07] bb 234 ag UNIVERSITY OF ILLINOIS Agricultural Experiment Station BULLETIN No. 234 A GRAPHICAL PRESENTATION OF THE FINANCIAL PHASES OF FEEDING EXPERIMENTS By H. H. MITCHELL 5 y 3 ) ! URBANA, OCTOBER, 1921 CONTENTS OF BULLETIN No. 234 PAGE INTRODUCTION © 0%. 95 ciclac 0 a.0 0 wae bv eieneta atarerete cote cele ete teen 271 A GENERAL STATEMENT OF THE PROBLEM. .........0. +) see 274 CHARTS INVOLVING TWO VARIABLE FACTORS... ... 3. .2. see 275 AN ILLUSTRATION IN SHEEP FEEDING...........-. +a s01c\s pennies 276 WHEN Lot GAINS ARE NEARLY EQUAL..............005 5 ae 283 ILLUSTRATIONS IN SWINE FEEDING (li 00505004 saad ss tae 283 CHARTS INVOLVING THREE VARIABLE FACTORS. ... 2)... 297 AN ILLUSTRATION IN STEER FEEDING............. WE . 297 AN ILLUSTRATION IN. SWINE FEEDING. .....0.000- s+ 0+." see 298 CHARTS INVOLVING MORE THAN THREE VARIABLE FACTORS.... 303 ILLUSTRATIONS IN MILK PRODUCTION. .<.«seee-ceess sue ye ess + oe 303 ILLUSTRATIONS IN STEER PEEDING......¢.csecst cass ecuen ele 0 en 304 CHARTS PERMITTING GREATER FLEXIBILITY IN FINANCIAL PREDICTIONS 2s cccceccacaece sve doacteeis oslo dah ILLUSTRATIONS IN STEER FEEDING. .:.......2... ca «aes ee a)cneneneen 315 SUGGESTIONS FOR INCREASING THE PRECISION OF FINANCIAL ESTIMATES oo: 0 dcce o nye cco clea a du biate aheh elilp (elo mnubats Nene (oot 316 APPENDIX (Construction of charts) (2... 20... s fs00 us «cso wns een 318 A GRAPHICAL PRESENTATION OF THE FINANCIAL PHASES OF FEEDING EXPERIMENTS By H. H. MITCHELL, Associate CHIEF IN ANIMAL NUTRITION INTRODUCTION In the ordinary type of feeding experiment there are essentially three experimental results; namely, the rate of gain of the animals, the economy of gain expressed in terms of the ration tested, and the market finish produced. The first two items can be measured accu- rately in any particular feeding operation, tho they are subject to a variable and oftentimes considerable experimental error when con- sidered as experimental data. The third item is not susceptible of exact measurement and can be described only by stating the grade of butcher stock as judged by competent buyers, or its selling price per hundredweight relative to the prevailing market prices. All statements made of the monetary cost of gains and of the profits returned from any experimental feeding operation are necessarily not experimental results, since they depend so largely upon factors not. under experimental control and not subject to any predictable varia- tion, i. e., the prevailing market prices of feeds and live stock. The economy of any system of feeding, expressed in terms of commodities, has a permanent value; whereas when expressed in terms of financial profits or losses for any given set of prices, it will have little if any value. The latter expression is, and should be, of interest only to the experiment station conducting the work, and then only as an item in its ledger accounts. In spite of these facts, it is in general only the financial phases of experimental feeding operations that are of primary interest to the live-stock farmer. Hence the universal custom of including financial statements, sometimes in minute detail, in reports of feeding experi- ments, showing how and why the experiment station gained or lost money on each experimental lot, and what such profit or loss amounted to per head. Generally these financial matters find their way into the summary and conclusions of the bulletin, sometimes even to the exelu- sion-of the bona fide experimental results themselves. In any ease, it is very often found that such financial statements receive the main emphasis in the accompanying discussion. The emphasis accorded the cost of experimental feeding operations, and the profits or losses realized, seems to be due to the undoubted 271 272 BULLETIN No. 234 [ October, demand for such information from practical live-stock men and also to the fact that a practical comparison of the economy of the different feeding operations under trial cannot be made upon any other basis. A discussion of the results of a series of experiments based entirely upon the feed consumption and the gains secured would be barren of interest to readers desiring information on the most economical meth- ods of feeding live stock, unless supplemented by calculations of re- ceipts and expenditures, probable profits and necessary margins, and the like, calculations, which many readers are reluctant to make be- cause they are not always straight-forward arithmetical calculations and often are time-consuming. The difficulties in meeting the justifiable demand for some consid- eration of the financial aspects of experimental feeding operations are well stated by Forbes:* ‘‘It is impossible to make a statement of the financial outcome of such a comparison of feeds, which will be at the same time useful and true. The reason is that market conditions are never the same at two different times, or in two different places. The relative prices of feeds today, in any given market, do not apply in any other market, and in all probability will never again recur.”’ Attempts are frequently made to overcome in part the unanswer- able objections to the unmodified ‘‘financial statement’’ of a feeding experiment, mainly in the direction of computations of the effect of variations in the prices of feeds on the profits or losses per head. A fairly satisfactory result may be secured with rations containing only two feeds, if the additional mass of tabulated figures is not considered to be detrimental; but with rations including three or more feeds, complicated and less serviceable tables result. Everything considered, this method of modifying the financial statement is not to be recom- mended. The large amount of tabulated data resulting must seem formidable to one not used to the study of figures, and it may require considerable study to discover just how to enter the tables to obtain values corresponding to any particular set of prices. Furthermore the accurate use of such a table must involve ordinarily two or more interpolations, since any prevailing set of feed prices will not in gen- eral correspond to the arbitrary prices used in the compilation of the table. In general no systematic attempt is made to determine the effect of variations in the cost of feeders and in the margin of selling price over cost, on the profits or losses to be expected in steer and sheep feeding operations. And yet fluctuations in the live-stock market have a preponderating effect in determining the success or failure of the live- stock business. The financial result of the simplest steer or sheep feeding operation (and occasionally of swine feeding operations) de- *Forbes, E. B., Specific Effects of Rations on the Development of Swine. Ohio Agr. Exp. Sta, Bul. No. 213. 1909. 192i | FINANCIAL PHASES OF FEEDING EXPERIMENTS 273 pends upon four main factors, no two of which can be considered to be sufficiently correlated to permit of simplification; these factors are: (1) the cost of feeders per hundredweight; (2) the margin of selling price per hundredweight over cost; (3) the cost of a cereal or nitrc- genous concentrate; and (4) the cost of a roughage. No tabulated computations can adequately deal with values influenced by four in- dependent variables, and when the number of variables increases as the rations used increase in complexity, any method heretofore tried, as far as the author is aware, fails completely. Swine feeding opera- tions are generally less difficult to deal with in the formulation of flexible financial statements suitable for use under variable market conditions, since ordinarily in computing profits and losses from such undertakings only the cost and selling price of the pork produced is considered. But even here the tabulated values based on a sliding scale of feed prices cannot be used with accuracy unless interpolation is resorted to. The nature of the problem of giving a proper financial interpreta- tion to experimental feeding data suggests the use of graphical meth- ods, the main advantages of which are four. In the first place, they do away entirely with large masses of tabulated figures, always con- fusing to one not used to the study of numerical data. Secondly, they may be used for