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"A CRITICAL EVALUATION AND TEST OF BREAK-EVEN ANALYSIS AS A TECHNIQUE FOR PROFIT PLANNING by SAY CHONG LIM B.A. (Hons.), University of Malaya, 1963 A Thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of MASTER OF BUSINESS ADMINISTRATION i n the Department of COMMERCE AND BUSINESS ADMINISTRATION We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 9 6 5 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y of \u2022 B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y , I f u r t h e r agree t h a t p e r  m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n * Department of Commerce and Business Administration The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada Date A p r i l 30th 1965 ABSTRACT This study provides a c r i t i c a l evaluation of break even analysis i n terms of i t s assumptions and uses and also i n terms of the economic theory of the firm i n the short and long run and under perfect and imperfect competitive con d i t i o n s . I t also includes a test of the hypothesis that break-even analysis can be better than the percentage of sales method as a technique for forecasting the future oper ating p r o f i t s of firms and the n u l l hypothesis that there i s no difference between break-even analysis and the percentage of sales method as a technique f o r forecasting the future operating p r o f i t s of firms. The test i s based on data (without adjustments) from Moody's I n d u s t r i a l Manuals. Although the break-even approach i s more s o p h i s t i  cated and requires more time, e f f o r t and expense, the test shows that at the 0.01 l e v e l of si g n i f i c a n c e , there i s no difference between the accuracy of i t s forecasts of oper ating p r o f i t s and that of the percentage of sales method. The hypothesis i s therefore rejected and the n u l l hypothesis accepted. The conclusion drawn from the test i s that the management of a f i r m should not make use of break-even analy-. s i s to forecast i t s operating p r o f i t s i f i t i s not prepared to make any adjustments to i t s data to recognise the effects of changes i n the determinants (excluding volume) of p r o f i t s . The percentage of sales method should be used instead. TABLE OF CONTENTS Chapter Page I. INTRODUCTION 1 Statement of the Problem 2 Hypothesis and N u l l Hypothesis . h Organisation . 8 Limitations of the Study 9 Def i n i t i o n s . . . 11 Summary Ih I I . THE NATURE OF BREAK-EVEN ANALYSIS 15 Introduction 15 Use of Break-Even Analysis 15 The Development of Break-Even Analysis . . . 16 The Break-Even Chart 20 The Break-Even Point 25 Cost Breakdown 29 Summary 39 I I I . A CRITICAL EVALUATION OF BREAK-EVEN ANALYSIS . U-l Introduction hi S t a t i c Analysis hi A Short-Run Concept Mr- Linear and Curvi-Linear Charts Mr- Separation of Costs ^8 Constant S e l l i n g Prices h9 Total Cost and Constant Unit Variable Costs. $h Production Equals Sales . 60 Sales Mix 63 Planning and Control 67 P r i c i n g P o l i c i e s 69 C a p i t a l Expenditures 70 Make or Buy Problems 72 Cost Control 73 Summary 75 IV. TEST OF BREAK-EVEN ANALYSIS 77 Introduction 77 Source of Data 78 Forecasting Operating P r o f i t s 79 The Sample 83 Method of Analysis 89 Summary 100 Chapter V. SUMMARY AND CONCLUSION Summary . . . . . . Conclusion BIBLIOGRAPHY APPENDICES LIST OF TABLES Table Page I Number and Percentages of Companies Inter viewed Indicating Various Types and Frequencies of Break-Even Analysis 17 II Number and Percentage of Companies Answering Questionnaires Indicating Types and Fre quency of Preparation of Break-Even Analysis as Reported by 3kk Companies 18 III Computation of the Standard Deviation of the Universe 87 IV Difference between Actual and Forecast P r o f i t s - Percentage of Sales Method 90 V Difference between Actual and Forecast P r o f i t s - Break-Even Method 93 LIST OF ILLUSTRATIONS Number Page EXHIBIT 1 Conventional Break-Even Chart 22 2 Profit/Volume Chart 23 3 Scatter Chart 38 h Modified Conventional Break-Even Chart . V3 5 Curvi-Linear Break-Even Chart -^6 6 The Limits of Constant Prices 52 7 Constant Average Variable Cost 55 8 Economists' Cost Curves 56 9 Economists' Average Variable Cost Curve. 58 CHAPTER I INTRODUCTION There has been a great deal of controversy i n recent years regarding the objectives of p r i v a t e l y operated business organisations. Some people argue that a business organisation ought to have long-run p r o f i t maximisation as i t s sole objective while others argue that the management of a business should not only think of p r o f i t s but also t r y to provide s a t i s f a c t i o n f o r the partic i p a n t s i n the organisation, take the lead i n technological developments and secure s o c i a l approval.