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COST-VOLUME PROFIT ANALYSIS

        Today the manager is a principal factor in the success or failure of any business
enterprise. The primary function of management is to make a profit for the firm. Essentially,
profit is generated by effective sales and/or distribution of products or services.
        Any decision-making organization actively concerned with profits will find itself
involved in the analysis of costs and revenues. Since the firm must first recover its costs
before it can make a profit.
        There are definite relationships between costs, revenues and profits. There are three
levels of activity that are of the greatest concern to the management of any profit-seeking
business.
        1. Break-even point
            The activity level at which the firm has exactly enough revenue to recover all
            costs.
        2. The firm is operating at a loss.
            The revenue that is penetrated is not sufficient to recover all costs that have been
            incurred (Total costs > Total Revenue ).
        3. The firm may be operating at profit.
            The revenue of the firm completely recovers the costs and has funds left over.

                      Production (Purchasing) costs
                      These are costs incurred in making or acquiring products for sale.

                      Promotional Costs
                      These costs are the costs that are associated with the creating of
                      consumer interested in the product. (advertisements)
   Cost Factors
                      General Administration Costs
                      This category includes those costs that are incurred in the day-to-day
                      operating of the firm (salaries, heat).

                      Marketing Costs
                      These are any costs associated with preparing & distributing the
                      product throughout the sales territories (packaging, shipping, expenses
                      of traveling sales representatives).

               Revenue = Unit Selling Price X Sales ( in units )
               (sales)

       In Decision making process, it is more useful to classify costs as follows :
       Fixed Cost : A cost that remains constant (within a specified range) regardless of the
                    level of operations. (Taxes, salaries for executive personnel)
       Variable Cost (Direct costs) : are cost which fluctuate in direct proportion with the
                    level of manufacturing output or unit sales.
       Sunk Costs : are previous investments which have no effect on a current decision.

               Total Cost = Total Fixed Cost + Total Variable Cost
                                                                                              355

             Cost
                                                                    Total Cost


                                                                    Variable Cost


                                                                    Fixed Cost



                                                                    Units
                     Fig.1 : Graphic representation of costs.

        In the analysis of BEP, much attention is given to the concept of contribution.

        Contribution / unit = Selling Price / unit - Variable Cost / unit

e.g..            Selling Price / Unit               27.50 MU
                 - Variable Cost / unit             17.50 MU
                 Contribution / Unit                10.00 MU

Linear Analysis

        Total Revenue (Total Income)          =   Selling Price / Unit X Sales ( Units)
                             E                =    P X
                     Total Cost               =    Total Fixed Costs + Total Variable Costs
                             K                =    F + vx

        Income                                                      E ( p, x)
        Cost
                                                                            K (F + vx)

                                                       Profit

        BEP(MU)                Break-even

                                                    Variable Cost
                           Loss


                                                    Fixed Costs
                                                                                    Units
                                           BEP (units)
                  Fig.2: Break-Even point.

At Break-Even :
                       E = K
                     px= F + vx
                     px- vx = F
                                                                                            356

                   x(p- v) = F
                                        F
                                X0 
                                       pv



                                            Fixed Cost
       Break Even (units) =
                               UnitSelling price  var iable cos t / unitı

                                           Fixed Cost
       Break Even (units) =
                               M arg inal revenue  M arg inal cos t

Example 1

       Total Cost = 200 + 5 X                           Fixed Cost = 200 MU
       Total Revenue = 7 X                              Marginal Revenue = 7 MU
                                                        Marginal Cost = 5 MU

       Application of formula
                                          F      200
                      BE = X 0                =     = 100 units
                                       MR  MC   75

       or        7 X = 200 + 5 X
                 7 X - 5 X = 200
                         2 X = 200
                        X = 100 units
         The firm must produce and sell 100 units. If the firm produces and/or sells than 100
units it will incur a loss, if it produces and sells more than 100 units, it will make a profit.

