__A DISCUSSION OF BREAKEVEN ANALYSIS__

__AND ITS PRIMARY INDUSTRIAL APPLICATIONS
__

Engineering economists are fortunate in having at their disposal a wide range of tools for determining the most efficient methods of achieving profitable, yet low-cost and consistently high-quality productivity. Regardless of the industries in which these tools are applied, by properly analyzing the firm's primary parameters and deriving meaningful indicators, companies can achieve optimal ratings in all key performance areas. Several of these analytical systems and methods are shared with the field of industrial engineering by several otherwise distinctly non-engineering disciplines, such as marketing, merchandising or management.

One of the most basic analytical concepts applicable across the board to all manufacturing, industrial or service-oriented enterprises is Breakeven Analysis. This well-known and universally accepted methodological tool, falling generally under the descriptive heading of financial or cost analysis, defines and clarifies the fundamental relationships among several crucial variables, namely a company's sales income, its fixed and variable costs, as well as its profit margin, related, in turn, to price mark-up. Breakeven analysis can be used either with the assistance of a firm's detailed cost-related records, or can be effectively employed without a backlog of supporting data by utilizing estimates or more recent empirical input. In both cases it provides an insightful glimpse into the vital operating costs of any manufacturing entity.

Without accurately pinpointing the breakeven point, the point quite simply at which a company's gross income equals its gross costs, industrial managers are unable to proceed with further analysis of the firm's entire cost and price structure. Knowing the breakeven point, that is knowing how many units of merchandise must be sold, or what quantity of services must be rendered, to cover production costs, both fixed and variable, is indispensable to calculation of other operating parameters. Raw information is, of course, necessary to enter into the equations and formulas used by analysts to determine the breakeven point.

Most importantly, a firm's operating statement is needed since it contains the main facts and figures from which the breakeven point, among other parameters, can be arithmetically calculated. At the outset, calculations need not be complex. In fact, a truly significant breakeven figure, one of which all corporate personnel should be aware, can be derived from the well-known formula B = F + D. In this simple equation, B is the volume of sales required to break even, F is the fixed cost of production with D representing the total direct costs incurred, expressed in percentage terms, at the breakeven level. If a given firm does not achieve sales at the breakeven point (B), then an operating loss will occur and measures will have to be taken either to sell more merchandise or to cut costs to the extent required.

Taking this simple formula one step further, when D is
known, it is possible to use this *variable cost rate* [R] to draw
comparisons among industry groups and thus rank one's own firm, in terms
of cost-effectiveness, within similar 'competitor firms' or within a broader
spectrum of industrial manufacturers.

The formula for deriving this industry comparison breakeven point, shown below, is a permutation of the foregoing equation:

**B =_ F_**

**1-R**

The above equation utilizes a composite approach put forward slightly differently in both Riggs and Park, which explains the discrepancies in symbols utilized in our class discussions and in these two classic texts spanning more than two decades or research in the area of BEP analysis (1996, 1973, passim).

In fact, there are a number of insights that can be readily obtained by glancing at various industries' breakeven points that incorporate a predictable function of sales, as well as variable and fixed costs. Utilities, such as electric companies, have high fixed costs, whereas retail distribution outlets, for example, generally have low fixed costs. Being aware of these dynamics can assist the industrial manager in assessing his own firm's position and requirements in terms of internal cost structure.

A parallel point requiring further explanation involves the zone beyond the breakeven point in which profit is generated. All enterprises are in business to produce services or merchandise at a profit. The extent of this profit is determined, in part, by the factors mentioned above, plus the mark-up, a percentage added to labor and materials in order to receive compensation for certain intangibles involved such as time and ingenuity. Calculations involving mark-up are determined by market conditions and by the laws of supply and demand, to a large extent. Ideally, the mark-up serves to compensate for all facets of manufacturing, distribution and R&D associated with the industrial process. To effectively establish mark-up parameters, the breakeven point, as a neutral indicator, must be known, and must have been calculated properly on the basis of solid cost and production data. When graphed (income vs. sales volume), the mark-up appears above the break-even point, whereas cost, income and loss (if any) appear below that point.

Because the breakeven point is related to and defined by specific variables, such as overhead costs and mark-up, if either of these variables fluctuates the productivity of the firm must be adjusted dramatically to compensate. Assuming a 10% markup, if one adds a single employee to the payroll of the average firm, each dollar of salary must be matched by eleven dollars in sales, according to Park (1973, 175). It is reasonable to assume that the classic breakeven point, therefore, varies in a constantly shifting pattern that must be monitored closely by engineering economists and industrial managers.