^\" Whatever the arguments, i t cannot be denied that, i n a fre e enterprise system, no p r i v a t e l y operated business can a f f o r d to make les s than a 'healthy 1 p r o f i t f o r any apprec i a b l e period of time. The s u r v i v a l of a business, therefore, depends on the a b i l i t y of the management to earn, at l e a s t , a 'healthy' p r o f i t f o r the business. In order to achieve t h i s , under ex i s t i n g competitive conditions, the management of a business has to provide f o r proper f i n a n c i a l planning and con t r o l . In other words, management must be able to plan i t s p r o f i t per formance and r e a l i s e i t s p r o f i t plans to j u s t i f y i t s existence. 1. Assuming no d i s t i n c t i o n between the management and the owners of a business, i t should also be recognised that maximi sati o n of the value of owners' common stocks could be the objective of business. - 2 - To do t h i s e f f i c i e n t l y , management has developed and adopted various t o o l s . One of the more basic of these tools i s break-even analysis. As w i l l be seen i n chapter I I , t h i s t o o l has been used by a f a i r number of firms as an ai d f o r t h e i r f i n a n c i a l planning and control. Graphically, or mathematically, i t per mits management to study the probably e f f e c t s on p r o f i t s of changes i n single f i n a n c i a l factors or combinations of them. Statement of the Problem Break-even analysis does not provide a completely r e l i a b l e forecast of future p r o f i t s . The forecasts are made under a given set of assumptions regarding such factors as production and sales, p r i c e s , costs, and sales mix. A change i n any of these assumptions w i l l a f f e c t the forecast. But, given the assumptions, break-even analysis may show the ex pected p r o f i t s at various volumes. P r o f i t , then, becomes a single valued function of volume. I f break-even analysis i s to be used to give more accurate r e s u l t s , then changes or expected changes not only i n volume but also i n the other variables which a f f e c t p r o f i t s , must be c a r e f u l l y watched f o r and adjustments must be made f o r such changes. This, however, does not seem to go along well with the advantages of break-even analysis. One of the strongest points of break-even analysis, as a to o l f o r forecasting - 3 - future p r o f i t s , i s that i t i s simple, quick and cheap to pre pare. But, i f a prerequisite to the use of break-even analysis i s a forecast of a l l the variables that a f f e c t p r o f i t s and i f adjustments have to be made i n break-even analysis on the basis of the r e s u l t s of the forecasts of these variables, then the very advantages of break-even analysis w i l l be defeated. I f , on the other hand, management does not go to the trouble to make the preliminary forecasts and adjustments but merely makes use of break-even analysis to show p r o f i t expectations under a s p e c i f i c set of assumptions regarding external market conditions and i n t e r n a l management strategy, then p r o f i t s w i l l be shown to vary only with volume. But, i n break-even analysis, sales revenue i s often used as a measure of volume, on the assumption that volume (output) and sales are synchronised. Under the circumstances, the question a r i s e s , \"Isn't i t simpler, quicker and cheaper to determine the average of p r o f i t s as a percentage of sales f o r several past years and apply t h i s percentage to arrive at the expected p r o f i t s f o r d i f f e r e n t volume l e v e l s ? \" This method of forecasting p r o f i t s i s known as the percentage of sales method. With t h i s method, the problem of cost separation and a host of other problems do not a r i s e at a l l . This study attempts to compare the accuracy of the r e s u l t s of the break-even method with that of the percentage of sales method. On the basis of t h i s comparison, a con-- i n  c l u s i o n w i l l be drawn on the merit of using break-even analy s i s f o r forecasting the operating p r o f i t s of firms and i t s managerial implications. Hypothesis and Null Hypothesis The hypothesis i s that break-even analysis can be better than the percentage of sales method as a technique f o r forecasting the future operating p r o f i t s of firms. Since break-even analysis i s more sophisticated, i t i s expected that, at worst, i t w i l l be as good as the percentage of sales method. Therefore, the p o s s i b i l i t y that the l a t t e r may be better than the former w i l l not even be considered here. In order to t e s t the hypothesis, f i r s t l y , a sample of firms has to be