Break-Even in MU
                           F
               X0  p        p
                          pv
                                             F
               BE (MU) = X 0 ( MU ) 
                                                 v
                                          1
                                                 p

Break-Even as % Capacity

                                     F
               BE (%)                                100 %
                          ( p  v)(unit capacity t )

                                 F
       or      BE (%)                       100 %
                          (1  v / p) t  p
                                                                                           357

Example 2

        Demir Furniture Co. manufactures and sells bedroom suites. Each suite costs 250MU
and sells for 400 MU. Fixed costs at Demir Furniture total 75 000 MU. Determine the Break-
Even point using
        a). Algebraic analysis
        b). The general formula approach

Solution:

       Data Summary :        Unit selling price = 400 MU
                             Cost per unit = 250 MU
                             Total fixed cost = 75000 MU

   a) Use of the algebraic approach requires us to equate the total revenue equation and the
      total cost equation. The breakeven point is the output (X0) where this equality is valid.
                             TR = TC
                              E = K
                             pX = F + vX
                           400 X = 250 X + 75000
                  400 X – 250 X = 75000
                              X0 = 500 units
      Demir Furniture Co. has a breakeven point of 500 units.

   b) The general formula approach for strict breakeven requires the use of following
      formula
                               F        75000
                   BE = X 0        =            = 500 units
                              pv     400  250

       The breakeven point equals 500 units.

Example 3

       Best Cut Shops Ltd. Operates 10 haircut shops in Famagusta on a 250-days-per-year, 8
hours-per day basis. They charge 10 MU for a haircut. One shop has annual fixed costs of
84000 MU and variable costs estimated at 3 MU per customer.
   a) What is the contribution per customer?
   b) How many customers per hour must the shop average in order to break even?

Solution:
            a) Contribution = p – v = 10 MU – 3MU = 7 MU per customer
                      F     84000 84000
            b) X 0       =                12000 customers/year
                     p  v 10  3       7

                          12000 Customer / year
            i.e.                                         6 customers/hour
                      (250 days / year )(8 hours / day)
                                                                                          358

Example 4

        If fixed costs are 40000 MU and available costs are estimated at 50% of the unit
selling price of 160 MU, what is BEP?

Solution:
                       F     40000
               X0         =          500 units
                      p  v 160  80

Example 5

       The owners of a professional football team have leased a 30000-seat-stadium for six
games for a fixed cost of 1680000 MU. They expect variable costs to run 4 MU per spectator
and tickets will sell for an average of 24 MU each. How many tickets, on average, must be
sold per game for the owners to just break even?

Solution:
                       F    1680000 1680000
               X0        =                 84000 seats / year
                      pv    24  4    20

                                 84000 seats
               Seats / game                   = 14000 seats / game
                                6 games / year



Example 6

     A computer company plans to produce 30000 computers next year. They will sell for
700 MU each. The fixed cost of operation care 5 million and total variable costs are 6 million
MU. What is the break-even point?

Solution:
                       F                    6000000 MU
               X0              where v                 = 200 MU / unit
                      pv                    30000 units

                           5000000 MU
               X0                              = 10000 units
                      (700 MU  200 MU ) / unit

Example 7

       A DVD player sells for 350 MU and has variable cost of 85 MU.
       a) Find the contribution
       b) Find the contribution ratio

Solution:
              a) Contribution = p –v = 350 MU – 85 MU = 265 MU
                                                                                              359

                                               pv     v      85   265
                  b) Contribution margin           1  1           0.76
                                                p      p     350 350

Example 8

        Izmir Shoe-City Ltd. Produces 24000 pairs of running shoes per month. Annual fixed
costs are 840000 MU and the contribution from each pair is 60% of their 20 MU per-unit
selling price. Find the break-even volume.

Solution:
                          F    840000
                  X0                 70000 pairs            Where p – v = 0.60 (20) = 12
                         pv     12

                                  F       840000
       or         X 0 ( MU )                    1400000 MU
                                    v       0.6
                                 1
                                    p
                                 1400000 MU
                  X 0 (Units )                 70000 pairs
                                  20 MU / unit


Example 9

        Turkish airlines offers customers a vacation plan for 520 MU. The Airline estimates
that the fixed costs associated with this plan are 720000 MU and at a volume of 3000
passengers total variable cost would be 480000 MU and profits should be 360000 MU.
        a) Find the break-even volume
        b) If fixed costs remained constant, how many additional passengers (beyond Break-
           even) would be required to increase profits to 500000 MU?

