by James Β. Weaver and Frank S. Lyndall Atlas Powder Co.
Π
COSTS A
W O R K B O O K
F E A T U R E
E C
Round the Clock or Weekends Off? Economics may favor building a bigger plant to save weekend labor costs 365 X 24 = 8760 hours per year. H o w m a n y of these hours should your plant operate? After a plant is built, operation will be matched to the d e m a n d for the product—it's hard to do otherwise. However, if you are about to invest in new facili ties, the choice is u p to you. T h e chemical industry is famous for continuous operation. Most plants seem to operate 24 hours a day and continue through the week ends. However, large segments of the industry are concerned primarily with batch processing. T h e fol lowing comments apply only to
batch processes, and to that mi nority of continuous operations which can be shut down frequently with out costly corrosion, delay, or hazard. Savings from weekend shutdown will sometimes show a good return on the higher initial investment re quired. For chemical process equip ment, the labor force is almost independent of equipment size. Therefore, weekend labor m a y be saved by building larger equipment to make the same production in five days a week or less. Sometimes the added investment is worth it, sometimes not. O u r intent is to
Simplifying Assumptions
presented in terms of a rate per hour "labor-variable cost"; $10 per hour could represent four men, direct labor, at $2.50 per hour, or two men with added savings of 1 0 0 % overhead. No shift differential is assumed; labor force is assumed independent of equipment size. Service Facilities. Service facili ties are assumed available over the weekends at essentially the same unit costs as during the week. N o Overtime Costs. N o overtime costs are assumed for the sixth or seventh day. Including full over time costs for regular sixth and seventh day operation shows that building for this alternative is always uneconomic compared to five-day operation on larger equipment. However, four crews can be sched uled to cover all 21 shifts of a sevenday operation, with overtime pay ments of only two hours overtime per m a n per week on the average. Similarly, a six-day operation with an even n u m b e r of m e n per shift can be scheduled by using seven m e n for each pair of operators; a n d paying each about one h o u r / w e e k overtime
Production in Proportion to Time. Operations are considered at one, two, and three shifts per day, 5 days a week; also 6- a n d 7day operation at three shifts per day. I n all cases, volume of production is assumed exactly proportional to hours of operation. In actual prac tice, total cycle times (operation plus washup) would have to be divisible into 8 hours for such an approximation to hold for one shift per day. Delays required by startup or shutdown—heatup time or cooling time, for instance—are also assumed negligible. Constant Volume. T h e volume to be produced is assumed known and constant; sales growth is not considered. Labor-Variable Costs. It is as sumed that all costs that change with hours of operation can be expressed in terms of labor costs, and actual cost savings are presumed known. This assumption neglects changes in utility costs, etc., which would p r o b ably occur to some extent in larger equipment. T h e sample cases are
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show a useful approach to such a determination of plant size. For convenience some simplify ing assumptions are m a d e , which can be modified for application to a particular case. Basis for Decision T h e o p t i m u m size of a proposed piece of equipment, a n d the operat ing schedule, can be determined by comparing the increased investment, a n d the fixed costs added with it, to the savings in the labor-variable costs for the shutdown period. Fixed costs on the increment of investment
on the average. Even these minor amounts of overtime can be elim inated at five menper shift, by use of one extra m a n on all five jobs. T h e latter situation corresponds to the assumption used in the following calculations. Six-Tenths Factor. M a n y p u b lications (2, 4, 8) have indicated that the "six-tenths factor" is a rough approximation of the costvolume relationship. Although the literature also indicates (7, 2, 5) that seven-tenths or eight-tenths fac tors m a y apply m u c h better in some cases, the calculations assume that the six-tenths factor applies pre cisely. T h a t is, Fixed investment B _ / c a p a c i t y u V · 6 Fixed investmentx \capacityA/
Working capital is considered to be unchanged. For equal total sales, this approximation is good ex cept for possible changes in product and in-process inventories. T h e six-tenths-factor assumption neglects saving from the use of stand ard e q u i p m e n t sizes.
WORKBOOK FEATURES 61 A
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COSTS
Exhibit 1.
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A Workbook Feature
Sample Case of Investment and O p e r a t i n g Costs for Various O p e r a t i n g Levels
Case Shifts/day Days/week Hours/year Fixed investment, S Fixed charges, $/yr.
(Dollars in Thousands) C D 2 3 5 5
A 3 7
B 3 6
8760 1000
7510 1100
6260 1220
4180 1560
2100 2370
140
154
171
218
331
88 175 263 3S0 438
75 150 225 300 376
63 125 188 251 313
42 84 125 167 209
21 42 63 84 104
1 5
Labor-variable costs, f/yr. $10/hr. $20/hr. $30/hr. $40/hr. $50/hr.
Exhibit 2 .
Sample Case of Incremental Analysis, Labor Savings Compared to A d d e d Investment (Dollars in Thousands)
Incremental case (see Exhibit 1) Added fixed investment, $ Reduced hours of operation/yr. Added fixed costs, $/yr., 14% investment Reduced labor-variable costs, S/yr. (before taxes) $10/hr. $20/hr. $30/hr. S40/hr. $50/hr. Added depreciation, $/yr., 6 2 / 3 % investment Added cash generation, $/yr. (profit after taxes plus depreciation) $10/hr. labor-variable cost $20/hr. labor-variable cost $30/hr. labor-variable cost S40/hr. labor-variable cost $50/hr. labor-variable cost Interest rate of return on added investment (15-yr. project life), %/yr. $10/hr. labor-variable cost S20/hr. labor-variable cost $30/hr. labor-variable cost $40/hr. labor-variable cost $50/hr. labor-variable cost
include the added depreciation, maintenance, insurance, and prop erty taxes. Labor savings m a y be only the out-of-pocket labor sav ings for the weekend direct labor plus fringe benefits, or m a y include associated cost savings such as super vision. Comparison T e c h n i q u e . I n the calculations, the net income is com pared with the investment by de termining the interest rate of return on investment (7). T h e calculation includes, besides net income, the cash generation to the company from depreciation accrual on the incre ment of equipment concerned. Similar relationships could be developed by the more familiar but less accurate return on invest62 A
B-A 100
C-B 120
D-C 340
E-D 810
1250
1250
2080
2080
14
17
47
113
13 25 38 50 62
12 25 37 49 63
21 41 63 84 104
21 42 62 83 105
22
54
9 19 30 40 50
8 18 28 39 50
...
