459.646 + 0.737893X
b. Delta Air Lines break-even point:
        Contribution margin ratio = 1 – 0.827772 = 0.172228
        Break-even point = $7,236.175 million ($1,246.272/0.172228).
     Southwest Airlines break-even point:
        Contribution margin ratio = 1 – 0.737893 = 0.262107
        Break-even point = $1,753.656 million ($459.6459/0.262107).
c. Southwest Airlines profit at Delta Air Lines’ 2000 volume (millions):
        Revenue                                     $16,741.000
        Operating expanses:
             Variable            $12,353.067
             Fixed                   459.646        - 12,812.713
                                                    $ 3,928.287
d.
Based on Southwest’s lower fixed costs and variable cost ratio, the results suggest
Southwest’s profits would be more than twice the amount earned by Delta.
However, attempting to predict Southwest’s profits at Delta’s volume involves an
extrapolation beyond the relevant range. Hence, the results are not valid.
Delta is a much larger and more complex full service airline, with international
operations, several hubs, and many different types of airplanes. Southwest is
relatively small and nimble. Southwest is a no frills airline without international
operations, with a point-to-point route structure, and a single type of airplane.
                                                   Profitability Analysis and Planning 85


Problem 3-24

a. Annual break-even point in sales dollars:

      Break-even point = $300,000/(1  0.75  0.05) = $1,500,000

b. Annual break-even point in units:

      Break-even point = $300,000/{$60  [$60(0.75 + 0.05)]} = 25,000 units

c. On new books the contribution to other costs is 25 percent of the suggested retail
price. On used books the contribution to other costs is 50 percent of the suggested
retail price. Shifting towards more used books and fewer new books will increase
bookstore profitability.

d. Publisher project break-even point:

      Note: Solution is in terms of wholesale price to bookstore, not retail price to
      final buyer.

      Project break-even point = $260,000/(1  0.20  0.15) = $400,000

e. Profitability analysis of sales of 15,000 new books:

1. Bookstore’s unit level contribution
      Final retail sales $60  15,000                       $900,000
      Less unit level costs (0.75 + 0.05)                   720,000
      Bookstore’s unit level contribution                   $180,000

2. Publisher’s project level contribution:
         Sales to bookstores $60  0.75  15,000            $675,000
         Unit level costs (0.20 + 0.15)                     (236,250)
         Project level costs                                (260,000)
         Publisher’s project contribution                   $178,750

3. Author’s royalties: $675,000 net to publisher  0.15     $101,250
86 Chapter 3


Problem 3-25

a. Current break-even point in sales dollars:

      Contribution margin ratio = $400,000/$1,050,000 = 0.38095

      Break-even point = $240,000/0.38095 = $630,004

b. Unit contribution margin and break-even point:

      Unit contribution margin = $400,000/2,500 = $160

      Unit break-even point = $240,000/$160 = 1,500 units

c. The current average unit contribution margin is $160.

   Current unit contribution margin of individual products:
     Cozy Kitchen $100,000/1,000 units                    $100
     All House $300,000/1,500 units                       $200

   Shifting the mix to 80:20 will change the average unit contribution margin:
      ($100  0.80) + ($200  0.20) =        $120

   Contribution with proposed plan = 3,000 units  $120 = $360,000

   The current contribution margin is $400,000. The contribution margin with a
   shift in the mix, even with a 500 unit sales increase, is only $360,000. Hence,
   profits will decrease if the plan is implemented. In the absence of capacity
   constraints, sales should emphasize increased sales of the product with the higher
   unit contribution margin.
                                             Profitability Analysis and Planning 87