any values of the variables involved without the necessity of interpolation. Again, they afford a sort of bird’s-eye view of the situation, a more or less clear visual representation of the effect of variation in the market prices of commodities on the value under consideration. And, finally, it is possible and entirely feasible in most cases, to superimpose charts representing different experimental lots, upon one another, and thus to afford ready means of comparison. The - method also possesses the considerable advantage of being economical of space: In this study an attempt has been made to apply a few graphical methods’ to the problem under consideration. The methods selected and illustrated in the following pages may be used with accuracy, and in many eases afford a quick and simple method of perform- ing complicated arithmetical calculations. Many of them are undoubtedly simple enough to be used in experiment station bul- letins. Possibly some hesitation might be felt in including some of them in the ordinary bullétin for general distribution. It is hoped that all of them, however, will be found to have a distinct field of usefulness, and when not considered well adapted to bul- letins will in any case be of service to extension workers, farm ad- *Deming, H. G., A Manual of Chemical Nomography. University Press, Champaign, Ill., 1918. For a more pretentious and exhaustive presentation of nomographic methods see ‘‘Graphical and Mechanical Computation,’’ by Joseph Lipka. John Wiley and Sons, New York, 1918. 274 BULLETIN No. 234 [ October, visers, editors of farm papers and journals, and to all who are fre- quently called upon to aid the live-stock farmer in choosing well-bal- anced and economical rations with due regard to the feeds available, the prevailing market prices, and the probable fluctuations in market conditions during the fattening operation. The value of the methods in classroom work will be obvious. A GENERAL STATEMENT OF THE PROBLEM The financial aspect of a feeding operation is naturally resolved into the net receipts’ from the animal when sold and expenditures in- eurred in the fattening process. Of the latter the feed bill constitutes by far the larger fraction, and in computing profits or losses is gen- erally the only item considered. The less important items of expense, such as labor, interest, veterinary service, loss of stock by disease or accident, depreciation in buildings and other equipment, insurance, ete., are offset in part, if not entirely, by receipts from the animal other than cash, such as manure and, in the case of steer feeding on heavy corn rations, pork produced from the droppings. A farmer considering whether or not to fatten live stock during a given season, or to sell his grain directly; or, how much stock to fatten and on what rations, has before him the following more or less exact information. He knows fairly closely what feeder animals will cost him in his feed lot; he knows what feeds are most available to him, as well as something of their quality and their current prices, that is, what he ean sell his home-grown feed for, and what imported feeds will cost him. The information he must obtain by ealeulation or by less certain methods is: (1) his feed bill per head; (2) the necessary margin to cover his expenditures; and (3) considering a probable safe margin in view of the present live-stock market and its tendencies, his probable profit per head. The latter, in turn, he may compute as interest on the money invested or otherwise tied up in the venture, or as returns from his home-grown feeds in comparison with their possible selling price, or as some other value. The financial presentation of the results of experimental feeding operations should be such as to aid the practical farmer in these eal- culations and approximations, and, in fact, to encourage him in mak- ing them. A mere statement of the financial outcome under any given set of conditions not only gives him no aid or encouragement along these lines, but may actually mislead him into inferring that a sub- stantial profit realized by the experiment station, perhaps under un- usually favorable market conditions, may be expected under any con- ditions. *The term ‘‘net receipts’’ is used thruout this paper to mean simply the selling price of the animal minus the original cost. 1921] ‘FINANCIAL PHASES OF FEEDING EXPERIMENTS 275 CHARTS INVOLVING TWO VARIABLE FACTORS Fig. 1 illustrates a method of presenting one side of the question ; namely, the net receipts per head under given conditions of cost of feeders and margins.” | The net receipts per head from steer and sheep fattening opera- tions may be conveniently considered as being derived from two sources: viz. (1) the increase in market value of the initial weight of the animal, which depends of course entirely upon the actual initial weight and the margin of selling price per hundredweight over cost; and (2) the cash realized on the gain in weight produced, which de- pends upon the size of gain and its selling price. This division of the net receipts may be stated mathematically as follows: r= wm + g (e+m), or r =ge -- m (w+g), where w is the initial weight of animal; g, the gain per hundred- weight; ec, the cost of feeders per hundredweight; m, the margin per hundredweight; and r, the net receipts. It is evident, for example, from this equation that for a given margin the net receipts will vary directly with the cost of feeders; or, in other words, for a given mar- gin and feed bill the profits of a feeding operation will increase as the cost of feeders increases, simply because the gains will be marketed at a higher figure. It will be noted that Fig. 1 presents the results of a venture in baby-beef production in which the calves were raised at home instead of being bought on the market. In computing the net receipts of the baby-beef operation, the scale at the left, therefore, instead of repre- senting the cost of feeders, as it would in most feeding operations, rep- resents the price that the calves might have brought if disposed of di- rectly instead of being fattened. The scale on the right represents the margin of the selling price per hundredweight of baby beef produced over the possible selling price of the unfattened calves. The intermedi- ate scale, derived from the data given at the head of the chart, repre- sents the net receipts realized per head; or, from another point of view, the maximum cost of the feeding operations consistent with no loss or profit. Points on the intermediate scale correspond to any two points on the side scales situated on the same straight line. The chart is used by placing a ruler, stretched string, or other straight-edge, across it connecting any value for cost of feeders, on the left scale, with the size of margin, on the right, and reading off the *The charts explained and discussed in the following pages were constructed two or three years ago, when the prices of feeds and of live stock were at the highest levels; hence the wide range of prices on the scales of all charts and the high prices chosen in illustrating the method. The fact that practically all the charts are still serviceable when the prices of farm products have dropped enor- mously is a commentary on the great flexibility of the graphical methods used. 276 BULLETIN No. 234 [October, point of intersection on the intermediate scale. For example, if the possible selling price of the calves was $12 per hundredweight and the baby beef sold at a $5.00 margin, the net receipts per head, as indi- eated by the line drawn across the chart connecting these two values on their respective scales, would be something less than $127.50— approximately $127.30. This value also may be considered as the maxi- mum feed bill consistent with no loss or profit. Every dollar the feed bill falls short of this value represents a dollar profit, if incidental expenditures are left out of consideration. The chart may be used also in computing the necessary margin in a feeding venture. Suppose the feed consumed per head in this fattening operation should be found to cost at prevailing prices $127.30. Then the straight-edge will be set at this value on the inter- mediate scale and on the point