...
6 12 18 24 30
6 12 18 24 31
10 18 25 32
5 12 18 24
4 10 13
ment techniques—i.e., return on original investment. Interest r a t e of return is used, as the simpler methods do not apply when grow ing products are analyzed by this approach to sizing. This subject will be attempted in a subsequent column. Sample Cases. For the cases used for illustration, certain costs were assumed proportional to fixed investment as follows." Depreciation-straight line Maintenance Taxes and insurance Total fixed costs
6 2 A% (15-year life) 5'A% 2% 14%
Considering the other approxi mations incorporated in the sample cases, a 5 0 % tax rate has been used instead of 5 2 % .
INDUSTRIAL AND ENGINEERING CHEMISTRY
Exhibit 1 shows five sample cases. Case A is based on an investment of $1 million for continuous operation (7 days per week, 3 shifts per day, four-crew operation). Based on the six-tenths factor, the investment is shown which would be required at each of the common partial-week operations (cases Β through E ) . Incremental Analysis. Each in crement of investment must be con sidered separately. Additional in vestments cannot all be compared with the m i n i m u m $1,000,000 in vestment level. Presumably, one would continue to invest in added facilities only to the point where the savings on the last increment of in vestment yield less than the accept able m i n i m u m rate of return of the c o m p a n y (6). Exhibit 2 presents such an incre mental analysis on the various steps of added investment from case A to case E. T h e increments are in dicated as differences—i.e., B-A C-B, etc. Added fixed costs a n d reduced labor-variable costs are based on Exhibit 1. Net profit is obtained by deducting added fixed costs a n d income taxes from labor savings. Net profit is not shown in Exhibit 2 ; instead total cash generation is presented, the sum of profit after taxes and the depreciation accrual. Exhibit 3 shows graphically the labor-variable costs necessary to justify the various levels of operation. T h e log-log plot enables one to choose t h e proper operating level for the sample case for any mini m u m interest rate of return from 0 to 1 5 % . R e a d i n g horizontally at the actual labor-variable cost, to the intersection with the m i n i m u m required rate of return, the indicated common operating level for which design should be m a d e is the next vertical dashed line to the right. Similar graphs could be d r a w n for a n y set of assumptions, b u t it is unlikely that all such assumptions would result in lines so close to straight and parallel. Choice of Process
This technique m a y be utilized in some cases where alternative processes for t h e same end product have very different labor require ments. O n an equal capacity basis,
A Workbook
Feature
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COSTS
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Exhibit 3. Sample case of incremental investment justified by l a b o r - v a r i a b l e cost level Basis $1,000,000 investment at 7-day, 3-shift operation
the process requiring less labor may be more economic. However, considering labor savings available, a larger plant by the other process, operating only part of the week, m a y be still more profitable. Reserve Capacity
T h e advantage of reserve capacity has not been considered, because of the simplifying assumption that product volume was not growing. Operation of a plant only 5 days a week allows 4 0 % reserve capacity for expansion; this m a y be a determining factor in building larger equipment, even if the return on investment on the above basis is 0 % or breakeven. A subsequent column will consider the sizing of equipment for a growing product. Conclusion
T h e deciding factor on the most economical level of operation is the ratio of labor-variable cost to fixed investment. T h e values in the example have very real counterparts in the chemical industry. Average capital investment per production worker for chemical and allied products in 1954 was about $25,000 (3). A $1,000,000 investment is therefore equivalent to 40 production jobs or 10 men per shift on a 7-day operation. Assuming a rate of $2.50 per hour a n d 1 0 0 % overhead, the labor-variable cost would be $50 per hour, which might justify the additional investment required by a two-shift, 5-day operation (see Exhibit 3). Building for 7-day operation m a y be most desirable, but it's far from a foregone conclusion. Literature Cited (1) Babcock, A. B., Chem. Eng. 6 1 , 244 (July 1954). (2) Chilton, G. H., Ibid., 57, 112-4 (April 1950). (3) Gates, T. R., éd., "Economic Almanac 1958," p. 216, National Industrial Conference Board, New York, 1958.
2088
4176
6264
7512
O p e r a t i n g Hours per Year
(4) Nelson, W. L., Oil Gas J. 55, 113 (July 22, 1957). (5) Sherwood, P. W., Ibid., 48, 81-4, 95 (March 9, 1950). (6) Weaver, J. B., Caplan, R. H., I N D . ENG.
CHEM. 50,
65 A-66
A
(Feb-
ruary 1958). (7) Weaver, J. B., Reilly, R. J., Chem. Εης. Progr. 52, 405-12 (correction 448) (1956). (8) Williams, R., Chem. Eng. 54, 124-5 (December 1947).
Our authors like to hear from readers. If you have questions or comments, or both, send them via The Editor, l/EC, 1155 16th Street N.W.. Washington 6, D.C. Letters will be forwarded and answered promptly. VOL. 50, NO. 5
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MAY 1958
63 A
