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Budgeted BES To Earn The Target Profit

 Budgeted BES to earn the target profit

Problem 1:

Budgeted BES to earn the target profit:

         A company which has started developing the annual profit plan has just reviewed the draft annual income statement & is concerned with the $ 220000 indicating profit on a sales volume of 40000 units. The fixed cost structure of $ 1980000 appears to be high and regarding departing from the annual sales price of $ 200, they have some doubts. Profit target of $ 440000 is a general agreement. Several tentative alternative plans have been suggested during the meeting of the executive’s committee which has just reviewed the tentative profit plan.

Compute:

 (a) The budgeted breakeven point in $ & in units & the number of units that needed to be sold for earning the target profit.

(b) You are required to directly respond to each of the following two alternatives which are being considered by the management. (Consider each independent of other & state any assumption that needed to be made)

         Alternative1: A sales price increase of 20% is contemplated; it has been estimated by the sales executives that drop in units will be resulted from this that can be sold by 15%. What would be the new breakeven point in $ & in units? What would be the new profit figures? For earning the target profit, how many units would have to be sold?

         Alternative 2: A decrease in variable cost of 6% & a decrease in fixed cost of $ 110000 are contemplated. What would be the new breakeven point in $? For earning the target profit, how many units would have to be sold?   
                                                                                                           
Solution: We know that Sales – Variable cost = Fixed cost + Profit

Sales Volume (units)                                                                  20000 units
                                                            Total ($)                         Per unit ($)  
Sales (a)                                              4000000                          200.00
Fixed cost                                            1980000                          99.00
Profit                                                     220000                           11.00
Contribution (b)                                  2200000                         110.00
Variable cost                                       1800000                           90.00

P/V ratio = (Contribution / Sales) * 100 = 2200000/4000000 = 55%

B.E. in sales in units = Fixed cost / Contribution per unit = $ 1980000/110 = 18000 units

B.E. in sales in $ = 18000 units * $ 200 = $ 3600000
Target Profit                                               $   440000
Fixed cost                                                      1980000
Target Contribution                                       2420000    …… (i)

Number of units to be sold = Target contribution / Contribution per unit

                                           = $2420000/ $110 = 22000 units

          (a) Alternative 1

20% increase in price = $ 200 *120% = $ 240
Less: Variable cost per unit                         90
Contribution                                               150

B.E. point = $ 1980000 / $ 150 = 13200 units

B.E. Sales = 13200 * $ 240 = $ 3168000

Net profit figure with 15% reduction in sales (17000 units) is:

Contribution (17000 units * $ 150)                   $ 2550000
Less: Fixed cost                                                    1980000
Net Profit                                                                570000

No of units to be sold to earn target contribution of $ 2420000 as per (i) above

= Target contribution / Contribution per unit

= $ 2420000 / 150 = 16133 units

          (b) Alternative 2

Revised fixed cost                                                                     $ 1870000
Revised Variable cost per unit $ 90 less 6%                              $ 84.60
Revised contribution per unit = $200 - $84.60                          $ 115.40
P/V ratio = 115.40/200                                                              57.7%

B.E. Sales = Revised Fixed cost / Revised P/V ratio = $ 1870000/57.7% = $ 3240901

Target Profit                                                                                 $ 440000
Revised fixed cost                                                                     $ 1870000
Revised Contribution                                                                 $ 2310000   
      
No of units to be sold = $ 2310000/ $ 115.40 = 20117 units
                                                                                                  
         Problem 2:

Break-even analysis before/after allocated H.O. expenses- Evaluation of Profit Plans:

         Cost-volume-profit analysis has been prepared by a company named X for each plant as per details below:

(a)Annual budgeted fixed costs of $ 360000, variable cost $ 2520000 & sales value of production of $ 6600000 has been shown by the profit plan for Plant A. Allocated head office budgeted fixed costs are $ 960000. Prepare an analysis which indicates the breakeven point before & after the cost allocation. Also, explain why the breakeven points change (in $) is greater than the allocated amount.