Solution:
                   F     720000                                      48000
       a) X 0                    2000 passengers      Where v           160MU/passenger
                  p  v 520  160                                    3000

       b) Contribution = p – v = 520 – 160 = 360 MU/passengers
                                500000
              # of passenger =           1389 passengers
                                  360

Example 10

        Cyprus Packing Ltd. Packages orange juice in 300 cl. – cans which they sell to grocery
distribution warehouses for 48 MU/case. The packing company has fixed costs of 324000 MU
and variable costs of 30 MU/case. The plant has a capacity of 100000 cases per season.
        a) Find the contribution
        b) How many cases must be sold to break-even?
        c) What is the profit (or loss) if the plant operates at full capacity for the season?
                                                                                        360



Solution:

       a) Contribution = price/unit – variable cost/unit = p – v = 48 MU/case – 30 MU/case
                                                                 = 18 MU/case
                 F     324000 MU / season
       b) X 0                                 18000 cases / season
                pv        18 MU / case

       b)  = (100000 – 18000) (18) = 1476000 MU


Example 11

        Azim Electronics has the capacity to produce 30000 networking devices per year at a
plant in Cyprus. Their variable costs are 12 MU/Unit. They are currently operating at 80% of
plant capacity, which generates a revenue of 720 000 MU/year, at current volume, the fixed
costs are 360000 MU.
        a) What is the current annual profit or loss?
        b) What is the break-even quantity?
        c) What would be the firm’s profit, if they could operate at 95% of capacity?

Solution:

       a) Current volume = 80% ( 30000 units) = 24000 units
          Profit =  = TR – TC = 720000 MU – ( 360000 + 24000 x 12 )
                                = 720000 – (360000 + 288000)
                                = 720000 – 648000 = 72000 MU
                 720000 MU (TR )
       b) p                         30 MU / unit
                  24000 units ( X )
                 360000 360000
          X0                      20000 units
                 30  12     18
       c) What would be the profit for 95% of capacity?
          Capacity = 95%,  Volume = 0.95 (30000) = 28500 units
           = (Sales Volume – BEP) (Contribution) = (28500 – 20000) (18) = 153000 MU

Example 12

       Tahil Ticaret Company has 30 employees and handles 1500 loads per year of grain
from a konya warehouse. The firm has fixed costs of 70000 MU/year and variable costs of
170 MU/load.
       The production and operations manager is considering installing an 80000 MU
automated material handling system that will increase fixed costs by 20000 MU/year. It will
also increase the per unit contribution of each load by 20 MU. The firm operates 250
days/year and they receive an average of 300 MU revenue for each load passed through the
warehouse.
       a) what is the current annual profit (or loss)?
       b) What is the new BEP volume if the investment is made?
                                                                                           361

Solution:
                    F      70000     70000
       a)   X0                           538 .46 units
                   p  v 300  170    130

          = (1500 – 538.46) (300 – 170) = 125000 MU
     or  = TR – TC = 1500 (300) –  70000 + 1500 (150)  = 450000 – 325000
                                                          = 125000 MU
     b) New Fixed Cost = 70000 + 20000 = 90000 MU
        Contribution = 300 – 170 = 130 MU
        New Contribution = 130 MU + 20 MU = 150 MU
                           F     90000
                    X0                 600 units
                          pv     150
Example 13

       Process A has fixed cost of 80000 MU per year and variable cost of 18 MU/unit,
whereas process B has fixed costs 32000 MU per year and variable costs of 48 MU/unit. At
what production quantity X0 are the total costs of A and B equal?

Solution:

       Set total costs equal :       TCA = TCB
                                FA + VA X = FB + VB X
                             80000 + 18 X = 32000 + 48 X
                                    48000 = 30 X
                                      X0 = 1600 units

Example 14

        A firm has annual fixed costs of 6.4 million MU and variable costs of 14 MU/unit. It is
considering and additional investment of 1600000 MU, which will increase the fixed costs by
300000 MU/year and will increase contribution by 4 MU/unit. No change is anticipated in the
sales volume or sales price of 30 MU/unit.
        What is the BE quantity if the new investment is made?