on the left scale corresponding to the possible selling price of the calves, say $12.00. Then the point of inter- section on the right scale gives the necessary margin to just cover expenses, in this case $5.00. AN ILLUSTRATION IN SHEEP FEEDING Inspection of Fig. 1 shows the possibility of placing several inter- mediate scales, representing different experimental lots, between the same two principal scales, affording a ready method of comparing lots, and incidentally economizing space. It is also evident that the same alignment-chart principle illustrated here may be applied to the com- putation of feed bills for rations consisting of two feeds, under a wide range of price conditions. These statements are illustrated by Figs. 2 and 3, which together constitute a complete financial interpretation of the sheep feeding results upon which they are based. Fig. 2 permits of rapid estimation of the total feed bill per head - for each lot, with a wide range of prices for each of the feeds used (corn and alfalfa hay). As in Fig. 1, the principal scales are at the sides; here they represent a serviceable range in price for each feed. There is an intermediate scale for each of the four lots. By laying a straight-edge across the chart in such a way as to intersect the side scales at points corresponding to the prevailing prices of corn and alfalfa hay, the feed bill per head for each lot may be read off the corresponding intermediate scale. The cross line drawn in, intersect- ing the side seales at $1.80 corn and $32 alfalfa hay, shows that at these prices the feed bill of Lot 1 would be $5.85; of Lot 2, $5.07; of Lot 3, $4.52; and of Lot 4, $4.27; as near as the scales can be read. Turning now to Fig. 3, the net receipts per head may be similarly calculated for any cost of range lambs and any margin of selling price per hundredweight over cost. With feeders at $12, and a margin of $2.35, the intersecting line drawn thru the chart indicates upon the intermediate scales the net receipts per head for the different lots. 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS lowa Buttetin No. I8Il. Basy Beer Propuction 277 CALCULATION OF NET RECEIPTS PER HEAD oF BABY BEEVES Possible selling price of calves per cwt. $14.50 14,00 1500 AVERAGE INITIAL WEIGHT OF CALVES, 417 LBS. Gain oF G26 Bs. in 386 Days Net receipts per head, or maximum cost of feeding operation without loss or profit Margin of selling price of baby beef per cwt. over possible selling price of calves per cwt. 6,00 575 5.50 475 450 425 400 375 3.50 4 Eee ee COS ; : . : >» | mtg og ‘ a a j , ; + 6 Lave = * 8 , ee + a 1921] Cost of corn per bushel #200 $1390 FINANCIAL PHASES OF FEEDING EXPERIMENTS 279 ILvinois Buttetin No: 167. Fattreninc Western Lames CALCULATION OF EXPENDITURE FOR FEED AVERAGE FeeED Consumen: LOT CorRN ALFALFA Hay U. Tons | 1.993 0.0552 2 1682 0.0638 3 1138 0.0771 4 0.87! 0.0842 TOTAL FEED BILL PER HEAD. Lots Cost of alfalfa \ 2 3 4 hay per 4h 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 281 ILLinois Buttetin N2167 FATTENING WesTERN LamBs CALCULATION OF NET RECEIPTS PER HEAD AVERAGE. INITIAL WEIGHT IN ALL LOTS, SOLBS AVERAGE GAINS IN 90 DAYS Lot |,270|bs.; Lot 2,242 Ibs. ;Lot 3, I94lbs. | Lot 4, 18.3 lbs. Cost of lambs Net receipts per head Margin of selling price per cwl. Lot | z oe per cwt. over aay VPs $3.75 $350 $15 $325 $14 $3.00 $13 $275 + $250 *Il $225 %10 $2.00 $95 $1.75 56 $1.50 $7 125 $6 $1.00 $5 $0.75 $0.50 $0.25 $0.00 FIG.3 : 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 283 Profits per lot for these four values of corn, alfalfa hay, feeders, and margin, may be readily calculated by subtraction, as follows: Loti Lot? Lot 3 Lot 4 Net receipts per head (Fig. 3)..........0.. $5.47 $5.08 $4.38 $4.23 Pecuenil perinead (FIP, 2) se cccccrcres acc 5.35 5.07 4.52 4.27 Profit per head, by difference........... +$0.12 +$0.01 —$0.14 —$0.04 Evidently the particular margin chosen for illustration 1 1s or near to the necessary margin for each lot. If the necessary margin is desired for given values of feed and eost of feeders, the procedure is as follows, for, let us say, $1.50 corn, $25 alfalfa hay, and $11.50 feeders. Using Fig. 2, we see that the feed bill for Lots 1, 2, 8, and 4 for the above prices of feeds is $4.36, $4.10, $3.63, and $3.41, respectively. Taking Fig. 3 and placing the straight- edge at $11.50 on the left scale and at $4.36 on the intermediate scale for Lot 1, we find that the necessary margin for this lot, read off the right-hand scale, is $1.32. Placing the straight-edge still at $11.50 on the left scale and at $4.10 on the intermediate scale for Lot 2, the neces- sary margin is found to be $1.42. Similarly, the necessary margins for Lots 3 and 4 are $1.60 and $1.50. Evidently, on the basis of the prices used, the system of feeding accorded Lot 1, consisting of a maximum of corn, offers better prospects for profit than any other, with Lots 2, 4, and 3 following in order. WHEN Lot GAINS ARE NEARLY EQUAL In experiments in which nearly equal gains are made by different lots the inclusion of intermediate scales for the various lots, as in Fig. 3, presents some difficulties. This is illustrated by Fig. 4, in which are given scales for the calculation of the net receipts per head with steers weighing initially 1,000 pounds and gaining 200, 250, 300, 300, and 400 pounds, respectively. Evidently three or four lots of animals gaining within 50 pounds of each other would be represented by intermediate scales clustered so close as to render their proper graduation and reading difficult. This difficulty may be obviated by making single charts for each lot, or by adopting the expedient illus- trated in Fig. 5, of using different scales for the cost of the feeders but the same scale for margins. ° In this case, the side scales for Lots 1 and 4, whose gains differed by 65 pounds, are identical, while with Lots 2 and 3 different scales of cost of feeders are used. While this modifi- cation complicates matters somewhat, the chart is just as serviceable as the others when understood. ILLUSTRATIONS IN SWINE FEEDING In swine feeding experiments, in which, very often, the ration consists of only two feeds (corn and a supplement), and in which the 284 BULLETIN No. 234 [ October, profits in feeding are ordinarily figured entirely on the cost of gains (based only on the feed consumed) and the market price of pork, the alignment-chart principle may be used to decided advantage. Take, for example, a recent publication of the Michigan Agricultural Col- lege’ by Norton, in which different supplements to corn are compared on the basis of average figures of the feed consumed per 100 pounds of gain, from a large number of feeding trials from different agri- cultural experiment stations. The average data thus obtained by Norton are given at the top of Fig. 6. The practical application of these data must evidently involve variations in the market price of eorn and the different supplements. The practical question to be an- swered is, What will pork cost in dollars and cents when swine are fed according to the rations specified? The question is completely an- swered by the accompanying chart. At the extreme left is the seale of prices of corn per bushel, at the extreme right the scale of prices of supplements per ton, or, in the case of skim milk, per hundredweight. The intermediate scales give the cost of gain per 100 pounds when the swine are fed according to the ration indicated at the upper end of the scale. The cost of gains for corn alone are given on the right side of the line serving as the corn price scale. As an illustration of the use of the chart, consider the relative cost of the gains produced by the six methods of feeding, with prices at the following ievels: COP. co rele eee wees POR oe er ee ee $ 1.50 per bushel Danka vey) Giiae eva tle) cle ee ele eee 110.00 per ton iki :milks 4a Fasc h etante as hiss tee nee OO per cwt. Middlings 2077.5 septa sae kectem tees ees 55.00 per ton Oil: meal ers cs sates ae ais wise a ov Ree eee epee 75.00 per ton SOyDeAD Meal. sie ic as sat bisle kre teleet erat eeemmrety 70.00 per ton From the left-hand seale it is evident that with corn at $1.50 per bushel the corn-alone method would yield pork costing about $13.04. By placing the edge of a ruler at $1.50 on the left scale, and at $110 on the supplement seale on the extreme right, the point of intersection on the corn-and-tankage scale indicates a cost of $12.48 per hundredweight. Keeping the straight-edge still at $1.50 on the corn scale, and shifting the other end to 55 cents on the skim-milk seale on the right, brings the point of intersection on the corn-and- skim-milk seale at the value $11.47. The other values desired, deter- mined in exactly the same way, are $12.87 for corn and middlings, $12.03 for corn and oil meal, and $10.65 for corn and soybean meal. Evidently a ration of corn and soybean meal furnishes the cheapest gain under these conditions, with corn and skim milk next. * Norton, H. W., Jr., Feeding Value of Skim Milk for Swine. Mich. Agr. Col., Special Bul. 92. December, 1918. 