(b) A product which sells at $ 120 is produced by Plant B. When 15000 units are produced, it costs $ 127.50, whereas cost per unit is $ 114.375 when 20000 units are produced. What is the break-even point in $ & in units.

(c) Budgeted income & cost estimates of Plant C are as follows:                              $

Sales (annual)                                                                             $                   3000000
Costs: Fixed                                                                               1200000
           Variable                                                                              900000
            Head office expenses allocated                                     1050000      3150000
Loss                                                                                                                     50000

         Sale of Plant Z is under consideration. On the basis of the data given, what will be your recommendation? Also justify your recommendation.

(d) Plant D produces 1 product: the budgeted income & cost estimates are as follows:

Sales (annual) @ $ 600 per unit                                                                      6000000
Costs: Fixed                                                                               2242500
           Variable                                                                           4050000
            Head office expenses                                                     1507500       7800000
Loss                                                                                                                 1800000  

         In order to break-even, how many additional units need to be manufactured in the plant?
Above the breakeven, what would be the profit pick-up per unit?
           
Solution: (a) Sales Value                                                          6600000
                      Variable cost                                                        2520000
                      Contribution                                                         4080000

P/V ratio = (4080000/6600000) = 61.82%

Breakeven point before allocation: BES * P/V ratio = Fixed cost

                                                         BES * 61.82% = 3600000                    

                                                         BES = $ 5823358
                                                                                                  
 Breakeven point after allocation: BES * P/V ratio = Fixed cost including allocated expenses

Or, BES * 61.82% = $ 3600000+ $ 960000

Or, BES = $ 7376253

(b) Cost for 20000 units = 20000*114.375 =                            $2287500
     Less: Cost for 15000 units = 15000*127.50 =                       1912500
                             5000 units                                                         375000
                                                                                                                       
    Variable cost per unit = change in cost / change in quantities

                                       = $ 375000 / 5000 units = $ 75

Thereby, Variable cost for 15000 units = 15000 units * $75 = $ 1125000  
                                                                                                                    
Fixed cost = Total cost at level of 15000 units – Variable cost at level of 15000 units

                 = $ 1912500 - $ 1125000 = $ 787500

P/V ratio = (120-75) / 120 = 37.5%

BEP * P/V ratio = Fixed cost 
   
BEP = $ 787500 / 37.5% = $ 2100000

BEP in units = $ 2100000 / $ 120 = 17500 units

(c) P/V ratio of Plant C = (3000000 – 900000) / 3000000 = 70%

Fixed cost of Plant C = $ 1200000

BES of Plant C = $ 1200000/70% = $ 1714285

         The Plant is operating above the break-even the point & it is yielding contribution for absorbing head office expenses. As head office expenses will be there in any case, the plant should not be closed down. Decision to close Plant 1 will lead to a loss of contribution of $ 2100000.

(d) Sales of Plant D                                                                   $ 6000000
     Variable cost                                                                            4050000   
     Contribution                                                                             1950000

BEP * P/V ratio = $ 2242500

BEP * (1950000/6000000) = 2242500

BEP * 32.5% = 2242500

BEP = 2242500/32.5% = $ 6900000 or 11500 units

Additional units required to break even = 11500 – 10000 = 1500 units.

Profit pickup will be equal to contribution per unit = 1950000 / 10000 = $ 195 per unit.

Problem 3: Break-even analysis of candidates – semi-variable cost

         For the post of junior officers, competitive examinations are conducted by a bank every year for the selection of candidates. For admission to the examination, each candidate is charged an entrance fee of $ 300. From the last 2 years the data gathered are as under:

                                                                                                2009 ($)           2010 ($)          
Fees collected                                                                         1200000          1500000
Costs:
Valuation of answer books                                                        480000           600000
Question papers                                                                        320000           400000
Hire of Hall                                                                                 48000               48000
Honorarium to Examination Superintendent                             40000                40000
Invigilators at the rate of one invigilator for every
50 students at $ 400 per day for 2 days                                 64000                80000
General expenses                                                                     48000                48000
Total                                                                                      1000000            1216000      
Net Income                                                                              200000              284000

         In 2011, it is expected that for the entrance examination, 6000 candidates will appear. The hall rent & general expenses are expected to increase by $ 12000 & $ 32000 respectively. For the year 2011, calculate the following:

(a) Budgeted income;
(b) Break-even number of candidates;
(c) For the purpose of earning net revenue of $ 400000, number of candidates required to sit for the examination.

