The separation of costs into fixed and variable components helps provide relevant information about costs for making decisions. VARIABLE, DIRECT OR MARGINAL COSTING assigns only variable manufacturing costs to products.

Short-term VARIABLE COSTS vary in direct proportion to the level of activity.  

FIXED COSTS remain constant over wide ranges of activity for a specified time period.

Under certain assumptions, given the fixed costs, variable costs, and the selling price the BREAK-EVEN POINT (Level of activity which results in a no profit no loss situation) can be calculated using the formula :

BREAK-EVEN POINT (BEP) = TOTAL FIXED COST / CONTRIBUTION PER UNIT.

The assumptions are - 

1. The behaviour of costs and revenues have been reliably determined and is linear over the relevant range
   
2. All costs may be divided into fixed and variable elements.
   
3. Fixed cost remain constant over the relevant volume range of the break-even analysis.
   
4. Variable costs are proportional to volume.
   
5. Selling prices to be unchanged.
   
6. Prices of cost factors are to be unchanged.
   
7. Efficiency and productivity remain unchanged.
   
8. The analysis either covers a single product or it assumes that a given sales-mix will be maintained as total volume changes.
   
9. Revenue and costs are being compared on a common activity base.
   
10. Perhaps the most basic assumption of all is that the volume is the only relevant factor affecting cost. Of course other factors also affect costs and sales ; Ordinary CVP analysis is a crude over simplification when these factors are unjustifiably ignored.
    
11. Changes in beginning and ending inventory levels are insignificant in amount.
    

Constant

Constant

Not Constant

Constant

Constant

Not Constant

Not Constant

Not Constant

Examination Fee per student

Variable cost in conducting an examination (Answer papers, question setting etc.)

Fixed costs associated with the examination (Hall rent honorarium etc.)

In addition to the above cost supervisor have to be hired to supervise the students. One supervisor is required for every 100 candidates. The charge per supervisor is Rs. 200.

In the above situation the supervision cost are constant over a range of 100 students. Once the range is exceeded i.e. the 101st student writes the exam an additional supervisor would be required. Such costs are described as Step-Fixed costs.

Costs are analysed within a RELEVANT RANG in marginal costing. Once the given range of activity changes fixed costs tend to vary as depicted in the graph.

The formula used in the calculation of the BEP has to be modified for a situation containing step-fixed costs.

The approach is as below (Solution to Illustration 1) :

Tentative BEP (Students)

No. of supervisors

Additional costs (Rs.)

Additional Students

20000/20 = 1000

10

10 * 200 = 2000

2000/20 = 100

100/1100

11

1 * 200 = 200

200/20 = 10

10/1110

12

1 * 200 = 200

200 / 20 = 10

10/1120

12

NIL

NIL

Therefore the BEP is 1120 students.

Variable cost per unit is assumed to be a constant. But in some situations they vary in the same manner as step-fixed cost. For instance where discounts are offered as in Illustration 2, variable costs become STEP-VARIABLE COSTS.

All the multiple BEP's will fall within the full loss and full profit zones. A full-loss zone is a range where any activity level within the range will result in a loss. In the like manner, a full-profit zone is the one where any activity level within the range will result in a profit.

A second BEP can be recognised by calculating a tentative BEP at the immediately next range. If it falls outside the range there is no other BEP. If it does fall within the range then we have the second BEP and the possibility of a third cannot be ruled out.

FORMULATIONS FOR EVALUATING THE FIRST AND SUBSEQUENT BREAK EVEN POINTS

Case 1 : When the first break even point lands on the extreme point of the range over which the fixed cost is constant there will be a second BEP in the immediately succeeding range. The step fixed cost becomes a variable cost at the extreme point.

Such a situation can be recognised even without computing the first BEP for the first category of step fixed cost which we have previously mentioned i.e with the following assumptions :

1. The range over which the step-fixed cost varies is a constant.
   
2. The change in step fixed cost is a constant.
   

Using the data from illustration 1, change the base fixed cost to Rs. 18000.

N = 18000/( (1000 * 20) - 200 )

The first BEP = 10 * 100 = 1000

There will be a second BEP since 'N' is a Integer. The second BEP is calculated as follows :

Step fixed cost = 200
No. of students to cover the cost = 200/20 = 10

Therefore the second BEP = 1000 + 10 = 1010
( The results can be verified by working back from the BEPs)

The conclusion is that when 'N' is an integer there will be atleast 2 BEPs.

Another intresting derivations is that when fixed cost is a multiple of Rs. 1800 (Denominator in the formula), more than one BEP is possible.

Note :
It is to be noted that when the net recovery at a step (Denominator in the formula) is nil, there will be no BEP i.e. if R * C = SFC, then 'N' tends to infinity. Hence, there is no BEP. Similarly when R * C < SFC the denominator is negative leading to a negative step. Since this also is an impossibility there will no BEP when R * C <= SFC.

Case 2 :

Supposing 'N' from case 1 is not an integer then still there is a possiblity of a second BEP if the step fixed cost associated with a range is grater than the recovery from the excess capacity at the level in which the first BEP falls. In other words total cost at the next higher step (Step next to the one in which BEP falls) is greater than the total recovery at the extreme point of the previous level.

The assumptions laid down in case 1 hold. 'N' calculated using the formula will not be an integer. Replace 'N' with the immediately higher whole number to signify the step in which the BEP falls.

Total recovery at the extreme point of the current step = (N * R) * C

Total Step fixed cost at the next step = (N + 1) * SFC

if FC + (N + 1) * SFC > N * R * C --------I

there will be another BEP

or

i.e., FC > [N * (R * C - SFC) - SFC] --------II

or

The excess capacity at the current level = N * R - BEP

The recovery from the excess capacity = [ (N * R) - BEP] * C

Therefore if [ (N * R) - BEP ] * C < SFC --------III

there will be another BEP.

Equations I, II and III can be used to indicate the existence of another BEP.

Illustration 4

Rs.

Revenue per unit

50

Variable Cost per unit

25

Fixed cost

500

Step (Range)

50

Step fixed cost

800

[For every 50 units, the step fixed cost is Rs. 800]

BREAK-EVEN POINT IN A SITUATION CONTAINING A PRODUCT MIX

The procedure for computing the BEP is the same as in the other cases except that the contribution of the mix as a whole has to be taken to determine the BEP. It is also to be assumed that the production of the minimum component in the mix would automatically produce certain quantities of the other products.

A comprehensive Illustration is required to clarify this situation. Let us take up the case of a barber shop which offers only haircuts and shavings.

Thus, the annual BEP is 12times the monthly BEP when the monthly BEP falls on an extreme point. However this relation holds good only for the first monthly BEP and the first annual BEP. Second and subsequent BEP which do not fall on the extreme point will not satisfy the relation. It can be noticed that this is just a specific case of the general conditions that we have put forth. Here 'N' is always an integer and hence need not be rounded to compute the BEP. Similarly, N1 is also rounded. Hence, our original formulation stating N ( Rounded ) must be equal to N1 ( Rounded ) is always satisfied.
      (Illustration 1 with a monthly fixed cost of Rs. 21600 will result in such a situation. ) 

Conclusion

Step fixed cost is very interesting area in Marginal costing and possesses certain unique characteristics and leads to interesting revelations. Very little has been written on the subject and a deeper analysis would reveal interesting derivations. In this article a couple of things have been stated but not proved ; The phrase 'As many step increases in fixed cost there will be a maximum of so many BEPs possible'. Interested readers can take up such statements for further analysis once the basic concepts about step fixed costs are understood.