PREDETERMINATION OF COSTS-EXPENSE 1. Preparation work is divisible into two stages, namely, preparation and actual operation. Thus, it will be noted that in Figure 28 (page 320) , the time for preparation, and the time for changing the machine at the end of the operation, are planned as separate items. The importance of the time re quired to get ready to do a piece of work is often over looked, in spite of the fact that it may have a great ef fect upon the cost per piece; no one thing shows more clearly the desirability of making parts in quantities.
Referring to Figure 29 (page 324), suppose that it takes four hours to prepare for a piece of work. This constant value, no matter how many pieces are made, is indicated by the vertical ordinates of the line AB. Suppose, further, that it takes one hour to do the op eration on each piece, after preparation has been made. Then the number of hours consumed in actual operation on any given number of pieces is indicated by the vertical ordinates between the line AB and the line AC; and the total time required to prepare for, and produce, any given number of pieces will be in dicated by the ordinates between om and AC. Thus, it will require fifty-four hours to prepare for and pro duce fifty pieces; twenty-nine hours to prepare for and produce twenty-five pieces, and so on.
The unit time, or time per piece, is found by divid ing this total time, or the sum of the time for tion and the time of operation, by the number duced. For one piece, then, the unit time is 4 + 1 ÷ 1 = 5 hours ; for two pieces, it is 2 + 4 2 = 3 hours; for five pieces, it is 4 + 5 5 = 1.8 hours; and for fifty pieces, it is 4 ± 50 ÷ 50 =1.08 hours. The curve DE is the curve of unit times, its vertical ordinates being one-tenth the value of those used for C. The rapid fall on the first part of this curve should be carefully noted. The greatest fall in unit values occurs when two pieces are made instead of one, a constantly decreasing gain per piece being obtained as the number increases, till, after thirty or forty pieces, the preparation time becomes almost negligible, so far as the unit cost is concerned. This principle, which holds good whether the preparation is measured in time or dollars, is, in fact, the basic principle of mass production; and the larger the number that are to be made, the more the time and money that can be economically expended on preparation and planning of all kinds. Data bearing on preparation are there
fore very important in cost prediction.
2. Application to special tools.—The general prin ciple discussed in the preceding section applies also to all special tools, such as jigs, fixtures, etc., and, in fact, to all preparatory work such as making drawings and patterns, that may be chargeable to any particular piece of work. Suppose, for instance, that the manu facturing expense is equal to the direct labor, and that the labor cost on a given piece of work is two dollars. Then the cost of production (aside from the material values) will be four dollars. Suppose, further, that by making a special tool worth $60 the labor cost can be reduced to fifty cents, and the productive cost, not including cost of material, is consequently reduced to one dollar. Since the gain in productive cost is three dollars per piece, twenty pieces must be made before the tool will be paid for. The unit cost when just twenty pieces are made, will be 60 + 20 = $4, or the 20 same as when no special tool is used. If more than twenty pieces are made, the unit cost will be decreased; and if less than twenty pieces are produced the unit cost will be more than $4, and the special tool will be the cause of a loss. Thus, if 100 pieces are made, 60 ± 100 the unit cost will be 100 = $1.60; while if only four pieces are made, the unit cost will be 60 + 4 4 $16.
If sixty pieces are made, the cost of the tool equals the cost of the labor and the expense. Up to this number of pieces, the controlling factor in the unit cost is the cost of the tool; but beyond this number, the controlling factor is the labor cost, and the cost of the tool soon becomes a small part of the unit cost. Thus, it has been shown that when 100 pieces are made, only 60 cents is added to cover the cost of the tool. Intelli gent cost prediction, where • the use of labor-saving tools is involved, must take account of these factors. It has already been shown that in the case of all equip ment the interest on the investment must also be taken into account.