Problem 3-26
a.
                                 Accu Meter
                        Contribution Income Statement
                              For the Year 2004
Sales                                                 $2,000,000
Less variable costs:
       Direct materials                  $500,000
       Processing                         750,000
       Setup                              200,000
       Batch movement                      40,000
       Order filling                       20,000     (1,510,000)
Contribution margin                                   $ 490,000
Less fixed costs:
       Factory overhead                  $800,000
       Selling and administrative         300,000     (1,100,000)
Net income (loss)                                     $ (610,000)
b.
                                 Accu Meter
                  Multi-Level Contribution Income Statement
                              For the Year 2004
Sales                                                 $2,000,000
Less unit level costs:
       Direct materials                  $500,000
       Processing                         750,000     (1,250,000)
Unit level contribution                               $ 750,000
Less lot level costs:
       Setup                             $200,000
       Batch movement                      40,000
       Order filling                       20,000      (260,000)
Lot level contribution                                $ 490,000
Less facility level costs:
       Factory overhead                  $800,000
       Selling and administrative         300,000     (1,100,000)
Net income (loss)                                     $ (610,000)
88 Chapter 3


Problem 3-26 (cont.)

c.

     Sales (500 at $40)                                      $20,000
     Less unit and lot level costs:
        Direct materials (500 at $10)     $5,000
        Processing (500 at $15)            7,500
        Setup                              2,000
        Batch movement                       400
        Order filling                        200             (15,100)
        Contribution per lot                                 $ 4,900

d.

     Unit contribution margin:
     Selling price                                 $60
     Less unit level costs:
        Direct materials            $12
        Processing                   15            (27)
     Unit contribution                             $33

     Lot level costs:
        Setup                                  $2,000
        Movement                                  400
        Order filling                             200
        Total                                  $2,600


        Lot level costs          $2,600
        Desired contribution        700        $3,300
        Unit contribution                      $33
        Required lot size                         100     units
                                                     Profitability Analysis and Planning 89


Problem 3-27
a. 1.
   Current contribution:
     Fixed costs                   $21,000
     Profit                        - 9,000
     Contribution                  $30,000
   Contribution margin ratio = $30,000/$50,000 = 0.60
   Current break-even point = $21,000/0.60 = $35,000
a. 2.
                                   Super       Super
                                   Burgers     Chickens
        Selling price              $2.50       $3.00
        Variable costs             -1.00*      -1.80
        Unit contribution          $1.50       $1.20
        *$2.50 × (1.0 – 0.60)
                                      Short-run
                                   Volume     Mix
        Super Burgers              10,000     0.50
        Super Chickens             10,000     0.50
                                   Unit
                                Contribution         Mix Weight
        Super Burgers              $1.50             0.50 $0.75
        Super Chickens              1.20             0.50 0.60
        Average unit contribution                             $1.35
Short-run monthly profit:
      Contribution (20,000 units × $1.35)             $27,000
      Less fixed costs ($21,000 + 7,760)              -28,760
      Profit (loss)                                   $ (1,760)
Short-run contribution ratio:
      Contribution margin                                     $27,000
      Revenue ([10,000 × $2.50] + [10,000 × $3.00])           ÷55,000
      Contribution ratio                                       0.4909
Short-run break-even point = $28,760/0.4909 = $58,586
90 Chapter 3


Problem 3-27 (cont.)
a. 3.
                                    Long-run
                                 Volume    Mix
        Super Burgers            30,000    2/3
        Super Chickens           15,000    1/3
                                 Unit
                           Contribution            Mix Weight
        Super Burgers            $1.50             2/3 $1.00
        Super Chickens            1.20             1/3   0.40
        Average unit contribution                       $1.40
Long-run monthly profit:
     Contribution (45,000 units × $1.40)            $63,000
     Less fixed costs ($21,000 + 7,760)             -28,760
     Profit                                         $34,240
Long-run contribution ratio:
        Contribution margin                               $ 63,000
        Revenue ([30,000 × $2.50] + [15,000 × $3.00])     ÷120,000
        Contribution ratio                                   0.525
Long-run break-even point = $28,760/0.525 = $54,781

b.

