Other items of expense, on the other hand, are af fected quickly by changes in the volume of business. Thus, clerical help, indirect labor and operating sup plies are directly affected by such changes, moving up and down as the volume varies—tho not, asp a rule, in direct proportion to such variations. For instance, it requires a definite minimum amount of oil to lubti cate the shafting of a factory, whether any machines are in operation or not, and any further amount of oil that may be necessary is obviously dependent upon the volume of work passing thru the shop. This re lation is usually so complex that it cannot be ex pressed in terms of any fixed factor of production. In general, however, the relation between the amount of oil used and the volume of output may be expressed thus: (V) where Q = the quantity of oil, K = a constant, and f (v) = some function of the volume of work. Many other expense items, such as power, light, and some kinds of indirect labor, are of this general char acter.
It is important to notice, however, that from this it is clear that profits do not vary proportionally with the volume of business. Half-volume does not mean half-profits, since there is always an irreducible min imum of expense; and if this irreducible minimum is high compared with the variable expenses due to the activities of the business, a comparatively small de crease in business may eliminate all profits, if it does not actually cause a deficit.
3. Variations of expense due to time.—Expense, again, may vary according to time. Thus, a large amount of coal may be purchased, either to take ad vintage of the market, or to provide for emergencies; but the use of this coal may extend over weeks or even months. The demand for certain kinds of expense material may vary with the season. Thus more coal is needed in the winter season, while ice is needed par ticularly in the summer. Extensive repairs may be made to buildings or machinery because of the wear and tear incident to the work of previous weeks or months. These and similar expenses may fluctuate greatly and with little reference to the volume of busi ness. Yet, clearly, it would not be fair to current pro duction to charge off such heavy expenses against it, thus unduly favoring either future or past production. Such expenses must be averaged over a reasonable pe riod of time, even tho the method of fixing such an av erage may be more or less arbitrary. Of course, when the products of the factory are seasonable—that is, when some kinds are made only in the winter, and other kinds only in the summer—there may be ex penses that can be allocated justly on a seasonable basis, but this case is uncommon.
Expense must often be charged off by an average rate, for still other reasons. Once a month is about as often as it is convenient or desirable to close the general books and summarize all accounts, direct and indirect. If it were possible to start each job on the first day of the month and finish it on the last day, it would be possible to allocate to each job, with fair accuracy, a proper and fair share of the total monthly expense. Such conditions, as a matter of fact, are never found, since all work must be started and finished regardless of the day of the month. Expense must, therefore, be allocated on the basis of sum marized expense costs of the past month; or months, the data for the current month not usually being avail able.
Some cost accountants prefer to use the expense data of the preceding month only, on the ground that conditions do not change from one month to the next as much as they do during a period of several months. If this is done, however, special attention must be paid to large periodic expenses which are properly chargeable over a considerable period of time. This difficulty of determining with accuracy the expense items that have been incurred during the time a particular piece of work has been in process of production, and the expenses which are logically an in tegral part of the cost of producing that work, should be carefully considered, for the problem that it pre sents 'invokes factors that prevent any cost system from being very accurate.
4. Expense variation with character and size of work.—The amount of expense which any part should bear will also vary with the character of the opera tions performed upon it. Thus, in a plant manufac turing electrical appliances some parts must be dipped in insulating material and perhaps baked. Other parts will not require such treatment and, clearly, they should not, to be exact, bear any of the expense of the insulating department. In fac tories producing different lines and involving both intermittent and continuous manufacturing processes, such conditions are often met, and they sometimes offer a difficult problem in cost finding.
The amount of burden that a part is justly en titled to bear may vary also with its size or weight. Strictly speaking, small parts should not bear any part of the expense due to crane service and large equipment in general. Theoretically at least, a large casting should bear a greater share of the repairs to the cupola than should be charged against a small one.