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 285 Net RECEIPTS PER HEAD FOR FEEDERS WEIGHING IOOOLBS. AND GAINING 200-400LBS.IN THE FEED Lot Net receipts for gains of : o0lb. Margin of selling price per cwf. Cost of feeders per cwt. over cost 214.50 #6.00 14.00 5.75 13.50 5.50 13,00 525 12.50 3.00 12.00 4.75 11.50 4,50 11,00 425 10.50 4.00 10,00 3.75 2950 3,50 9,00 325 650 3.00 800 2.75 7.50 2.50 700 2.25 650 2,00 FIG. 4 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 287 Purpbue Butretin No.220. Steer Feepine IS!I7-1918 CALCULATION OF NET RECEIPTS PER HEAD oF FAT CATTLE lO50.B. FEepERS. FEEDING Perion 120 Days AINS : Lot |, 212 Ibs. Lot 2,199 Ibs. Lot 3,224|bs. Lot4,287|bs. Margin of selling price per cwt. over cost Cost oF Feepers Per Cwr. Net RECEIPTS PER Heap Ou LOTS land4 . 14,50 $600 14.00 5.75 13.50: 5.50 1300 525 12,50 5,00 12:90 475 11.50 450 1L00 425 10.50 400 10.00 375 2.50 350 200 325 850 300 B00 2.75 7.50 250 700 2.25 650 2.00 600 175 PbGeo - a ie eo >? a . i iin * , #¥ a < oo on OF SK.MILK TANKAGE LoTl ord Lor2 tor4 tor5 Lor6é mee on $2.00 —, 120 ?, $14 1.00 15 3 180 A5¢— 110 170 12 105 60 A0* 100 1 1.50 95 140 10 35 90 1.30 85 iS) ,20— 30 80 8 1.10 15 1.00 7 254 — 70 90 65 6 ¢ .80 20 60 5 70 8 60 50 Gi Gal 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 295 Onto Butretin No. 335. Errect or Ace or Pics on tHE RATE AND Economy oF Gains CALCULATION OF THE Cost OF GAINS AT DIFFERENT WEIGHTS Feep Consumep Per |OOcBs. of Gain : From 50 to l00lbs. 282 |!bs. corn. 507Ibs. tankage Wale) “Yal0loy ahi ts ie redo - | Za CncOOmOO0m 4. * 800 °400“ 425 ° * 904°" 52). 2) 400! 500) 454. - 5265 Price of Cost oF GAINS PER IOOLBS. com per bu 14 Lo (t wane Price OF Ue Seer PER TON 2.10 120 1.10 1,00 80 10 FIG.8 ve “Pap! as ‘bs * porary. '. ’ ‘ ' . >: ~_ . “a < \ . : . = ‘ _ ‘a = ' f Z ' © bad ’ » 1 , i 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 297 — CHARTS INVOLVING THREE VARIABLE FACTORS We have thus far considered the financial presentation of results involving only two variable factors: either (1) the cost of feeders and (2) the margin of selling price over cost, in the estimation of the net receipts per head, or of the necessary margin for a given feed bill and eost of feeders; or the prices of two feeds in estimating the feed bill of a ration involving these feeds only. With the presence of three or more variable factors, such as are met in estimating the cost of many of the common rations used in the fattening of steers, sheep, and swine, the graphical interpretation increases somewhat in complexity, tho it is still perfectly straightforward and readily followed on brief study. AN ILLUSTRATION IN STEER FEEDING The first illustration of the graphical computation of a feed bill involving three feeds is given in Fig. 9. In the chart on the right, the cost of the feed bill for Lot 2 may be computed. The ration con- sists of three feeds: clover hay, cottonseed meal, and corn silage. In this case, the price of corn silage is based on the price of corn, a ton of the silage being valued at 6.5 times the price of a bushel of the grain, or 0.182 times the price of a ton of corn. The scale on the left repre- sents the price of clover hay; the scale at the extreme right represents the price of cottonseed meal and corn per ton. The horizontal scale at the bottom facilitates the conversion of corn prices from the bushel to the ton basis. The use of the chart is best illustrated by an ex- ample: With corn at $1.60 per bushel, clover hay at $30 per ton, and cottonseed meal at $75 per ton, what will be the feed bill per head for Lot 2? From the horizontal scale it is seen that corn at $1.60 per bushel is valued at about $57.20 per ton, as near as the scale can be read. With a ruler placed at the $30 mark on the clover hay scale, and at the $75 mark on the principal scale at the extreme right, a light line is drawn until it intersects the intermediate ungraduated line as shown. A line is then drawn connecting this point of intersection with the $57.20 mark on the principal scale. Where this line intersects the scale immediately to the left of the principal scale, the cost of the ration ($54.00) is indicated. The dotted lines on the chart for Lot 1 illustrate the method of com- puting the cost of ration for this lot, with corn at $1.60 per bushel, clover hay at $30, and cottonseed meal at $73. At these prices, the feed consumed per head would cost $63.30, the corn silage being valued on the basis of the price of corn, as explained above. In the use of these charts. it is not necessary to draw in the lines, but simply to indicate, with’ pencil, the intersection points on the ungraduated line and on the feed-bill scale. 298 BULLETIN No. 234 [ October, AN ILLUSTRATION IN SWINE FEEDING An illustration of the way in which such three-feed charts may be superimposed upon one another is presented by Fig. 10, which gives a financial interpretation of some unpublished swine feeding data from the Illinois Experiment Station. The two side scales, one for tankage and the other for corn, middlings, and oats, are used for both lots. The body of the chart consists of two ungraduated perpendicular lines for the location of intersection points for oats and middlings, respect- ively, and two other perpendiculars graduated to give the cost of gain per 100 pounds, for each lot. At the bottom of the chart are two conversion scales for corn and oats, equating prices per ton and prices per bushel. The dotted cross lines indicate the use of the chart when corn is valued at $1.68 per bushel, or $60 per ton (see lower scale) ; oats 65 cents per bushel, or approximately $40.50 per ton; tankage at $100 per ton; and middlings at $65 per ton. At these prices the cost of 100 pounds of gain would be $15.00 for Lot 14 and $18.05 for Lot 15. The chart may also be used in answering such a question as this: With corn and tankage at the prices quoted and middlings at $65, how high would oats have to be per ton to raise the cost of pork pro- duction in Lot 15 to that of Lot 14; i. e., $15.00? aes ae 10 TON: > t—=75 acs ea i ee 100 <[—s50 a ie@4 Ww Slee : shee $15 OF ,. Pane ou case wl Papest i (ae peas 2.00 Pig 80 {3 a 4 Po 12 ah A a . 70 n Kb a 10 . 60 eg 9 aa é 7 50 ts 1.00 40 6 5 30 FIG. 14 * ' . < ‘ a . : 2 = ee ~ ® tee 7 — . ~~ ere 4 and: ~ t w ~— es + Mntr . ' “~~ and “ Par os ‘ ' 7 ~ ~ 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 313 Puroue. ExrerRiMeENnt STATION CHART BASED ON AVERAGE OF TEN YEARS EXPERIENCE IN FATTENING STEERS ON A RATION OF SHELLED CORN, COTTONSEED MEAL, CoRN SILAGE, AND CLOVER HAY IOOO LB. FEEDERS, GAINING SGOLBS. DURING A FATTENING PERIOD OF [50 DAYS AVERAGE FEED CONSUMED PER STEER Daily Total Shelled corn 12.98 lbs. 0273 ton Price of clover hay Cottonseed meal ato] Diente 0210 - per ton and cost of Corn silage 28.85 ” 2.162 Derararen cw 20-4 Clover hay S4)] ° UY dole Weg f a 7 : 235 : H Price of corn and : Aa cottonseed meal 8355 6 per _ton ry %— Clover yet 4 hay hellea corn . Cotton seed meal aA. 190 954 i 2 . 160 20 $30 $5 8 170 85 3 7: 160 60 150 75 25 £ 140 5g $4—4 70 g € ae 8 ieee c “ 2 *. 38 in of corn ” : Dai 0 =, 120 silage = ~ A 60 200 © er-ton| > ma Q = = | 2 ae Te 55, o = ae ba = Go o 3 ee Se geen 8 50 = a4 od ep pat ee 8 On ey, yen EH coe 5 N6 $154 Oo pst eat he &E 9 45 Ise = el lhe Se © fe) o a = g o Seid i) 80 40 = 3 0 2 JP ° 8 Bed |Z . 