Solution:

       The 4 MU increase in contribution will decrease variable cost per unit to
              14MU – 4 MU = 10 MU/unit
       The addition to Fixed Costs makes them 6.4 million + 300000 MU = 6.7 million MU
                       F     6700000
              X0                     335000 units
                     pv      30  10

Example 15

        Mohuiddin Computer Ltd. Produces a computerized monopoly game and wishes to
establish a break-even analysis report. The game sells for 37.50 MU each, but volume has
never been dropped below 4000 units and the costs are not accurately classified into fixed and
variable costs. Although 72000 MU of costs are reported as “fixed”, some of the “variable”
                                                                                                 362

cost items (e.g selling and administrative) have fixed components. The following cost data is
available for two representative volumes.


                                               Costs at volume of
                                        4000 units           12000 units
               Labor                    20000 MU              40000MU
               Material                 50000                110000
               Overhead                 78000                 88000
               Sell& Adm.               30000                 40000
               Total other costs       178000 MU             278000 MU
               Known fixed costs        72000                 72000
                                       250000 MU             350000 MU


Solution:

                                                    change in Total Costs
       a) The slope of the total cost line, i.e.                            , gives us the
                                                   change in Total Quantity
       variable cost / unit.

                    350000 MU  250000 MU 100000 MU
               v                                          12 .50 MU/unit
                     12000 units  4000 units   8000 units

       b) In order to find fixed costs, we can subtract total variable cost from total cost of
       either for 4000 units or 12000 units.
                      F = Total Cost @ 4000 units – 4000 x 12.50
                         = 250000 MU – 50000 MU = 200000 MU

       c) Contribution is = p – v = 37.50 MU – 12.50 MU = 25.00 MU/unit
                 200000
       d) X 0            8000 units
                   25
       e) Estimation of profit at a volume of 10000 units
          Profit = TR –TC   = (10000 x 37.50) – (200000 + 10000 x 12.50)
                                   = 50000 MU
       or     = (Total Sales – BEP) (p – v) = (10000 – 8000) (37.50 – 12.50) = 5000 MU

Example 16

       Cheap-Shot Retailing is currently purchasing a certain commodity at a cost of 7
MU/unit and is selling the item at a price 10 MU/unit. Total fixed cost is 15,000 MU. An offer
is made by the wholesaler to provide the item at a cost of 6 MU/unit, if Cheap-Shot will
guarantee a minimum annual purchase of 7,500 units. In considering the offer, it is
determined that acceptance will require a 20% increase in fixed costs; and, because of the
reduced unit cost, the product could be sold at a 15% lower price than the current retail price.
The current sales level is 6,000 units per year; it is estimated that the price reduction will
increase sales by 30%.
       Should the offer be accepted or rejected?
                                                                                        363

Solution:

       Data Summary:
                             Current Operating Data       Projected Operating Data
       Fixed Cost            15000 MU                     40000MU
       Variable cost/unit    7                            6
       Unit Selling price    10                           8.5
       Estimated Sales level
       (units)               6000                         7800
       Units Purchased       6000                         7800

              * F.Cost = 15000 MU + 0.20 (15000 MU) = 18000 MU
                S. Price / unit = 10 MU – 0.15 (10MU) = 8.50 MU
                Sales (units) = 6000 + 0.30 (6000) = 7800 units




a) Method 1 : Break-Even Analysis
                     15000
              X 01           5000 units (For current operations)
                     10  7
                     18000
              X 02            7200 units (For projected operations)
                     8.5  6

        Acceptance of the wholesaler’s offer will increase the BEP_ from its current level
       of 5000 units to 72000 units, a 44% increase.
          This, in turn, will REDUCE the sales above the BEP from 1000 units (6000 –
       5000) to 600 units (7800 – 7200).

       Decision : The wholesaler’s offer should NOT be accepted.

b) Method 2 : Cost-Profit Analysis
       i.   Current operations
               = (6000 – 5000) (10 – 7) = 1000 (3) = 3000 MU
       or
              Total Revenue : 10 (6000) = 60000 MU
              Total Cost     : 15000 + 7 (6000) = 57000 MU
              Profit         : 3000 MU
           The current operation produces a profit of 3000 MU.

       ii.    Projected Operations
               = (7800 – 7200) (8.5 – 6) = 600 (2.5) =1500 MU
       or
            Total Revenue : 8.5 (7800) = 66300 MU
            Total Cost     : 18000 + 6 (7800) = 64800 MU
            Profit         : 66300 – 64800 = 1500 MU
          The projected operation will result in a profit of only 1500 MU.
                                                                                             364

       Decision : The wholesaler’s offer should be rejected because it will decrease the profit
       level.