picked since i t i s not possible to study the performance of the two methods i n a l l firms. Secondly, the average difference between forecast p r o f i t s and actual p r o f i t s by each of the two approaches has to be determined and f i n a l l y a comparison has to be made of the two averages. In establishing the averages, the mean, the median or the mode can be used. In t h i s study, the mean i s preferred to the other two measures since i t i s l e a s t subject to sampling v a r i a t i o n . ^ The a l t e r n a t i v e to the hypothesis i s that there i s 2 . In chapter IV, an explanation i s given of the manner i n which random sampling has been used to p i c k the f i f t y - seven firms, which form the sample. 3 . Frederick E. Croxton and Dudley J . Cowden, Applied  General S t a t i s t i c s , 2 n d Ed.; Englewood C l i f f s , N.J.: Prentice- H a l l , Inc., 1 9 5 5 , p. 1 9 7 . no difference between break-even analysis and the percentage of sales method as a technique f o r forecasting the future operating p r o f i t s of firms. This a l t e r n a t i v e hypothesis i s c a l l e d the n u l l hypothesis. With the symbol p^ used to represent the mean difference between actual and forecast p r o f i t s obtained by the percentage of sales method, and the symbol p 2 used to represent that obtained through break-even analysis, the n u l l hypothesis may then be formulated as p l = P2* Since the p o s s i b i l i t y that the less sophisticated percentage of sales method may prove to be more accurate, has been ruled out on the grounds that i t i s u n l i k e l y to happen, the a l t e r n a t i v e to p.^  = p 2 i s p^ &gt; p 2 . This a l t e r n a t i v e implies that the average difference between actual and fore cast p r o f i t s by break-even analysis i s smaller and, therefore, the hypothesis as stated e a r l i e r , i s correct. From the above discussion, i t i s obvious that the acceptance of the hypothesis depends on the r e j e c t i o n of the n u l l hypothesis. But, before a decision can be made on the n u l l hypothesis, a t e s t of significance has f i r s t to be ca r r i e d out. The purpose of such a test of significance i s to determine whether there i s any s t a t i s t i c a l s i g n i f i c a n c e between p-^  and p 2 . In order to do t h i s , i t i s necessary to set a .criterion of s i g n i f i c a n c e and to determine the proba b i l i t y of z, where z i s the r a t i o of p-^  - p 2 to an estimate of the standard error of the difference between the two sample means. The c r i t e r i o n of s i g n i f i c a n c e established - 6 - depends on the type of error that i s to be avoided. In tests of s t a t i s t i c a l s i g n i f i c a n c e , there are two types of errors. A type I error arises when a n u l l hypothesis i s act u a l l y correct but the difference involved i s declared to be s i g n i f i c a n t . A type II error arises when a n u l l hypothesis i s ac t u a l l y wrong but the difference i n  volved i s declared to be not s i g n i f i c a n t . If the in t e n t i o n i s to reduce type I errors to the minimum, then the c r i t e r i o n of s i g n i f i c a n c e established should be such that the l e v e l of signi f i c a n c e i s very small. On the other hand, i f type II errors are to be reduced to the minimum, then the l e v e l of signi f i c a n c e ought to be larger. Whether type I or type II errors ought to be minimised depends very much on i n d i v i d u a l situations and circumstances. In this study, a type I error would be committed i f the difference between the sample means i s so small that i t can almost be said that there i s no difference between them but i t i s declared that the difference between them i s s i g n i f i c a n t . The consequence of t h i s may be that people who would otherwise not use the break-even method to forecast operating p r o f i t s , may now use the break-even method. The reverse would be true i f a type II error i s committed. In such a case, the difference between the sample means i s act u a l l y very large but a declaration i s made that the d i f f e r  ence i s not s i g n i f i c a n t . The r e s u l t of such an error may be k. I b i d . , p. 61+0. - 7 - that people, who would otherwise make use of break-even analysis to forecast operating p r o f i t s , may now consider that, a f t e r a l l , i t i s not worthwhile to go to a l l the extra e f f o r t , time and expense to use the break-even method. The above discussion suggests that, i n t h i s study, i t i s more serious to commit a type I error since when such an error i s committed, extra costs are incurred f o r which no appreciable benefits are received. A type II error appears to be l e s s serious since i t merely r e s u l t s i n a l o s s of benefits, i n the form of greater accuracy i n the forecast, which can otherwise be obtained. But, at the same time, no extra costs are incurred. In short, t h i s means that i n committing a type I error, extra costs are incurred f o r no appreciable benefits whereas, i n committing a type II error, no new benefits are received but no extra costs are i n  curred. I t was stated e a r l i e r that i f type I error i s to be minimised, then the l e v e l of significance ought to be very small. The l e v e l of significance that i s customarily used 6 i s 0 . 