Solution: Statement showing the nature of cost & variable cost per unit

2009                2010              Nature     Variable cost   
                                                                          Per candidate

Fees ($)                                               1200000          1500000         
Fees collected per candidate ($)                 300                  300
Number of candidates                                          4000                5000
                                                                        $                      $                                  $
Valuation of answer papers                480000             600000          Variable           120
Question papers                                 320000             400000          Variable             80
Hire of Hall                                            48000               48000          Fixed
Honorarium to Examination Suptd.      40000                40000          Fixed
Invigilators
($400 / 50) * 4000 * 2                            64000          
($400 / 50) * 5000 * 2                                                     80000          Step cost
General expenses                                   48000               48000          Fixed

(a)                                                        Budget for 2011
Number of candidates                                                                                             6000
Fees @ $ 300                                                                                      $ 1800000
Less: Variable costs/ Semi-variable cost
            Valuation of answer papers                            720000                                   
            Question papers                                              480000
         Step cost
Invigilators ($400 / 50) * 6000 * 2                   96000                 1296000
         Contribution                                                                                                  504000
Less: Fixed cost
            Hire of Hall                                                       60000
            Honorarium to Examination Suptd                   40000
            General expenses                                           80000                               180000
Profit                                                                                                                     324000

Consideration per candidate after considering Invigilators cost = 504000 / 6000 = $ 84

Consideration per candidate without considering Invigilators cost = 600000 / 6000 = $100           
           
          (b) Breakeven point is that point of sales where contribution is just sufficient to meet fixed cost. At this point, there is no profit no loss, because all costs (variable, step & fixed) are recovered. In the given situation, in 2011, the position will be as follows:

Variable cost                                                               $ 1200000
Step cost                                                                            96000 
                                                                                       1296000

Therefore, contribution available to recover the fixed cost was $ 504000

Thus, P/V ratio at the level 2011 was = (Contribution / Sales) * 100

 = ($ 504000 / 1800000) * 100 = 28%

We know that Break-even point: Break-even Sales * P/V ratio = Fixed cost

Or, Break-even sales (in $) = 180000/28% = $ 642857.14

Or, Break-even sales (in units) = $ 642857.14/300 = 2142.86 candidates.

Here consideration has to be given to 2 points:

(i) For each 50 candidate, step cost increases @ $ 800.

(ii) Thereby, at the level of 2142.86 candidates, all costs have not been recovered.

Now, Break-even sales (in units) =     2142.86 candidates
Candidates in multiple of 50 =            2100.00 candidates
Balance                                                 142.86 candidates

But invigilator’s cost (step cost) increase for 50 candidates =           $ 800

Invigilator’s cost (step cost) recovered for 42.86 candidates =
(800 /50) * 42.86         $ 685.76
Balance                                                                                               $ 114.24

Thus, for breaking even additional candidates required = $ 114.24 / $ 100 = 1.14

Break-even points (in candidates) = 2142.86 + 1.14 = 2144

(c) Net income required =                                                                   $ 400000
      Fixed cost required =                                                                       180000
      Contribution required                                                                       580000

No of candidates required = $ 580000 / 84 = 6904.76 candidates

In multiples of 50                                            6900.00                                              
Balance                                                                 4.76
Minimum invigilation cost =                            $ 800.00

Invigilation cost recovered from 4.76

 Candidates = ($ 800/50) * 4.76                          76.16
Balance invigilation cost                                      723.84

Additional candidate required = $ 723.84/ 100 = 7.24 candidates

Thus total candidates required = 6904.76 + 7.24=6912 candidates

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