Example 17

        ABC Inc., operates a medium-sized assembly line. At the present time the
management of ABC, Inc., is considering the addition of a new press to its assembly
operation. If the press is added, it will reduce variable cost by 20% per unit; however, the cost
of the new press will increase fixed cost-by 75,000 MU. Assuming no other change, and given
the following current operating data, determine whether or not the new press should be
purchased.

       Current operating data:
              Fixed cost                      250,000 MU
              Variable cost per unit               40 MU
              Unit Selling price                   65 MU
              Projected Sales                  20,000 units

Solution:

       Data Summary.
                              Current Operating      Addition of New Press
       Fixed Cost             250000 MU                 325000MU (increased by 75000MU)
       Unit Selling price     65 MU                         65 MU (no change)
       Unit variable cost     40 MU                         32 MU (reduced by 20%)
       Projected Sales
       (units)                20000                           20000

a) Method 1 :
                                            F      250000
       current operations : BE  X 0                      10000 units
                                          p  v 65  40
                                            F      325000
       New Press               BE  X 0                   9848 .49 units
                                           p  v 65  32
       Under linear analysis, the best decision with a fixed level of output is simply “select
the program that has the lowest breakeven volume”. ABC Inc. should install the new press.
Although this decision will increase fixed costs by 75000 MU, it will decrease unit costs
enough to more than compensate for the change.

b) Method 2 : total contribution analysis
                              Current Operations              Addition of New press
       Total Revenue :        1300000 MU                      1300000 MU
     - Cost of Goods sold 800000 MU                           640000 MU
       Gross Margin
       (contribution)         500000 MU                       660000 MU
     - Total fixed cost       250000 MU                       325000 MU
       Profit                 250000 MU                       335000 MU

       Or
        (current operations) = (20000 – 10000) (65 – 40 ) = 10000 (25) = 250000 MU
                                                                                              365

        (new press) = (20000 – 9849) (65 – 32) = 10151 (65-32) = 334983 MU

      Using total contribution analysis, addition of the new press will increase profit from
250,000 MU to 335,000 MU. ABC Inc., should install the new press.

Example 18

       A producer of digital cameras sells his product through a credit card firm at 60 MU
each. The production costs at volume 10,000 and 25,000 units are as follows:

                                     10,000 units             25,000 units               .
      Labor                          120,000 MU               200,000 MU
      Materials                      240,000                  400,000
      Overhead (F + V)               180,000                  220,000
      Selling & administration       100,000                  120,000
Depreciation & other fixed cost      160,000                  160,000
                                     -----------------        -----------------
       Total                         800,000 MU               1,100,000 MU
                                     -----------------        -----------------
       Use the data to determine the BEP.
Solution:

        Note that the slope of the total cost line (that is, change in Y/change in X) is the
variable cost per unit.
                     Y      change in Total Costs            1100000  800000
                v                                        
                     X change in Total Quantity                25000  10000
                     300000
                v            20 MU / unit
                     15000
        In order to find Fixed Costs, we can subtract total variable cost from total cost of E.G.
10000 units.
        F = Total Cost @ 10000 units – 10000 x 20 = 800000 – 200000 = 600000 MU
                       600000 60000
                X0                      15000 units
                       60  20     40

Example 19

        Data for a break-even analysis revealed that total costs at volumes of 600 and 800
units were 160,000 MU and 192,000 MU respectively. Revenue is 288 MU/unit. Based upon
this information, what are
        a). the variable costs per unit
        b). the fixed costs

Solution:
                          Total Cost 192000  160000 32000
       a) Variable Cost                                          160 MU/unit
                            quantity         800  600       200
       b) F = TC@600 - vx@600 = 160000 – 600 (160) = 160000 – 96000 = 64000 MU
                                                                                           366



Example 20

         Guzel Havuz Ltd. Sells their product for 6,000 MU each, at a volume of 20 units, their
labor, materials, overhead and other costs total is 120,000 MU and at a volume of 40 units the
total is 160,000 MU.
         a) What is your best estimate of the variable cost per unit?
         b) Estimate the fixed costs.
         c) At what volume does the firm break-even?
         d) Estimate the profit at a volume of 60 units.