3 %, 70 35 o* 14 Z 5 $10 ry, : 60 30 eee “2 al a - 50 25 e 40 20 6 ry $5 30 15 5 4 ° ° 3 $0 FIG.IS — 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 315 we then find that when the difference between the actual and the necessary margins is $2.13, the profit per steer is $29. Obviously, if the steers sold at the necessary margin, no profit would be realized, while if the selling price had been at a margin of, say $3.75, twenty- seven cents less than the necessary margin, the loss would be, according to the same scale, about $3.70 per head. CHARTS PERMITTING GREATER FLEXIBILITY IN FINANCIAL PREDICTIONS The chart just described, constituting a financial interpretation of experimental results at the Purdue Station, is flexible as far as vari- ations in market conditions for live stock and feeds is concerned, but it is nevertheless too rigid to meet all conditions confronting the live-stock man desiring to profit by this valuable experimental work. The rigidity impairing the universal usefulness of the chart is due to the fact that no variation is possible in the weight of feeder steers or in the gain secured. It would of course, be impossible for a farmer to secure feeders weighing just 1,000 pounds. In fact, variations of 100 or 200 pounds from this figure would many times be unavoidable. And yet any variation would influence the necessary margin or the esti- mated profits. This fact, perhaps, is not emphasized fully enough in experiment station bulletins. Feeder steers bought on the market will vary from 850 to 1,150 or 1,200 pounds, and it cannot be assumed that animals of any given average weight can be secured as desired. Again, if feeder animals as secured on the market, varying from 850 to 1,150 pounds, are fed the daily ration prescribed in the manner prescribed, it cannot be expected that at all times gains will be secured at the aver- age rate of 2.4 pounds per head. As a matter of fact, the results at Purdue during the last ten years, obtained from lots of ten animals, have shown gains varying from 2.02 to 2.63 pounds per day, or 303 to 394 pounds in five months of feeding. Of course, a variation in the gains secured may materially affect the necessary margin. ILLUSTRATIONS IN STEER. KEEDING A chart that permits of flexibility in financial interpretation along the lines mentioned is presented as Fig. 16. The use of the chart is illustrated by the broken transverse lines, involving the same prices and experimental data as Fig. 15; 1. e., feeders at $11.50 per 100 pounds, a gain of 360 pounds, a feed bill of $96 per head, and a final weight of 1,360 pounds. A straight-edge placed at the $11.50 mark on the cost-of-feeder scale at the extreme left, and at the 360-pound mark on the inclined seale for gains in weight, is extended to intersect the vertical to the immediate right, and the point of intersection is 316 BULLETIN No. 234 [ October, indicated in light pencil. This point is then connected by a straight- edge with the $96 mark on the feed-bill scale at the extreme right. The point of intersection on the ungraduated vertical line just to the left of the latter scale is then marked in pencil. The straight-edge is then revolved until it passes thru this point and the 1,360-pound mark on the scale of final weights of steers. This line cuts the intermediate inclined line at the $4.02 mark, thus indicating the necessary margin and duplicating the determination made with Fig. 15. If, however, the feeder steers had been bought at 900 instead of 1,000 pounds, it may be shown from the chart that the necessary margin would have been $4.36; if bought at 800 pounds, it would have been $4.73; or at 1,100 pounds, $3.16; in all cases assuming a gain of 360 pounds. With 1,000 pound feeders and a gain of only 300 pounds, the necessary margin is $4.54; or with a gain of 400 pounds, $3.68. A farmer can- not, of course, make a better prediction of the gains he will secure with a given ration than the experiment station whose directions he is fol- lowing, but if after two or three months of feeding the ration, his daily gains are much greater or less than those which the experiment station secured, he may modify his prediction, and, with the aid of this chart, his estimated necessary margin. Fig. 17 permits a further step in financial computations. If with the aid of a feed-bill chart and Fig. 16, a certain necessary margin is computed, the fattening operation is about completed, and the stock man wishes to compute probable profits in view of prevailing prices on the live-stock market, this chart will be of aid. Suppose that with 885-pound feeders costing $10.43 his estimated necessary margin is $4.92 and that the probable gain at the end of the five months of feed- ing will be 375 pounds. Suppose further that beef such as he expects to produce is selling on the market for $17.50; i. e., at a margin of $7.07. This figure is $2.15 above his necessary margin. Now by using Fig. 17, and connecting the point 1,260 (885+875) on the left seale of final weight of steers, with $2.15 on the inclined seale, his profit, if he secures the above price for his beef, would be indicated by the intersection point on the right vertical scale; namely, as $27.12. SUGGESTIONS FOR INCREASING THE PRECISION OF FINANCIAL -ESTIMATES In the discussion thus far it has been assumed, as is generally done, that the receipts in feeding operations include only the net returns (as defined on page 274) from the sale of the animals, and that the expenditures include the feed bill only. Some of the incidental expenses are of course allowed for if the cost of feeders is taken to mean the cost in the feed lot and the margin to mean the margin of mw THe Pao Frege Os ik. Pitcay: Viiwee, oF het % hive eer Or Lose Poa Mean tain | Re Pasion, “fey ' ‘ s € a st ‘ Je fe “4 ma Os oie | be jew f | E. ere ee te ~ mena, ' ‘, a, ee eee Eh oe as pea SA i ; = 6 Ll ' , ee w i. " ‘ me ‘ * 6 ’ 1 , aa aya ; ry ie? , } enasts CALCULATION OF NECESSARY MARGIN OF STEER FEEDING OPERATION FOR VARYING Cost oF FeeperS, GAIN SecurEp, FEED BILL. AND FINAL WEIGHT OF STEERS CALCULATION OF THE PRoFIT oR Loss PER HEAD IN STEER FEEDING OPERATIONS FROM: 1. THe FinAL WEIGHT oF THE STEER,AND 2. THE DIFFERENCE BETWEEN THE ACTUAL AND 50 Necessary Marcins Bet Ea $8 1350 504 |= = E o : | : iG x 1300 a 940 Wd s =; Seeks : e = ee See : 304 Wd su : a ‘ —— off at 30 Vi El Gott ae Uo i ts BAN) Eo Omid eu Ee Est) 50 FIG.AT FIG.I6 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 317 selling price minus shipping and other incidental expenses, over the eost of the feeders in the feed lot. However, other receipts than the net cash receipts from the sale of animals, such as manure and pork produced from the same, must be recognized, as must also other ex- penditures than the feed bill, mainly labor, interest, insurance, and taxes. The frequent assumption that the value of manure produced offsets the cost of labor is obviously unsatisfactory. Of greater weight is the conclusion reached in the recent statistical résumé of the meat situation in this country’ to the effect that in baby beef production the manure and the pork produced almost exactly offset items of expendi- ture other than feed; but even this conclusion must be discounted in view of the lack of system in the method employed of evaluating the manure, a procedure which was left entirely to the unaided judgment of the live-stock farmer. It would seem advisable in feeding experi- ments to determine as precisely as practicable the amount of manure produced, its average composition, and its fertilizing value. The collec- tion of the manure should conform only to the best farm practice in collecting manure for distribution as fertilizer on the fields. Only in this way can an accurate estimation of the value of this important item in feeding operations be obtained. The frequent practice among experiment stations of crediting all pork profits from undigested corn to the steer feeding operation, re- gardless of the additional corn or supplemental feeds given the hogs, the cost of the latter feeds being deducted from the value of the pork produced, is unsound from every standpoint. Only when check lots of hogs, fed the same way except for the access to steer droppings, are employed, can the actual amount of corn thus utilized, the actual amount of pork produced, and the actual profits realized from this practice be determined (see Iowa Exp. Sta. Bul. 182). When this is done, the results may, perhaps, best be stated as a given amount of pork per bushel of corn in the ration. (Purdue Exp. Sta. Bul. 146, page 605). Another difficulty in the proper financial interpretation of feeding operations is the evaluation of home-grown feeds of no definite market value. Among these feeds silage is of great importance, figuring largely in steer feeding operations especially. And yet, as far as the author is aware, there is no systematic or commonly recognized method of valu- ing this feed. Investigation along this line is undoubtedly needed, that it may be ascertained whether there is any close relation between the yield of corn per acre (and possibly its composition) and the amount of corn per ton of silage—to the end that some fair relation may be determined, if possible, between the price of corn and the inherent value of silage. Much of the current discussion as to whether it is profitable to feed corn in rations containing corn silage fed ad libitum, *U. S. Dept. Agr., Report No. 111, Part ITI, pages 62-63. 