Cost Structure: Ideas for a Practical Calculation - Pt. 1

The analysis of the Break Even Point , of fundamental importance in an era characterized by economic crisis, energy crisis and double-digit inflation to monitor company profitability, presupposes the reclassification of costs relating to the characteristic area based on their behavior in the face of variations in production volumes.

By examining a balance sheet reclassified into fixed and variable costs, it is:

• to define what contribution the single product, the product line or the entire company makes to covering fixed costs and, at the same time,
• to know the point at which costs and revenues balance and profits and losses are equivalent, i.e. the Break Even Point .

Such variations in production, in fact, do not determine equal effects on all production factors. Some of them will react in one way, others in a different way; some will demonstrate a greater or lesser sensitivity, while others will remain more or less insensitive.

Faced with an increase in production, if a factor has sufficient production capacity for the new commitments, its increase will not be necessary. On the contrary, if the production capacity is not sufficient, additional doses of that factor will have to be acquired.

So, with respect to a given cost driver (which we will identify with the production volume ) and within a well-defined area of ​​relevance (and within a given time frame!), based on their behaviour we can arrive at a distinction between:

• Fixed Costs
• Variable Costs
• Mixed Costs

Fixed Costs are those that do not vary with the volume of production (which we said is our cost driver ), such as the costs for renting premises, leasing machinery, depreciation, administrative staff, accountant, IMU, cleaning services, assistance fees, insurance premiums, etc.

In a graph with the quantities produced on the x -axis and the economic values ​​on the y -axis, the estimate of the total Fixed Costs can be represented by a function y = constant , for any quantity from 0 up to the maximum usable production capacity.

In this regard, see the following example figure, in which the Fixed Costs are equal to €2,340 and in which the unit Fixed Cost is also represented on the right axis, which obviously decreases as the production volume increases due to the dilution of the Fixed Costs as the units produced increase.

Variable costs are those costs that vary, according to certain methods, as production varies: for example, raw materials, consumables, packaging, electricity for production companies, external processing, fuel, commissions, etc.; in the same Cartesian graph they are represented by a function of the type y = b × q , where:
y = Total Variable Costs
b = Unit Variable Cost (represents the slope of the line)
q = Quantity produced

See the Excel example below, where the unit Variable Cost is equal to €7.20, so the line of total Variable Costs will be a straight line that passes through the origin of the axes, while the unit Variable Cost will obviously be a constant straight line at the level of 7.20.

The one just represented in the figure is the line of proportional Variable Costs which, as the cost driver (production volume) varies, undergo an exactly proportional variation. In the example, if the production volume goes from 300 to 600 pieces, the Variable Costs also double, going from €2,160 to €4,320.

Still within the scope of Variable Costs, in addition to the theoretical hypothesis of perfectly proportional costs, it is possible to identify more realistically:

• Progressive Variable Costs , whose total amount increases more than proportionally with respect to the quantities produced (for example when the level of full employment of the production factors is approached, or when the optimal level of use of a certain production factor is exceeded, etc.):

• Degressive Variable Costs , whose amount increases less than proportionally with the increase in the cost driver , i.e. the quantity produced (for example the purchase costs of raw materials which, above certain thresholds, can benefit from quantity discounts). The Excel representation of these costs could be the following:

Finally, Mixed Costs include:

• Step costs , which occur when there are increases in costs within the area of ​​relevance, on the occasion of certain intervals of variation of the cost driver . Thus, for example (see figure below), faced with the decision to increase the production capacity to 300 pieces, the fixed cost of €1,940 could undergo a “step” increase, starting again, upon reaching this production threshold, from a higher value, in the example equal to €2,740. In fact, this new level could correspond to new costs deriving from the depreciation (or rental, or leasing) of new investments, from additional rented premises, from hiring new staff, etc., for a total of €800. The same reasoning applies in the case of an increase in production to 700 units, as shown in the figure:

• Semi-variable costs , which are made up of a fixed and a variable portion, such as telephone costs, which include a fixed portion for the fee and a variable portion relating to telephone traffic. These costs are represented by a function of the type y = a + b × q , where a is the fixed component, while b is the unit value of the variable component, all as shown in the following figure:

For simplicity, most break-even analyses only consider:

• Fixed Costs
• Proportional Variable Costs.

However, it is also important to know the existence of other types of costs that we have seen so far, this is because if this other type of costs were prevalent (for example, stepped costs, degressive variable costs, etc.), approximating them only with proportional fixed and variable costs would lead to imprecise results, for which it would be necessary to resort to the use of corrective measures to be evaluated from time to time on a case-by-case basis.

As already mentioned, these are extreme cases, so our journey through the cost structure can be satisfactorily continued by considering only Fixed Costs and proportional Variable Costs (henceforth simply “Variable Costs”).

With these two types of cost, we now arrive at the representation of the Total Cost , which will therefore be made up of the sum, for each quantity, of the Fixed Costs and the Variable Costs.

In the Cartesian graph, the Total Costs will be represented by a function like y = a + b × Q , where:
y = Total Costs
a = Fixed Costs (represents the intercept of the line)
b = Unit Variable Cost (represents the slope of the line)
q = Quantity produced

The Excel example in the figure below shows a cost structure where:

• Fixed Costs = €2,340
• Unit Variable Cost = €7.20

so the Total Cost will be equal to CT = 2,340 + 7.20 × Q

As can be clearly seen from the graph, the Total Costs line is parallel to the Variable Costs line (in fact, it has the same slope equal to the unit Variable Cost!) and is translated upwards with respect to the latter by an amount equal to the Fixed Costs.

Conversely, the unit Total Cost curve is a decreasing hyperbola that – but only in theory! – tends asymptotically towards the unit Variable Cost due to the dilution of Fixed Costs over an increasingly higher number of units produced.

(continued in part 2 )