Solution:

               Total Cost 160000  120000 40000
       a) v                                            2000 MU/unit
                 quantity          40  20          20
       b) F = TC@20 - vx = 120000 – 20 (2000) = 80000 MU
                   80000       80000
       c) X 0                       20 units
                6000  2000 4000
       d)  = (60 – 20) (6000 – 2000) = 40 (4000) = 160000 MU


Example 21

       ABC, a medium-sized manufacturing firm, is considering the addition of a new
machine to its present assembly operation. The machine is expected to reduce variable cost by
15% per unit; however, it will add 60,000 MU to total fixed cost. Assuming no other change,
and given the following current operating data, determine whether or not the new machine
should be purchased.

       Current operating data:
              Fixed cost                      200,000 MU
              Variable cost per unit               20 MU
              Unit selling price                   30 MU
              Expected annual sales           30,000 units
Solution:

       Data Summary.
                             Current Operating               Anticipated Operating
                             Data (before purchase)          Data (after purchase)
       Fixed Cost                   200000 MU                260000 MU
       Unit variable cost           20 MU                    17 MU
       Unit Selling price           30 MU                    30 MU
       Estimated annual sales       30000 Units              30000 units

Method 1 : Break-Even Analysis
                                         200000
       a) Prior to acquisition : X 0             20000 units
                                         30  20
                                                                                               367

                                      260000
       b) After acquisition : X 0             20000 units (For projected operations)
                                      30  17

        Break-even analysis suggest that ABC should be indifferent with regard to the
purchase of the additional equiptment.
        The decrease in variable cost per unit is exactly offset at the level by the increase in
fixed cost. So the firm does not appear to benefit from the acquisition.

Method 2 : Cost-Profit Analysis
      a) Prior to acquisition
             Total Revenue : 30 (30000) = 900000 MU
             Total Cost      : 200000 + 20 (30000) = 800000 MU
             Profit          : 900000 – 800000 = 100000 MU
      or
              =  Sales (units) – BEP (units)   p – v 
               = (30000 – 20000) (30 – 20) = 100000 MU

       b) After acquisition
               Total Revenue : 30 (30000) = 900000 MU
               Total Cost     : 260000 + 17 (30000) = 770000 MU
               Profit         : 900000 – 770000 = 130000 MU
       or
                =  Sales (units) – BEP (units)   p – v 
                 = (30000 – 20000) (30 – 17) = 130000 MU
       If the new equipment is purchased, ABC will receive a profit of 130000 MU.

       Break-Even Analysis alone may no be sufficient to solve a DECISION problem. If
Sales Levels are known or can be estimated with a satisfactory degree of accuracy, these
should be incorporated into the analysis.
       The joint utilization of BE and C-P calculations is one way of extracting meaningful
information for Decision Making.

Example 22

        Azim Industries is considering a revision of its current advertising program. The
current program requires a fixed investment of 15,000 MU. The proposed program will
require a fixed investment of 25,000 MU. Azim’s products currently retail at 125 MU/unit and
cost 100 MU/unit.
        a) Using the data at hand, what effect would the revised program have on Azim’s
            break-even volume?
        b) If the maximum output for the Azim is 1,500 units, should the revised program be
            undertaken? Why or why not?

Solution:

               Data Summary.
                            Current Program                    Revised Program
       Fixed Cost                  15000 MU                    25000 MU
       Selling price / unit        125 MU                      125 MU
       Cost / unit                 100 MU                      100 MU
                                                                                           368



a).    i. Break-even using the current program
                          15000
                 X 01             600 units
                        125  100
          ii Break-even using the revised program
                         25000
                X 02             1000 units
                       125  100
       The revised program has a break-even point of 1000 units

b) Since Azim’s output is fixed at 1500 units, a decision on implementing the revised
program can be made on the basis of optimum profit.
                             Current Program                Revised program
       Sales (units)         1500                           1500
       Total Revenue         187500 MU                      187500 MU
      Cost of Goods          150000 MU                      150000 MU
       Gross Margin          37500 MU                       37500 MU
       Total variable costs      0                             0
       Total contribution    37500 MU                       37500 MU
       Total fixed cost      15000 MU                       25000 MU
       Profit                22500 MU                       12500 MU

       or
        (current) = (1500 – 600) (125 – 100) = 900 (25) = 22500 MU
        (revised) = (1500 – 1000) (125 – 100) = 500 (25) = 12500 MU