1916. 318 } BULLETIN No. 234 [ October, properly supplemented with hay and a nitrogenous concentrate, is of doubtful significance unless a satisfactory method of valuing the silage can be agreed upon, since when the corn is not fed the consumption of silage is enormously increased and becomes an important item in the feed bill. APPENDIX Construction of Fig. 1 This type of alignment chart is suitable for the solution of all equations of the form aP + bQ = R, or aP — bQ = R, where P, Q, and R are any functions of three variables. The scales for P and Q are the outside scales, while the scale for R is situated somewhere between them. The general equation for its location is bpk aq -- bp >. where x is the distance between the scales for P, on the left, and for R; k is the distance between the scales for P and Q; a and b are the constants in the above equation; and p and q are the unit distances (moduli) on the seales for P and Q, respectively. The side scales are placed at some arbitrary convenient distance apart, and a reasonable range of values laid off on each, choosing a convenient unit distance, or modulus, for the dollar in each case. In choosing these units, consideration should be given the fact that, ac- cording to the equation from which the values on the intermediate scale are to be computed, 1. e., ge+ (w+g)m=—r, rae the margin, m, dollar for dollar, is a more important determinant of r than is the cost of calves, ec. Hence its unit should be larger. Having constructed the two side scales, the distance between the left scale and the intermediate scale is computed from the relation ee We (2) gm’ + (w-+ @) @” in which x is the distance desired; ¢’ is the distance chosen to represent a dollar on the left-hand seale; k is the distance between the two side scales; m’ is the distance chosen to represent a dollar on the right-hand scale (the modulus) ; and w and g have the same significance as in the preceding equation. (See Deming’s Manual, page 38; also Lipka, Graphical...Computations, pages 44-64.) Having located the posi- tion of the intermediate scale, two points fairly wide apart, say those x 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 319 for $85 and $150, are located on it by long-hand calculation of equation (1), using a straight-edge to connect the values taken for selling price of calves and margin. The distance between these two points is then divided into the proper number of equal parts, in this case 65. (See Deming, page 23.) Construction of Fig. 2 This chart is similar in general to Fig. 1. In the case of Lot 1, for instance, the equation for the feed bill is x == 1.993 times the price of corn -++ 0.0552 times the price of alfalfa hay. The location of the intermediate scale for this lot is given by ut 0.0552 ct k ~ 1,998 at + 0.0552 ct’ in which x is the distance from the left-hand scale to the scale for Lot 1; ¢1, the distance representing one dollar on the left-hand scale; k, the distance between the two side scales; and a, the distance repre- senting one dollar on the right-hand scale. The seales for the other lots are similarly located. Good judgment should be shown in choosing suitable values for c! and a!. A glance at the rations given at the head of the chart shows that a dollar’s vari- ation in the price of corn exerts 10 to 75 times as great an effect on the feed bill as a dollar’s variation in the price of alfalfa hay. The units chosen should therefore stand in a somewhat similar relation in order to insure a proper centering of the intermediate scales and a consequent greater accuracy in their use. With the intermediate scales thus located, definite points on each are found by direct calculation and the use of a ruler or string, and the distances between points on any one scale are divided into the proper number of equal parts in determining the dollar unit distance for each scale. Construction of Figs. 3 and 4 No additional instructions need be given for these charts. The directions and formulas given for Fig. 1 apply here. Construction of Fig. 5 The construction of this chart is similar to that of Fig. 1. Equation (2) is used in locating the intermediate scales, varying k as required. Construction of Fig. 6 After setting up the two extreme side seales for the price of corn and the price of supplements, the intermediate scales are located and graduated in the usual way. Points on the ‘‘corn-alone’’ scale are 320 BULLETIN No. 234 [October, located as follows: 486.5 pounds of corn are equivalent to 8.69 bushel. The $18 mark is located on the corn price scale by simple division of this figure by 8.69; similarly to $5 mark. The difference between these two points is then divided into 65 equal parts for a 20-cent interval. The location of an intermediate scale is accomplished as follows. The eorn-and-oil-meal ration calls for 377.3 pounds of corn and 51.7 pounds of oil meal, or 6.74 bushel of corn and 0.02585 ton of oil meal. The equation to be solved is therefore 6.74 ¢ + 0.02585 o = r, where ¢ is the price of corn per bushel and o is the price of oil meal per ton. The distance between the corn price scale on the left and the intermediate scale desired is 0.02585 ¢1 k 6.74 01 + 0.02585 c!’ pq eS where c! is the distance taken to represent one dollar on the corn price scale; o!, the equivalent distance on the supplement scale; and k, the distance between the two extreme scales. Points on the intermediate line thus located are best found by connecting points on the two outer scales corresponding to even dollar values for r, according to the above equation. Construction of Figs. 7 and 8 No additional instructions need be given for these charts. The directions given for Fig. 6 apply here. Construction of Fig. 9 Just as the graphical solution of an equation of the first degree for one variable in terms of two others may be carried out with a triple- parallel chart, so the graphical solution of a linear equation for one variable in terms of any number of other variables, such as . aw + bx+cy+dz+...