0 5 or 0 . G 1 . In t h i s study, 0 . 0 1 w i l l be used. From the t-table i n Appendix I I , i t may be noted that by i n t e r - 5 . I t i s , however, possible that the loss i n accuracy, i f measurable i n d o l l a r terms, may be large enough to more than o f f s e t the extra costs and the ultimate costs of committing a type II error may i n f a c t be higher. 6 . John E. Freund and Frank J . Williams, Modern Business  S t a t i s t i c s . Englewood C l i f f s , N.J.: Prentice-Hall, Ine*, 1 9 5 8 , P. 22*f. - 8 - pola t i o n , f o r f i f t y - s e v e n degrees of freedom, the value of z at the 0.01 l e v e l of significance, i s 2.667. In thi s study, a on e - t a i l t e s t i s used since the alternative to the n u l l hy pothesis that p-|_ = p 2 i s one-sided, i . e . p^ ^ &gt; p 2\u00AB With this information, i t may be stated that the n u l l hypothesis should be accepted i f z 4 2.667 and should be rejected i f z &gt; 2.667. This i s the same as saying that the hypothesis, that break even analysis can be better than the percentage of sales method as a technique f o r forecasting the future operating p r o f i t s of firms, i s acceptable i f z &gt; 2.667 and should be rejected i f z &lt; 2.667. Organisation Chapter I i s the introductory chapter to this t h e s i s . Here, the statement of the problem, the hypothesis and the n u l l hypothesis, the li m i t a t i o n s of the study, the organisation and the d e f i n i t i o n s of terms are given. To pro vide a basis for the c r i t i c a l evaluation of break-even analysis, chapter II i s devoted to a f a c t u a l description of the nature of break-even analysis. B r i e f l y , an idea i s given of the extent to which break-even analysis i s used, the dev elopment of break-even analysis, the break-even chart and the break-even point. An idea i s also given of how costs of firms are separated f o r the purposes of break-even analysis. Against t h i s background, a c r i t i c a l evaluation of - 9 - break-even a n a l y s i s i s made i n chapter I I I , i n terms of the assumptions used and the uses to which break-even a n a l y s i s i s p u t . The e v a l u a t i o n i s a l s o i n terms of the economic theory o f the f i r m i n the sh o r t and long run and under per f e c t and im p e r f e c t c o m p e t i t i v e c o n d i t i o n s . T h i s chapter and chapter I I are based p r i m a r i l y on a c l o s e examination of the v a r i o u s p u b l i c a t i o n s r e l a t i n g to the a n a l y s i s of cost-volume p r o f i t r e l a t i o n s h i p s . Chapter IV deals w i t h the t e s t of the hypothesis and the n u l l h y p o t h e s i s , u s i n g data taken from Moody's Indus t r i a l Manuals. A t e s t of t h i s n ature, to be ve r y a c c u r a t e , r e q u i r e s a very i n t i m a t e knowledge of the o p e r a t i o n s o f the f i r m s under study. U n f o r t u n a t e l y , f i r m s w i l l i n g to p r o v i d e such d e t a i l e d , c o n f i d e n t i a l i n f o r m a t i o n are d i f f i c u l t to f i n d . The problem i s p a r t i c u l a r l y s e r i o u s s i n c e there are 7 as many as f i f t y - s e v e n f i r m s i n the sample. Under the c i r  cumstances, r e s o r t has to be made to p u b l i s h e d d a t a . F o r the purposes of t h i s study, Moody's I n d u s t r i a l Manuals p r o  v i d e the most d e t a i l e d , p u b l i s h e d i n f o r m a t i o n and have t h e r e f o r e been chosen as the source of data . Chapter V p r o v i d e s the summary and c o n c l u s i o n of the study. L i m i t a t i o n s of the Study In t h i s study, i n f o r e c a s t i n g p r o f i t s by the break- 7. A d e t a i l e d e x p l a n a t i o n of the e s t i m a t i o n of the sample s i z e i s g i v e n i n chapter IV. - 10 - even method, no adjustments were made to take into account the e f f e c t s of possible changes i n the determinants of p r o f i t s . This i s due to the f a c t that the necessary data for such adjustments are not a v a i l a b l e . I t i s admitted here that f a i l u r e to make the adjustments w i l l most c e r t a i n l