Far from being useful exclusively in the major theaters of operation at the corporate level, breakeven analysis can also be applied to decisions in the microcosm. When reviewing the costs associated with specific pieces of construction equipment, for example, the same conceptual approach can be employed to determine the point at which it ceases, due to depreciation or devaluation, to become cost-effective to retain an aging item. Such analysis may also establish whether or not it may not be advantageous to sell the item in question at the calculated breakeven price on the used equipment market. Judicious use of the concepts involved can save a firm hundreds of thousands of dollars on this small scale level of application, whereas millions can be saved, generated or properly allocated on the broader corporate scale through astute interpretation of breakeven analyses conducted professionally.

Whether or not breakeven analysis is used in the macro or micro spheres of industrial administration, it can be implemented to account for two or more alternatives being considered. In fact, real-life situations often entail complexities that the simpler formulas do not always accommodate. There are occasions when alternatives being considered are interrelated with the same decision variable, and it becomes necessary to choose from among the alternative options at hand. Breakeven analysis provides a means not so much for actually choosing, but for determining the point at which equal costs are incurred under the multiple options being reviewed. In the classic formula provided, alternative one is set against alternative two and equalized, thus defining the breakeven point (Thuesen, 1993, 359).

In the case of more than two alternatives, the formula is adjusted and similar results are obtained. Breakeven points, generated by these formulas, are used by engineers and planners to assist in selection of the most feasible alternative. As implied earlier, these equations are able to validly incorporate the costs associated with (1) periods of time, (2) individual equipment items, or (3) broader units such as overall project-based costs, since breakeven points are definable in all of these terms. It is useful to point out that multiple-alternative breakeven calculations are quite common in the design and construction industries where potential costs of varying materials and design concepts are frequently encountered. The most appropriate material from among many must be selected, and knowing where excessive costs, in relation to value received, are incurred is important. Used in combination with optimization analysis, breakeven calculations can reveal the most cost-effective routes for engineers to pursue with respect to both large-scale decisions and individual equipment decisions affected by maintenance and depreciation factors.

Examining more closely the purposes of breakeven analysis,
it can be seen that its original function to establish *annual revenue
levels* required to compensate for costs incurred has been expanded,
not only to include paired or multiple comparisons of identical revenue
figures, but also to arrive at other insights. An extremely useful application
of breakeven computations involves two otherwise equally attractive investment
alternatives that may have only slightly differing *rates of return*.
Breakeven calculations can determine which is the better of the two options.
Also alluded to was the usefulness of this tool for implementation in the
area of *equipment maintenance*, *salvaging* and *resale*
of assets, all areas where capital recovery can be maximized through astute
interpretation and timely action based on breakeven results. A final application
of this analytical device, found especially indispensable in many large
organizations, is in the area of calculating *resource or capacity utilization*.
Planning requires knowledge of which alternative is more or most cost-effective
of two or several options for using time-sensitive (and hence costly) equipment
or manpower. Certain of the alternatives can be found to be equally acceptable;
whereas others can be ruled out under the breakeven methodology.

There are obvious limitations to the breakeven equation, some of which can be overcome through inclusion of additional mathematical functions. Care must be taken, for example, when calculating time-sensitive components. There is an underlying assumption implicit in the basic BE formula that the alternatives being compared involve projects of equal duration and that repeatability factors are operative (Degarmo 1993, 387). In fact, the fundamental principles of linear and nonlinear analysis, outlined in Riggs (1996, 477, 488) must be honored to achieve optimal accuracy.

If managers find that they are incurring a loss, after calculating the breakeven point, and wish to redress the situation, there are a few options other than the obvious cost reduction measures which most administrative managers might, by impulse, implement. One controversial method to bring the break-even point back into alignment is to "dump" excess unsold merchandise onto the market. This is often feasible in foreign lands, particularly in third world nations, where laws are lax. By selling this merchandise at somewhat below cost, plant utilization, and hence the appearance of production efficiency, is increased to the extent that the equation could be brought back into balance by (a) the revenue generated and (b) the efficiency leap. To be effective, this strategy must embody a drastic price reduction and fairly large quantities of merchandise. Tariffs and other customs imposts should not be charged by the host country to maximize the effects of dumping.

However, because other significant aspects of key components of all breakeven equations require elucidation, it would be worthwhile to clarify certain points thus far left inadequately described in our haste to explain the multifaceted usefulness of breakeven analysis.

Thus far, casual mention in these pages of important terms such as 'fixed costs' and 'variable costs' has been forthcoming. Because the accuracy of breakeven analysis is so dependent on proper insertion of critical plant operational data into the basic equation as well as into the more elaborate models, an elemental understanding of how these costs are identified is indispensable. Much of what is about to be stated is commonly shared, for purposes of model standardization, among accountants, financial managers and engineering economists.