Answers to requirement (b) will vary. Two possible recommendations are as
follows:

      Do not introduce the sandwich. There is too much risk. Introducing the
       sandwich causes a short-run loss, a permanent decline in the contribution
       ratio, and an increase in the break-even point. If the predicted increase in
       sales does not occur, the company will be in serious difficulty. Also, it is
       unclear what time the time period is for the short-run.
      Introduce the sandwich. While there is a short-run loss, a permanent decline
       in the contribution ratio, and an increase in the break-even point, these
       negatives are more than offset by the long-run increase in volume.
       Introducing the sandwich is taking the business to the next level of size and
       profitability.
                                                  Profitability Analysis and Planning 91


DISCUSSION QUESTIONS AND CASES

Question 3-28

It is important for senior management to set the ethical climate for the
organization. In this case, perhaps out of a true concern for employees, or perhaps
out of a desire for a “big bonus,” the plant manager is proposing an unethical
(illegal?) speedup of the assembly line.

We do not know if New City Automotive has a code of ethics. If it does, Art
Conroy should refer to it for guidance. Because Art is a management accountant,
he should also refer to the Standards of Ethical Conduct for Management
Accountants, presented in the Chapter 1 appendix.

Art has followed these standards so far. Faced with an issue that concerned him,
he went to the appropriate company official. At this point, he should follow the
procedures for resolution of ethical conflict. In particular, he needs to further
discuss the situation with Paula, expressing his concern about what may happen if
the speedup is detected (strikes, legal action, mistrust, plant closure) and what he
believes are the advantages of facing the situation directly.

He might recommend a general meeting with all employees and suggest that in
this meeting financial information be shared. Employees should be made aware of
the likelihood of closing the plant if financial performance is not improved. They
should also be shown how a small increase in productivity will make a big
difference in financial performance. They might even be invited to offer their own
suggestions for increasing productivity. They should be treated as team members,
rather than as adversaries. Finally Art might conclude his comments by noting
how the careers of all plant employees, including management, will be adversely
affected if the speedup is detected or if productivity is not improved. In this case,
including employees in the decision is less risky than the alternative.

If the conversation with Paula is unsatisfactory, Art should continue with the
additional steps for resolving ethical conflict presented in the Chapter 1 appendix.
92 Chapter 3


Question 3-29

   a. Using a unit level analysis, develop a graph with two lines, (1) representing
   Homestead Telephones cost structure in the 1940s and (2) representing
   Homestead Telephones cost structure in the late 1990. Be sure to label the axis
   and lines.
                                                                          (2) 1990s cost
            Total                                                         structure
            revenues
            and total                                            (1) 1940’s
            costs                                                cost structure




                                           Total volume


b. With sales revenue as the independent variable, the likely impact of the
changed cost structure on Homestead Telephone’s:

      Contribution margin percent: Because variable costs decrease, the
                               contribution margin percent will INCREASE

      Break even point           With an increase in fixed costs and a decrease in
                                 variable costs, the impact on the break-even point
                                 CANNOT BE DETERMINED. If there is a
                                 change, the BEP will likely increase because of
                                 downward pressure on prices.

c. Yes. Homestead has multiple services. The products may have different cost
structures and the may be sold to different customers. Homestead’s management
needs to know the profitability of each service.
                                                  Profitability Analysis and Planning 93


Case 3-30

a. To determine the break-even point, you must first find the contribution margin
as a percent of sales and the fixed costs per period. Because there are no taxes at
the break-even point, our analysis is based on before-tax information:

Variable costs as Change in total costs   $4,857,900  $4,430,000
a percent of sales = Change in Sales    = $5,520,000  $5,000,000 =
0.823

Fixed costs = $4,430,000  ($5,000,000  0.823) = $315,000

Break-even point = $315,000/(1 – 0.823) = $1,779,661

b. Sales volume required to earn an after-tax profit of $480,000:

Required before-tax profit = $480,000/(1 – 0.40) = $800,000

Required sales = ($315,000 + $800,000)/(1 – 0.823) = $6,299,435

c.

