Formulae for calculations

1.         Sales - Variable Cost = Contribution  = Fixed Cost + Profit

2.         P/V ratio (or C/S ratio)         = Contribution                       ¸ Sales                                  
                                                            = Contribution per unit        ¸ Selling price per unit
                                                            = Change in Contribution    ¸ Change in Sales

3.         Profit  = (Sales ´ P/V ratio) - Fixed Cost
                                    = P/V ratio ´ Margin of Safety sales(Rs.)
= Contribution p.u. ´ Margin of safety ( in units)

4.         Break-even Point

a.         Break Even (in units)             =    Fixed Cost         ¸  Contribution per unit

b.         Break Even ( in sales value )  =     Fixed Cost ¸  P/V ratio

c.         with semi - variable cost  :  apply the concept of apparent BEP 
d.         Composite BEP i.e. more than one product  with common fixed costs

(i)                 With out limiting factor ( non- attributable to a single product )

BEP in units = Fixed cost  ¸ Average contribution p.u. 
( when sales mix in units are given )
BEP in Rs.  =  Fixed cost ¸  composite  p\v  ratio
( when sales mix in rupee are  given )
   where composite p\v ratio = å [ Sales Mix  ´  P\V Ratio ]

(ii)               With limiting factor ( attributable to a single product )

Find contribution per limiting factor & give rank . Find total contribution from 1st rank product . Calculate the amount of fixed cost still to recover.  Whether it can be recovered by 2nd rank product or not ?

(iii)       For Perishable  product apply the same concept in case of opening stock with different variable cost.

e. BEP in case of process costing is expressed in terms of total raw material input

                        f. In capital budgeting , BEP is that sales volume
                        where Sdiscounted Cash in flow = Sdiscounted Cash out flow.

g. Potential BE : On the basis of sales out of current period  production only.

h. Multilevel BE :  Different BE due to change in sales price, variable costs & fixed costs for different production level.

Simple Problems :

1.         Three firms P, Q and R manufacture the same product. The selling price is Rs. 20 per unit of the product and is equal for all  the firms. The fixed costs for firms P, Q and R respectively are Rs. 2,00,000, Rs. 500,000 and Rs. 750,000, while the variable costs per unit are Rs. 15, Rs. 10 and Rs. 7.50.  Determine the break-even points for all the firms. How much profits are earned by the firms if each of them sells 70,000 units.

2.         Ronson  Ltd. which makes only one product, sells 10,000 units of its product making a loss of Rs. 10,000. Variable cost per unit of the product is Rs. 8 and the fixed cost is Rs. 30,000.       

Calculate i) the number of units to break-even, ii) the number of units to earn a profit of Rs. 6,000, iii) the amount of profit from a sale of 20,000 units.

3.         Maruti Uddoyge  Painters paints any car for Rs. 1,500. In the year just ended, the firm made Rs. 75,000 profit before taxes. The company had fixed costs of Rs. 1,20,000 and variable costs of Rs. 1,200 per paint job.

a)      How many cars did the firm paint last year ?
b)      What was the break-even point for the firm?
c) In the year just began,  the firm expects its variable costs to rise by 20% as a result of increases in labour and materials. What will be the break-even point this year?

d) Suppose the firm decides to pass along its cost increase by raising its price. What would be the new rate if the firm wanted to maintain its income before tax at Rs. 75,000 per year and  if the total demand remained at last year’s level

e) Suppose the firm wanted to hold the line on price and push for  more volume by staying open longer hours. How many paint jobs would be necessary to maintain profitability ?

4.         A company producing a single product sells it at Rs.50 per unit.  Unit variable cost is Rs.35 and fixed cost amounts to Rs.12 lakhs p.a.  With this data you are required to calculate the following, treating each independent of the other

(a)               P/V Ratio and Break-even sales.
(b)               New Break-even sales if variable cost increases by Rs.3 per unit, without increase in selling price.
(c)               Increase in sales required if profits are to be increased by Rs.2.4 lakhs.
(d)               Percentage increase/decrease in sales volume units off-set  an increase of Rs.3 in the variable cost per unit & a 10% increase in selling price without affecting existing profits quantum.
(e)        Quantum of advertisement expenditure permissible to increase sales by Rs.1.2 lakhs, without affecting existing profits quantum.                 