=r, may be carried out by a chart such as this. In this series of functions, a, b, e, d, ete., are constants, representing, in the present case, the weights of feeds consumed; while w, x, y, z, ete., are variables or func- tions of variables representing in the present case the prices of feeds. A chart for the summation of such terms is constructed by setting up at the extreme right a scale for the variables, and at intervals per- pendicular lines, the distance of each of which from the left scale is proportional to the reciprocal of the sum of the constants in the above equations up to and including the term in question. Thus, in the 1921]. FINANCIAL PHASES OF FEEDING EXPERIMENTS 321 equation given there would be four uprights, at distances from the ioe hand scale proportional to 1 1 1 aay fi a oatb a-bte Abed: In the present case the equation of the feed bill of Lot 2, involv- ing 3 feeds, is r = 0.250 x + 0.168 y + 3.255 z, in which x is the price per ton of clover hay, y the price per ton of cottonseed meal, and z the price per ton of corn silage. In the con- struction of feed-bill charts it is often inconvenient, on account of the ereat disparity in the price of feeds, to use the same seale for all feeds, according to the unmodified plan. For example, roughages are ordinarily much cheaper per ton than cereals and nitrogenous concen- trates, and their price scale should therefore have a greater unit dis- tance for the dollar. Technically speaking, the modulus of the rough- age scale should be greater than that of the concentrate scale. And this may be accomplished by multiplying or dividing the constant coefficient according as the modulus of the corresponding price seale is decreased or enlarged. In the present instance, taking the standard price scale as that suitable for cottonseed meal, it is advisable to in- crease the modulus of the price scale for clover hay by twice, so that the corresponding coefficient is divided by two. Furthermore, it was decided to value the corn silage per ton at 6.5 times the price of corn per bushel; that is 1 ton of corn silage equals in price 364 pounds, or 0.182 ton, of corn. The corn price scale is made the sameé as'the cotton- seed meal price scale. The above equation is changed, therefore, to r= 0,125'x + 0.168 y + [(3.255) (.182) = 0.592] 21, where z! is the price of corn per ton. The chart for Lot 2 consists of the scale at the right for corn and cottonseed meal, and three per- pendicular lines situated at distances from the scale proportional to the reciprocals of 0.125, (0.125 + 0.168 =) 0.298, and (0.293 -+- 0.592 —) 0.885. It will be noticed that the clover-hay price scale given on the first line at the left of the chart for Lot 2 has a modulus twice that of the right-hand scale and is arranged so that a given distance above the base line represents a price just half that at an equal height on the right-hand seale. The cottonseed-meal upright is not graduated but the corn line is graduated to represent the stat feed bill. This scale is readily constructed since its modulus is 74¢5 times that of the principal scale on the right. The $30 mark on the feed-bill scale, for example, is at the same level as the (30 ~ 0.885 —) $33.90 mark on principal scale. Two extreme points can be thus located on this seale, and then the distance between these points divided into the proper number of equal parts, 522 BULLETIN No. 234 [ October, The chart for Lot 1, to the left of the chart just considered, is con- structed in a similar way. If the price of corn silage can be based on the price of corn, as is here done, the four feeds of Lot 1 may be charted as three feeds. The equation to be solved is r = 0.240 x + 0.168 y + 2.841 z 4+ 0.249 z}, where x, y, z, and z! have the same significance as above. Pricing corn silage per ton at 6.5 times the price of corn per bushel, the last two terms can be combined. The clover-hay modulus is increased by twice and the coefficient correspondingly divided by two, so that the modified equation is r = 0.120 x + 0.168 y + [(2.841) (0.182) = 0.517 + .249 =] 0.766 2’. In this case the $30 mark on the feed-bill scale is at the same level as the (30 — 1.054 —) $28.46 mark on the principal scale, since the sum of the coefficients in the above equation is 1.054. Charts such as those just described, involving a reciprocal hori- zontal seale, are described in Deming’s Manual, pages 47 to 50, for the first time. Their use in the present instance is described in the Text The horizontal seale at the bottom of the chart, for the conversion of prices of corn per bushel into prices per ton, is very simple in con- struction. Since a bushel of corn is equal to 334,; ton, each point on the lower graduation equals 35.71 times the corresponding point on the upper graduation. The seale is conveniently made by first laying off the upper scale, using any convenient modulus, and then locating two extreme points on the lower seale. Thus, the $40 mark on the lower scale coincides with the (40 -—- 35.71 —) $1.12 mark on the upper. The distance between the two points thus loeated is divided into a convenient number of parts. Construction of Fig. 10 No new principles are involved, aside from the superposition of two charts. For Lot 14, the feed-bill equation is 0,025 x + 0.0585 y + 0.145 z =r, where x is the price of tankage; y, the price of middlings; and z, the price of corn per ton. The tankage price seale, given on the left, is taken as the standard, and the other scales for middlings and corn are constructed with a modulus twice as large as that of the tankage scale, and in such a way that any given price on the one seale is at the same level above the base line as twice that price on the other scale. Hence the coefficients for corn and middlings must be divided by two, and the equation reduces to r = 0.025 x + 0.0292 y + 0.0725 z. 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 323 The distances from the tankage scale to the principal scale on the right, from the middlings ungraduated perpendicular to the same scale, and from the perpendicular bearing the feed bill for Lot 14 per 100 pounds of pork, to the right-hand scale, stand to each other in the proportion of the reciprocals of 0.025, (0.025 + 0.0292 —) 0.0542, and (0.0542 + 0.0725 —) 0.1267. The feed-bill scale for Lot 14 is such that any price on it, say a, is at the same level above the base line as a —- 0.1267 on the tankage price seale. Lot 15 is charted in an exactly similar manner, the same side scales being used for the price of feeds, and the two intermediate lines being located, one ungraduated for oats, and the other so graduated for corn as to give the total feed bill. The corn conversion seale at the bottom is constructed as already explained. The oat conversion scale is constructed similarly, tho in this case each point on the lower graduation is (2000 + 32—) 62.5 times the coincident point on the upper graduation. Construction of Fig. 11 The equation to be solved in this ease is 2.42 v + 0.0195 w + 0.025 x + 0.022 y + 0.094 z—r, in which the variables are the cost of man labor per hour and the prices per ton of roughage other than hay or silage, hay, grain, and silage, respectively. The standard scale adopted is that for roughage, all three types, this scale being set up on the outside of the line on the extreme right. The modulus for the labor scale is 30 times that of the standard, and the scale will be found at the extreme left of the chart. Each value on this scale is at the same level as 30 times its value on the standard scale. The modulus for the grain scale is taken as one- third of the standard modulus. This scale is laid off on the inner side of the line at the extreme right of the chart. The above equation then reduces to 0.0807 v + 0.0195 w + 0.025 x + 0.066 y + 0.094 2=r. The five lines to the left of the standard seale are at distances from it proportional to the reciprocals of : Bera Or SGT. DOUT sales, side tt, 4 ate ove < 0.0807 Roughage other than hay and silage.... (0.0807 + 0.0195 —) 0.1002 Le A, Ne porte RN a nerd a Rah a se (0.1002 + 0.0250 —) 0.1252 Syren Sha eee oe tees cuter, nica eae 3s, « (0.1252 + 0.0660 —) 0.1912 SNE CAE Wee ade ena Mage ea ae ar (0.1912 + 0.0940 —) 0.2852 and each value on the scale representing the cost of milk per hundred- weight is therefore equal to 0.2852 times the value at the same level on the standard scale. 