Distinguishing between fixed and variable costs (those costs that vary with time and those that vary with the level of activity) is an old idea. This separation of costs by behavior is the basis for break-even analysis. The idea of “breaking even” is based on the simple question of how many units of product or service a business must sell in order to cover its fixed costs before beginning to make a profit. Presumably, unit prices are set at a level high enough to recoup all direct (that is, variable) unit costs and leave a margin of contribution toward fixed (period) costs and profit. Once sufficient units have been sold to accumulate the total contribution needed to offset all fixed costs, the margin from any additional units sold will become profit—unless a new layer of fixed costs has to be added at some future point to support the higher volume.
Understanding this principle will improve our insight into how the operational aspects of a business relate to financial planning and projections. This knowledge is also helpful in setting operational policies, which, especially in a volatile business setting might, for example, focus on minimizing fixed costs through outsourcing certain activities. But in a broader sense, it’ll allow us to appreciate the distorting effect which significant operating leverage might exert on the measures and comparisons used in financial analysis.
A word of caution must be added here. There’s nothing absolute about the concept of fixed costs, because in the long run, every cost element becomes variable. All costs rise or fall as a consequence of management policies and decisions, and can therefore be altered. As a result, the break-even concept must be handled with flexibility and judgment.
As we mentioned, introducing fixed costs to the operations of a business tends to magnify profits at higher levels of operation up to the point when another layer of fixed costs might be needed to support greater volume. This is due to the buildup of incremental contribution which each additional unit provides over and above the strictly variable costs incurred in producing it. Depending on the proportion of fixed versus variable costs in the company’s cost structure, the total incremental contribution from additional units can result in a sizable overall jump in profit.
Analyzing a leveraged operating situation is quite straightforward. Once all fixed costs have been recovered through the cumulative individual contributions from a sufficient number of units, profits begin to appear as additional units are sold. Profits will grow proportionally faster than the growth in unit volume. Unfortunately, the same effect holds for declining volumes of operations, which result in a profit decline and accelerating losses that are disproportional to the rate of volume reduction. Operating leverage is definitely a double-edged sword!
We can establish the basic definitions as follows:
Profit = Total Revenue - Total Cost
Total Revenue = Volume (Quantity) * Price
Total Cost = Fixed Cost + Variable Cost
The formal way of describing leverage conditions is quite simple. We’re interested in the effect on profit (I) of changes in volume (V). The elements that bear on this are the unit price (P), unit variable costs (C), and fixed costs (F). The relationship is:
I = VP - (VC + F)
This formula can be rewritten as:
I = V(P - C) - F
which illustrates that profit depends on the number of goods or services sold times the difference between unit price and unit variable cost—which is the contribution to the constant element, namely fixed costs.
As unit volume changes, the unit contribution (P C) multiplied by the change in volume will equal the total change in profit. Under normal conditions, the constant, fixed costs (F) will remain just that. The relative changes in profit for a given change in volume will be magnified because of this fixed element.
Another way of stating the leverage relationships is to use profit as a percent of sales (s). Using the previous notation,
s = I / VP
and defining I in terms of the components, the formula becomes:
s = (V(P-C)-F) / VP
and slightly rewritten:
The relationship indicates that the profit/sales ratio depends on the contribution per unit of sales, less fixed costs as a percent of sales revenue. We observe that, to the extent fixed costs are present, they cause a reduction in the profit ratio. The larger F is, the larger the reduction. Any change in volume, price, or unit cost, however, will tend to have a disproportional impact on s because F is constant.