5.         Bottom line ltd.. manufactures pressure cookers  the selling price of which is Rs. 300/- per unit. Currently the Capacity utilisation is 60% with a sales turnover of Rs 18 lakhs. The Cc. proposes to reduce the selling price by 20% but desires to maintain the same profit position by increasing the output. Assuming that the increased output could be made and sold, determine the level at which  the Co. should operate, to achieve the desired objective.

The following further data are available :
i)Variable cost per unit Rs. 60/-.
ii) Semi-variable cost (including a variable element of Rs. 10/- per unit) Rs. 1,80,000.
iii) Fixed cost Rs.3,00,000 will remain same up to 80% level. Beyond this an additional amount of Rs. 60,000 will be incurred.

6.         I co. & II co.  have decided to merge  into one company. The operating details of two companies are as follows:
                                                                           Company I                      Company II
Percentage of capacity utilisation                                90                                     60
Sales (Rs.)                                                      5,40,00,000                     3,00,00,000
Variable costs (Rs.)                                        3,96,00,000                     2,25,00,000
Fixed costs (Rs.)                                               80,00,000                        50,00,000

Assuming that these two companies merge into one, determine

a. the break-even sales  of the merged company :
b. the profitability of the merged company at the 80% level of capacity utilisation,
c. the turnover of the merged company required to earn a profit of Rs. 75,00,000, and
d. the percentage increase in selling price necessary to sustain an increase in fixed overheads  by 5% when the merged company is working at a capacity to earn a profit of Rs. 75,00,000.

7.         Sale Price -                 Rs. 50                                     Variable Cost -            Rs. 30
Semi - Variable Cost -            Rs. 4,200 per 500 units.         Fixed cost -                 Rs. 1,20,000

Find   (i) B.E.P            (ii) Required sales at a profit of Rs. 30,000 .

8.         Kalyan University conducts a special course on “Computer Application” for a month during summer. For this purpose, it invites applications from graduates. An entrance test is given to the candidates and based on the same, a final selection of a hundred candidates is made. The Entrance Test consists of four objective type examinations and is spread over four days, one examination per day. Each candidate is charged a for of Rs. 500 for taking up the entrance test.

The following data was gathered for the past tow years.

Statement of Net Revenue from the Entrance Test For the Course of “Computer Application”

2003                          2004
Gross Revenue (Fees Collected)                               Rs. 10,00,000                Rs. 15,00,000

Costs: Valuation                                                                     4,00,000                      6,00,000
            Question Booklets                                                      2,00,000                      3,00,000
            Hall Rent at Rs. 2,000 per day                                    80,000                         80,000
            Salary                                                                          60,000                         60,000
Supervision Charges (one supervisor for every
100 candidates at the Rate of Rs. 50 per day)           40,000                         60,000
General Administration Expenses                              60,000                         60,000
                        Total Cost                                                       8,40,000                      11,60,000

                        Net Revenue                                                   1,60,000                      3,40,000

You are required to compute:

(a)   The budgeted net revenue if 4,000 candidates take up the entrance test in 2004.
(b)   The break-even number of candidates.
(c)   The number of candidates to be enrolled if the net income desired is Rs. 20,000

Multi Product Problems:

9.         The following are the cost and the sales data manufacturer selling three products X, Y and Z.

Product           Selling price p.u.         Variable cost p.u.        % of Sales (Rs.)
                                    Rs.                              Rs.
X                                  400                              325                              20
Y                                  500                              350                              40
Z                                  850                              740                              40

 Capacity of the manufacturer : Rs. 80 lakhs  sales volume.  Annual fixed cost : Rs. 5,50,000.
i)                    Find the break-even point in rupees.
ii)                   Calculate his profit or loss at 90% of capacity.

10.       Major Ltd. manufactures  a single product X whose selling price is Rs. 40 per unit and the variable cost is Rs. 16 p.u. If the Fixed Costs for this year are Rs. 4,80,000 and the annual sales are at 50% margin of safety , calculate the rate of net return on sales , assuming an income tax level of 40% .