       On the basis of profit, the revised program should not be undertaken. Since there are
no adjustments in the selling price per unit or unit costs, the revised program will simply
decrease Azim’s profit by the amount of the cost increase.

IMPORTANT!


Under linear analysis, the best decision with a fixed level of output is simply “Select the
program that has the lowest BE volume”.
___________________________________________________________________________



Example 23

       Refinery operations at Altinoglu Station, a single-proprietor operation, necessitate the
leasing of certain equipment at the rate of 350 MU/month. Altimoglu has three employees
whose total wages are 1,650 MU/month. Utilities cost Altinoglu a total of 250 MU/month.
The contribution margin is 0.20 MU/gallon.
       What is the break-even point for Altinoglu?
                                                                                            369

Solution:

       Data Summary :
              Cost of Utilities      = 250 MU / month
              Employee wage          = 1650 MU / month
              Lease rate             = 350 MU/ month
                                       2250 MU / month
              Contribution margin       0.20 MU / Gallon
                             F      2250
              BEP  X 0                  11250 gallons
                            p  v 0.20
       Altinoglu will break even at a volume of 11250 gallons of gasoline.


Example 24

       Azim Consultants is operating on an annual volume of 750,000 MU revenue from
services. Total variable cost for Azim is 250,000 MU. If Azim has a total fixed cost of
200,000 MU, at what volume revenue does it break even?

Solution:

       Data Summary :
              Total variable cost / year     = 250000 MU
              Total fixed cost               = 200000 MU
              Total revenue                  = 750000 MU

                                 Fixed Cost             F      200000     200000
BE ( MU )  X 0 ( MU )                                                        300000 MU
                              Total var iable cos t      vx      250000       1
                           1                         1      1           1
                              Total annual sales         px      750000       3

       Azim Consultants will break even with an annual volume of 300000 MU.


Example 25

       Genel Saglik Hospital currently purchases a certain type of surgical supply at a cost of
15 MU/unit. When the surgical units are required, Hospital charges 25 MU/unit. A local
medical supplier has offered to provide the surgical supply a cost of 10 MU/unit if Hospital
will guarantee a minimum annual purchase of 4,000 units.
       In considering the offer, the directors of Saglik Hospital have determined that
acceptance will require a 30% increase in fixed cost; however the patient charge could be
reduced 20% on a per unit basis. At the present time, Saglik uses 2,500 units each year, but it
has been said that the hospital will increase its use rate by 40% in the coming year. In addtion
Saglik current policy requires a fixed investment of 30,000 MU in its supply program.
Acceptance of this offer will increase this fixed investment to 50,000 MU.
       Should the offer be accepted or rejected? Why?
                                                                                             370

Solution:

       Data Summary.
                              Current Policy         Revised Policy
       Fixed Cost             30000 MU               39000 MU
       Price / unit - service 25 MU                  20 MU
       Cost / unit - service 15 MU                   10 MU
       Annual purchase        3500 units             4000 units

Method 1 Break even Analysis
      a) Current Policy
                     30000
              X 0C           3000 units
                     25  15

        = (use rate – BEP) (p – v) = (3500 – 3000) (25 – 15) = 5000 MU

       b) Revised Policy
                       39000
               X 0R            3900 units
                       20  10
        = (use rate – BEP) (p – v) = (4000 – 3900) (20 – 10) = 1000 MU

        Under its current purchase policy, hospital can expect to break even when it uses 3000
units of surgical material. Its expected usage is 3500 units, a situation which will result in an
expected profit of 5000 MU.
        Under the revised purchase policy, hospital expected break-even point is 3900 units.
This leads the hospital to 1000 MU profit. Hospital should not accept supplier’s offer. The
current purchase policy is more economical.

				
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