                           Regional Distribution, Inc.
                         Contribution Income Statement
                               For the Year 2005

      Sales                                         $6,000,000
      Variable costs ($6,000,000  0.823)           (4,938,000)
      Contribution margin                           $1,062,000
      Fixed costs                                     (315,000)
      Before-tax profits                            $ 747,000
      Income taxes at 40 percent                      (298,800)
      After-tax profit                              $ 448,200
94 Chapter 3


Case 3-30 (cont.)

d. To solve this requirement it is important to understand that Regional
Distribution has activity cost drivers in addition to the cost of goods sold used in
requirement (a). Class discussions should lead to the following analysis of activity
cost drivers:

Unit level:
       Cost of goods sold, 0.75 sales dollars
       Shipping expenses, 0.02 sales dollars
Order level:
       Shipping expenses, $50 per order
       Sales order processing, $25 per order*
Customer level:
       Customer relations, $500 per customer**
Facility level:
       Depreciation, $80,000
       Administration, $250,000

*$52,500  $50,000 change in sales order processing costs
  2,100  2,000 change in number of sales orders

**$120,000  $100,000 change in customer relations costs
    240  200 change in number of customers

The unit level variable costs are 0.77, 0.75 cost of goods sold  0.02 shipping.

Minimum order size: Before an order can contribute toward covering customer
level and facility level costs, the order must cover costs that are fixed at the order
level. These costs amount to $75, the per order shipping and order processing
costs. Hence, the break-even order size is $326, computed as $75/(1  [0.75 
0.02]). Regional Distribution might specify this as a minimum order size, or it
might have an additional cost for lower orders.

Minimum annual sales: Before sales to a customer contribute to facility level costs
and profits, they must cover both the order level costs and the customer level
costs. The following break-even annual sales are for customers who place one or
two orders per year.
                                                    Profitability Analysis and Planning 95


Case 3-30 (cont.)

One order per year:

      Minimum = $500 customer level + $75 order level = $2,500
      annual sales      1 – 0.77

Two orders per year:
     Minimum = $500 customer level + $150 order level = $2,826
     annual sales      1 – 0.77

Regional Distribution loses money on customers who place one order per year for
less than $2,500 or two orders per year totaling $2,826.

While the determination of what exactly should be done is not clear, it is apparent
that Regional Distribution should not continue with customers who are unlikely to
exceed these minimum purchase requirements. It also appears that Regional
Distribution’s sales efforts would be better devoted to increasing sales to a smaller
number of customers rather than simply increasing the number of customers.

e. The answers to requirements (a) through (c) are only correct if the mix of
activities is constant. Because the mix of activities is not constant, there is a high
level of uncertainty concerning the accuracy of the answers for requirements (a)
through (c).
96 Chapter 3


Case 3-30 (cont.)

f.

                          Regional Distribution, Inc.
                         Multi-Level Income Statement
                               For the Year 2005

Sales                                                            $6,000,000
Unit level costs:
       Cost of goods sold (0.75 sales)       $4,500,000
       Unit level shipping (0.02 sales)         120,000         (4,620,000)
Unit level contribution                                         $1,380,000
Order level costs:
       Order level shipping
        (2,750 orders  $50)                 $ 137,500
       Order processing
        (2,750 orders  $25)                     68,750           (206,250)
Order level contribution                                         $1,173,750
Customer level costs:
       Customer relations (340 customers  $500)                    170,000
Customer level contribution                                      $1,003,750
Facility level costs:
       Depreciation                          $ 80,000
       Administration                           250,000           (330,000)
Before-tax profit                                                $ 673,750
Income taxes at 40 percent                                        (269,500)
After-tax profit                                                 $ 404,250

The number of customers is increasing faster than the sales volume. This change
in the mix of activities causes prediction errors when simple models with only one
cost driver are used to predict costs. This is seen comparing the solution to
requirement (e) with the solution to requirement (c).

				
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