For the next year , it is proposed to add another product line Y whose selling price would be Rs. 50 per unit and the variable cost Rs. 10 per unit . The total fixed costs are estimated at Rs.6,66,600 . The sales mix  of  X : Y would be 7: 3 . At what level of sales next year , would the co. break even ? Give separately for both X and Y the break even sales in rupees and quantities .
11.       A manufacturing process produces two joint products and a by-product , in the following proportions :
                                                                                                                        Joint product X(1.5 kg)            
            Input 3 kg. of material  A                      Process  P                        
Joint product  Y(2.0 kg )        
                      2 kg of material  B                                                        
By product    Z(1.0 kg )
The costs of manufacture in process P are as follows  :             
            3 kg of material A at Rs.60 per kg .                            180 
            2 kg of material B at Rs.55 per kg.                             110            
Direct labour , to  process 5 kg. of input material                   400
Fixed overhead (200 % of direct labour  )                               800    
Total                                               1,490
Fixed cost of the process : Rs. 34,58,000.

Sales prices are :        Joint product X            Rs. 350 per kg.
Joint product Y            Rs. 450 per kg.
By product     Z            Rs.  48 per kg.
Find the  break even input.

12.       In an oil-mill three processes are required to convert the raw material to chaff , oil & meal. In the first process (cleaning) the chaff is separated. In the second process (pressing) oil and cakes are produced.

The oil is transferred to finished stock and the cake is transferred to third process (grinding)where it is dried and ground into meal. For an input of 1000 kg. raw material, output are 450 litres of oil, 50 kg. chaff and 400 kg. meals.      
Raw materials purchase prices is Rs. 12 per kg. The Selling price of oil is Rs. 80 per litre. Selling prices of the chaff  and meals are Rs. 20 and Rs. 200 per kg. respectively.

            The processing costs are as follows :-

                                      Variable costs                                               Total fixed costs per month
            Process A       Rs. 10,000 per 1,000 kg.                                1,32,000
            Process B       Rs. 25,000 per 1,000 kg. cleaned material
                                          transferred to this process                       3,00,000
            Process C       Rs. 32,000 per 1,000 kg. of meal                   4,00,000

There is no opening and closing stocks in any process. How many kg. of raw material input per month must be processed in order to break-even ?

13.       A company manufactures a product by passing materials through 3 Processes. Conversion costs of which are Rs. 50, Rs. 70 and Rs. 80 respectively per tonne of input. The mixture in the process A consists of :
            Material Z 60% at Rs. 70 per tonne
                        Material Y 15% at Rs. 120 per tonne
            And Mixture from process B 25% .

In the process B, entire material (without any loss) is transferred form process A ; in this process 25% of input is substandard and re-transferred to process A for “reprocessing” as mentioned above and the balance, without any loss in transferred to process C. In the process C, 20% of input becomes valueless paste. The sale price is Rs. 250 per kg. of final output
Compute BEP.

14.       Even Forward Ltd. is manufacturing and selling two products: Splash and Flash at selling price of Rs 3 and Rs. 4 respectively. The following sales strategy has been outlined for the year :--

(i)                  Sales planned for year will be Rs. 7.20 lakhs in the case of Splash and Rs. 3.50 lakhs in the case of Flash.

(ii)                To meet competition, the selling price of Splash will be reduced by 20% and that of Flash by 12 ½ % .
(iii)               Break- even is planned at 60%  of the total sale of each product.

(iv)              Profit for the year to be achieved is planned as Rs 69,120 in the case of Splash and Rs 17,500 in the case of Flash. This would be possible by launching a cost reduction programme and reducing the present annual fixed expenses of Rs. 1,35,000 allocated as Rs. 1,08,000 to Splash and Rs. 27,000 to Flash.

You are required to present the proposal in financial terms giving clearly the following information:

Number of units to be sold of Splash and Flash to break-even as well as the total number of units of Splash and Flash to be sold during the year.

Reduction in fixed expenses product-wise that is envisaged by the Cost Reduction Programme.      

15.       Titan Engineering is operating at 70 per cent capacity and presents the following information  : -

                      Break-even point                       Rs. 200 corers
                      P/V Ratio                                          40%   
                      Margin of  safety                        Rs.  50 corers

Management has decided to increase production to 95% capacity level with the following modifications The selling price will be reduced by 8 per cent . The variable cost will be reduced by 5 per cent on sales .