324 BULLETIN No. 234 [ October, Construction of Fig. 12 In this case the sum of the coefficients, after price adjustments are made in the same manner as in Fig. 11, is 0.2337. However, since the sum of the five items enumerated in this case is only 79.58 percent of the total cost of the milk, this figure is divided by 0.7958, giving 0.2937. Hence any value on the seale representing the cost of milk per hun- dredweight is at the same level as 0.2937 times that on the standard scale. To be more specific, the $4.00 point on the former seale is at the same level as the ($4.00 + 0.2937 =) $13.62 point on the standard scale at the right. Construction of Fig. 13 This is a transversal alignment chart suitable for multiplying or dividing. In this case, multiplication is accomplished. The equation to be solved is pT ih where x is the ratio of the average price of milk for a given month to the average price per year; y is the average annual price of milk; and r is the average monthly price of milk. A uniform percentage seale (x) is laid off at the left from 70.6, the lowest percentage (for June), to 120.8, the highest percentage (for December). Instead of indicating percentages on this scale it is sufficient to indicate the name of the month at its proper position on the seale. At the right a uniform scale is laid off for the monthly cost of milk per hundred- weight (r), a range from $1 to $8 being ample. The cross-line con- nects the zero points on both of the side seales. In ease the zero point on one or both scales is so far removed as to make mechanical connec- tion inconvenient or impossible, the inclined intermediate scale may be located by geometry (see Deming, page 33). The scale on the in- clined line is not uniform, but projective. It may be laid off by locat- ing, by the use of a straight-edge, two extreme points and one inter- mediate point midway between the other two. The points of inter- section of any straight line on the inclined line (y) and on the two parallel lines (x and r) stand to each other in the relation indicated by the above equation. From the three points thus located the scale may be laid off by geometric means (see Deming, page 23). For a further discussion of transversal alignment charts see Deming’s ‘‘Manual,’’ pages 39 to 43, and Lipka’s ‘‘Graphical and Mechanical Computation,’’ pages 65 to 87. Construction of Fig. 14 This chart is concerned, first with the calculation of the feed bill for the ration indicated at the top; and second, on the basis of this result 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 325 and the cost of feeders, the calculation of the necessary margin when the initial weight of feeders and the gain are as indicated. The scales to be used in the determination of the feed bill involve no new principle. The standard price scale is taken as that for alfalfa hay and corn silage. The modulus for the corn and cottonseed-meal scales is one-third that of the standard, so that each value on this scale, laid off on the inside of the line at the extreme right of the chart, coincides with a value one-third as great on the standard seale, laid off on the outer side of the same line. The original feed-bill equation, r= 1.933 w + 0.2115 x + 0.181 y + 1.0865 z, in which w is the price of corn silage per ton; x, that of alfalfa hay ; y, that of cottonseed meal; and z, that of corn; becomes, on making the above scale adjustments, r = 1.933 w + 0.2115 x + 0.543 y + 3.2595 z. If from the feed bill thus determined is subtracted the product of the gain secured, expressed in hundredweight, and the cost of feeders, and the difference is divided by the final weight of the steers in hun- dredweight, the quotient is the necessary margin. Now the process of subtraction is performed on a chart of this character by working back- wards from right to left, just as summation is accomplished by work- ing from left to right. In this chart the vertical lines for the different feeds are located as usual, their distances from the standard scale being proportional to the reciprocals of the following numbers: PPPS Cr teow Som ence leat se gh oan, oh ose ial, Wah Ske eew ISS 1.933 Pe VTE LY | Wate te iette oi als nix sig ees iesewie's asks. ies S aS byes 2.144 DOE SR EGO SS Soe Doe eee ar Pere GAA ae 2.687 ESS 9 Ao ee aig ris roe inane age ee a ae 5.946 and the feed-bill scale on the corn upright, at any level, contains values 5.946 times the corresponding value on the standard scale. The sub- traction of the product of gain in hundredweight and the cost of feeders, 3.94 v, the standard scale being used for the cost of the feeders, locates a vertical scale removed from the standard scale by a distance proportional to the reciprocal of 5.946 — 3.94 — 2.006. Dividing this number by 13.19, the final weight in hundredweight, we get 0.1521. Hence any value on the scale of necessary margin equals 0.1521 times the value on the standard scale at the same level. Thus the $10 mark on the standard scale is at the same level as the $1.52 mark on the necessary-margin scale. Construction of Pig. 15 The construction of this chart is similar to that of Fig. 14. The lower horizontal scale, from which the profit or loss per steer is read 326 BULLETIN No. 234 [October, off for any given difference between actual and necessary margin, de- pends for its construction on the following fundamental equation: ge -+ (w+ g) mr, in which g is the gain in hundredweight and w the initial weight in hundredweight, these being constant; while of the variables, ¢ is the cost of feeders, m the margin per hundredweight, and r the receipts per head. When r just equals the feed bill, or, more generally, the cost of the feeding operation, m is the necessary margin. For every dollar by which the actual margin at which the steers are sold exceeds this necessary margin, the profit secured is obviously equal to (w + g), or the final weight of the steer expressed in hundredweight. For every dollar by which the actual margin falls short of the neces- sary margin, a corresponding loss of (w + g) dollars must be borne. Hence a scale is laid off on the upper side of the horizontal line representing differences in dollars and cents between the actual margin and the necessary margin as determined by the chart. A scale may now be laid off on the lower side of the same line to represent the gain or loss realized by making each value on the latter equal to 13.6 times the coincident value on the former scale. If the difference between the actual and the necessary margins is positive, the value read off the lower scale represents profit; if negative, it represents a loss. Construction of Fig. 16 The purpose of this chart is to facilitate the calculation of the necessary margin for steer feeding operations, for varying cost of feeders, initial weight of feeders, gain secured, and total feed bill. In the fundamental equation given above, if r, the net receipts per head, equals the feed bill, then m becomes the necessary margin and may be obtained by the following equation: f — ge Wwe” in which f is the feed bill. The left half of the chart represents a multiplication of gain in hundredweight and cost of feeders (see Fig. 13). Since this result in itself has no particular significance it need not. be indicated by a seale, which would naturally be placed on the same line as the scale for the final weight of steers. The right half of the chart involves two mathematical operations, a subtraction and a division. The product secured by the multiplication of gain by cost of feeders is subtracted from the feed bill scaled on the line at the extreme right. The difference thus secured is indicated by the inter- section on the vertical line situated between the feed-bill scale and the seale of the final weight of steers. Since this difference per se possesses no significance, this vertical line is not graduated. It might 1921] FINANCIAL PHASES OF FEEDING EXPERIMENTS 327 be said here that in triple-parallel.charts, such as this, when the two functions involved are scaled on the outside parallels in opposite diree- tions, one scale increasing in value from the bottom upwards and the other from the top downwards, subtraction of the two functions is indicated by the point of intersection on the intermediate line (see Lipka, ‘‘Graphical Computation,’’ page 45), instead of addition, as when the outer scales are graduated in the same direction. The differ- ence obtained by the point of intersection on the intermediate vertical line is then divided by the final weight of the steer in hundredweight, the scale for which is on the same line as that used to indicate the product of gain and cost of feeders. A straight line from the point representing the difference between feed bill and the product of gain and cost of feeders, to the final weight of steer intersects the inter- mediate inclined line (for the construction of which see Fig. 13) at the necessary margin required. Construction of Fig. 17 The construction of this chart involves the same ius inciples as are involved in Fig. 13 (q.v.). =o | | J I] ===) l