*Fixed costs*, by definition, are those simply that
do not fluctuate over a given period of time, even if the firm produces
different products and services during the timeframe involved; they remain
constant and often include general overhead expenses. Since a pre-specified
'duration of time' is not formally part of this definition, according to
most sources, there is some flexibility in determining which cost items
can be included in this category. There are several additional sub-categories
of costs, however, that could assist in clarifying the exact nature of
a fixed cost item, among them the following.

*Semi-variable *costs are those which are constant
for limited volumes of sales, but which fluctuate as a function of sales
volume. These costs generally increase as volume increases, but could decrease
at some calculable point. They are grouped with fixed costs only if they
are stable and constant over a given length of time. If not, they are classified
with variable (direct) costs. This type of arguably blurred definition
is what gives statisticians, accountants and cost analysts colossal headaches,
even though in recent decades fairly successful efforts at standardization
of specific cost items, as falling into this or other categories, seem
to have been made.

*Variable costs*, sometimes labeled direct costs,
job-related costs or, less formally, out-of-pocket expenses, are, as their
name would imply, flexible, shifting and changing since they are geared
to the requirements of specific tasks, most of which are short-lived and
ever-shifting in nature. Again, certain job-related costs considered by
some accountants or analysts to fall under 'overhead' could be amalgamated
within this category. Ultimate accuracy of the break-even point can be
called into question if such costs are not uniformly classified at least
within the firm.

Elsewhere in this report the remaining operative terms in all basic breakeven equations, such as mark-up and the BEP itself have been adequately defined.

What are some of the essential characteristics, relationships or dynamics revealed about the normal break-even point when graphed? Glancing at any typical BEP graph, the analyst can readily perceive the most obvious characteristic. As sales volume increases, assuming the minimal breakeven point has been attained, so does profit. Conversely, if the BEP is not achieved, loss increases as a function of descending sales volume. A much steeper slope is produced if there is an increase in fixed costs. Even if fixed costs increase only minimally, what appears to be an exponential effect is produced, forcing the BEP to tremendous height, minimizing profit potential and generally shifting the financial burden to a new point. At this point, total income must be quite elevated to simply "break even" and maintain solvency, at least for the product or project under analysis. Of course, these dynamics would apply equally dramatically to the macro sphere as well, affecting the entire firm if the equation were similarly skewed for all company operations in a given span of time.

Carrying these variations a bit further, and assuming charts could be overlaid or extended to reflect increasing sales volume ranges with proportionate increases in fixed costs, it would be observed that the breakeven point would rise with each incremental increase in those two factors (Park, 1973, 172). Interestingly, total income would increase as well, but in close proportion to total cost (variable plus fixed). One could almost be forced to wonder, under these delicate circumstances, why manufacturers even bother to market their products on a large scale, when costs rise in proportion to production and sales. Of course, the answer is that even a minimal profit margin of 1 or 2 % per annum results in steadily enhanced revenue as production and volume increase in tandem.

An illustrative case in point is that of the service-providing Venture Capitalist Fund Manager who may charge a commission of 1 to 3%, under law, for his VC portfolio managerial services. If he is managing a $40 million portfolio over five years, annual revenue from this account alone, in the form of a 2% commission flowing into the VC firm or directly to the Manager in whole or in part, amounts to an attractive Mercedes Benz existence of $800,000 per annum. Such an example, while limited in its analogous value, demonstrates handsomely that, as volume increases, along perhaps with costs, revenue can theoretically escalate under ideal conditions. There is definitely an incentive, in spite of some of the first-glance BEP indicators, to forge ahead in an attempt to gain increased sales and market share.

As the intrinsic usefulness of BEP analysis, with all of its variations and extended applications, becomes more familiar to even lower echelon employees in business and industry, not only will profit increase along with productivity and quality, but employee motivation and pride will be spurned to new heights. It seems safe to assert that even these two intangible factors can also be attributed to new insights gained by employees through this valuable analytical tool.

**REFERENCES**

Brigham, E., and Houston, J. *Fundamentals of Financial
Management, Eighth Edition,* Dryden Press, Fort Worth, 1998.

Degarmo, E.P., Sullivan, W., and Bontadelli, J.* Engineering*
*Economy*, MacMillan Publishing Company, New York, N.Y., 1993.

McGuigan, J., Moyer, R., Harris, F. *Managerial Economics:
Applications, Strategy and Tactics, Eighth Edition,* South-Western College
Publishing, Cincinnati, 1999.

Park, W. *Cost Engineering Analysis: A Guide to the
Economic Evaluation of Engineering Projects,* John Wiley and Sons, New
York, N. Y., 1973.

Riggs, J.L., Bedworth, D., and Randhawa, S. *Engineering
Economics, Fourth Edition,* The McGraw Hill Companies, Inc., New York,
N.Y., 1996.