The fixed cost will increase by Rs. 20 corers , including depreciation on additions , but excluding interest on additional capital . Additional capital of Rs. 50 corers will be needed for capital expenditure and working capital .

The management will be needed to earn Rs.10 corers over and above the present profit and also meet 20 per cent interest on the additional capital .
What will be the revised : Break-even point , P/V Ratio , Margin of safety .

Multiple break-even point

16.       You have been  approached by a friend who is seeking  your advice as to whether he should give up his job as an engineer, with a current salary of Rs. 15,000 per month and go into business on his own , assembling and selling a component which he has invented . He can procure the  parts required to manufacture the component from a supplier                

It is very difficult to forecast the sales potential of the component , but after some research , your friend has estimated the sales as follows  :
Between 600 to 900 components per month at a selling price of  Rs. 250 per component .
Between 901 to 1,250 components per month at a selling price of Rs. 220 per component for the entire lot.

The costs of the parts required would be Rs. 140 for each completed component . However if more than 1,000 components are produced in each month , a discount of 5% would be received from the supplier of parts on all purchases .

Assembly costs would be Rs. 60,000 per  month up to 750 components . Beyond this level of activity assembly costs would increase to Rs. 70,000 per month .

Your friend has already spent Rs. 30,000 on development , which he would write-off over the first five years of the venture .
Required :
Calculate for each of the possible sales levels at which your  friend could expect to benefit by going into the venture on his own .
Calculate the break - even point of the venture for each of the selling price .
Advise your friend as to the viability of the venture .
17.       A newly set up manufacturing unit proposes to produce and sell a single product ‘ZEE’. The following cost data is available in this regard:

ZEE’s selling price is in the range of Rs. 1,200 to Rs. 1,600 per unit and the demand is to be around 12,000 units at an unit selling price of Rs. 1,400, 10,000 for selling price of Rs. 1,600 per unit and 20,000 for selling price of Rs. 1,200 per unit

The material cost per unit would be Rs. 300 for procurements for requirements up to 15,000 units, beyond which a quantity discount is available at Rs. 25 per unit.  Labour cost per unit would be Rs. 275 up to 10,000 units. An increased production of 5000 units would involve second shift operations which would raise the labour cost per unit to Rs. 400 for the extra production in the second shift.

Any production beyond 15,000 units would call for additional machinery support; but this is likely to reduce the labour cost of the entire production to Rs. 150 per unit.
Variable overheads would be Rs. 275 per unit up to 15,000 units and Rs. 350 if the production is more than 15,000 units.

Factory fixed overhead cost would be Rs. 13.5 lakhs. This would increase by Rs. 8.5 lakhs if additional shift is worked and by Rs. 13 lakhs if extra machinery is required. Fixed administration cost would be Rs. 41.5 lakhs

            The management of the company is desirous of knowing the economies of the production at the 3 levels of unit selling price viz: Rs. 1,600, 1,400 and 1,200.
            You are required to advise the management on the following (working to be given);
a.                  Breakeven point (units) for each of the three unit selling prices proposed.
b.                  Budgeted Profit for the activity level of 12,000 units for each of the 3 unit selling prices.
c.                  Decision strategy of production (i.e.) by resorting to second shift operation or go for additional machinery for a budgeted level of 12,000 units for a unit selling price of Rs. 1,400.
d.                   Optimum selling price for different levels of demand.                                   

Potential B.E.P
18.       N.R.I Ltd. produces an unique product, the potential demand for which would diminish with any prolonged period of business recession.  A review of the price product over the past six months has become necessary in order to determine future market strategy.  A cost and profit statement has been prepared for this purpose.

You are required to calculate the Break even point for total sales, actual and potential. Why should the above procedure be adopted instead of the usual way of finding the B.E.Point ?

Cost and Profit statement for the six months January - June  2004
                                                                                                  Rs.                     Rs.

            Net Sales                                                                                            24,50,000
            Stock 1st January 2004                                               4,00,000
            Direct Labour                                                              8,95,000
            Direct Material                                                             7,45,800
            Indirect expenses :
                        Variable                                                           2,38,700
                        Fixed                                                               3,58,000
            Less stock 30th June 2004                                         8,00,000
            Cost of Sales                                                            18,37,500
            Gross profit                                                                 6,12,500
            Selling & Distribution Expenses :
                        Variable                                                           1,00,000
                        Fixed                                                               2,00,000            3,00,000
            Profit before Tax                                                                                   3,12,500
            Tax provision                                                                                         1,26,200
            Net Profit for 6 months                                                                          1,86,300                   

Increase in stock should be assumed as potential sales within the period.

Marginal Vs. Absorption Costing:

19.       A  Company produces formulations having a shelf  life of one year .  The company has  an opening stock of 15,000 boxes on 1/1/2004 and expects to produce 65,000 boxes as was in the just ended year of 2003 . Expected Sale would be 78,000 boxes . Costing   department has worked out escalation in cost by 25% on variable cost and 12% on fixed cost for the year 2004 . Fixed costs are estimated at Rs.18,50,000 . New price  for 2004 is Rs.70/- per box . Variable cost of the opening stock is Rs. 20 per box .

Required : To find out B.E volume for the year 2004, and  To estimate the profits  realised on sale during 2004 . Reconcile the profit under marginal & absorption costing

20.       PH Ltd. has a productive capacity of 2,00,000 units of  product of BXE  per annum, The Company estimated its normal capacity utilisation at 90% for 2004-05. The variable costs are Rs. 22 per unit and the fixed factory overheads were budgeted at Rs. 7,20,000 per annum. The variable selling overheads amounted to Rs. 6 per unit and the fixed were expenses were budgeted at Rs. 5,04,000. The operating data for  2004-05 are us under  :---

                    Production                                               1,60,000  units
                    Sales   @ Rs. 40 per unit                        1,50,000  units
                    Opening  stock of finished goods               10,000  units

            The cost analysis reveled an excess spending of variable factory overheads to the extent of Rs. 80,000. There are no variance in respect of other items of cost.

            Required :
            (i)    Determine the budgeted break even point for  2004-05
            (ii)    What is the profitability  for  2004-05 using  :---
                    (a)     marginal  costing basis
                    (b)     Absorption  costing  basis.
            (iii)   Reconcile these two profits.
21.       X Ltd. commenced business on March making one product only, the standard cost is as follows:
                    Direct  labour                                                5
                    Direct materials                                            8
                    Variable production overhead                       2
                    Fixed production overhead                           5
                    Standard  production                                   20 

            The fixed production overhead figure has been calculated on the  basis of a budgeted normal output of 36,000 units per annum.         You are  to assume that there were  no expenditure or efficiency variances and that all the budgeted fixed expenses are incurred evenly over the year. March and April are to be taken as equal period months.
            Selling, distribution and administration expenses are :
                                                            Fixed  £ 120,000  per annum
                                                            Variable 15% of the sales value

            The selling price per unit is £35 and the number of units produced and sold were :
                                                                                                               March                April
                                                                                                               Units                 Units
                                                            Production                                  2,000               3,200
                                                            Sales                                          1,500               3,000
            Prepare profit reconciliation statement for each of the months of March and April using :

Question 1.
            The following cost data are available from the records of M/s. ABC Ltd.  with regard to their product “Millennium” :

                                          Selling  price  per  unit                   Rs.  60.00

                                          Variable  cost per unit                    Rs.  36.00

                                          Fixed  cost  per unit                       Rs.  12.00

                                          Normal  output                               1,00,000 units

            Other additional data  available for four  consecutive periods are as under  :

                                                  Period I          Period II          Period III         Period IV      Total  units

                    Opening  stock              ---                    ---            30,000             20,000

                    Production          1,00,000         1,20,000         1,10,000             90,000         4,20,000

                    Sales                   1,00,000            90,000         1,20,000          1,10,000         4,20,000

                    Closing  stock               ---            30,000            20,000                    ---

            You are required to prepare a statement  showing profit for different period under both Marginal Costing and Absorption Costing methods, showing under/over absorption of overhead of any, and also giving your comments. 

Curtsy: Tax Shield Education  Centre.