y reduce the accuracy of the forecasts. Again, i n the break-even method of forecasting operating p r o f i t s , t o t a l costs have to be separated into f i x e d costs and variable costs. To achieve t h i s , as des cribed i n chapter IV, the s t a t i s t i c a l approach using the method of l e a s t squares i s used. But, i t has been found i n preliminary studies that t h i s approach i s possible only i f the data f o r the firms show that the firms have experienced losses over some of the periods i n the analysis. This draw- 8 back can be avoided i f the accounting or engineering approach i s used, but since the s t a t i s t i c a l approach i s l i k e l y to give the most r e l i a b l e r e s u l t s i n terms of the data a v a i l a b l e , i t 9 i s preferred to the other two techniques. Hence, the uni verse of firms, from which the sample i s chosen, i s r e s t r i c t e d to only those firms i n Moody's I n d u s t r i a l Manuals, which have had losses at some time i n the periods under study. The data of some firms do not appear i n Moody's I n d u s t r i a l Man uals f o r the period p r i o r to 1951\u2022 These firms have also 8. This i s explained i n chapter I I . 9. The data i n Moody's I n d u s t r i a l Manuals are not i n s u f f i c i e n t d e t a i l to enable the use of either the accounting or engineering methods, with reasonably accurate r e s u l t s . - 11 - been excluded from the universe. D e f i n i t i o n s Break-even analysis t Break-even analysis r e f e r s to the segregation of a l l costs, i n the short-run, between those that are f i x e d and those that are variable and to the cost- volume-revenue r e l a t i o n s h i p s , which determine the amount of p r o f i t s at d i f f e r e n t volume l e v e l s . Break-even point: Break-even point r e f e r s to the volume l e v e l at which t o t a l revenue exactly equals t o t a l cost and neither p r o f i t s nor losses are made. I t may also r e f e r to the : point of time i n the budgetary period when losses turn into p r o f i t s . Short-run; The short-run i s a time period so short that a f i r m cannot vary the quantities of some of the resources that i t uses. In actual f a c t , i t can l e g i t i m a t e l y be said that the short-run i s any time period between that i n which no resources can be varied i n quantity and that i n which a l l resources but one are var i a b l e . This would be a very broad d e f i n i t i o n . Throughout this thesis, a more r e s t r i c t i v e d e f i n i t i o n w i l l be used and the short-run concept w i l l be taken to r e f e r to a time period within which a f i r m cannot a l t e r or add to such items as i t s c a p i t a l equipment, b u i l d  ings, land and top management. These are the firm's short- run 'fixed resources'. The time period, however, w i l l be long enough f o r the f i r m to vary quantities of such resources - 12 - as l a b o u r , raw m a t e r i a l s and the l i k e . These are the f i r m ' s v a r i a b l e r e s o u r c e s . Long-run; The l o n g - r u n i s a p e r i o d of time t h a t i s long enough f o r a f i r m to v a r y q u a n t i t i e s o f a l l the r e s o u r c e s t h a t i t uses. Hence, i n the long-run, no problem e x i s t s as to whether r e s o u r c e s ought to be c l a s s i f i e d as f i x e d or v a r  i a b l e . A l l r e s o u r c e s are v a r i a b l e . F i x e d c o s t s ; F i x e d c o s t s may be d e f i n e d as those c o s t s whose amount i s not a t a l l i n f l u e n c e d by the l e v e l of a c t i v  i t y i n the s h o r t - r u n and w i t h i n the expected range of a c t i v  i t y . Examples of f i x e d c o s t s are such payments as r e n t , the s a l a r i e s o f top management and debenture i n t e r e s t . I n terms of the d e f i n i t i o n of the s h o r t - r u n , g i v e n above, f i x e d c o s t s are the c o s t s of f i x e d r e s o u r c e s . V a r i a b l e c o s t s : V a r i a b l e c o s t s may be d e f i n e d as those c o s t s , whose amount i s a f u n c t i o n of a c t i v i t y , i n c r e a s i n g or decreasing. .t i n the same d i r e c t i o n as i n c r e a s e s o r decreases i n the l e v e l of a c t i v i t y . Examples of v a r i a b l e c o s t s are pay ments f o r 'piece r a t e ' wages, raw m a t e r i a l s , f u e l and power and t r a n s p o r t a t i o n . I n terms of the d e f i n i t i o n of the s h o r t - run, g i v e n above, v a r i a b l e c o s t s are the c o s t s of v a r i a b l e r e s o u r c e s . E x p l i c i t c o s t s : The e x p l i c i t c o s t s o f a f i r m are the ex p l i c i t payments f o r r e s o u r c e s bought o u t r i g h t or h i r e d by the f i r m . Examples of e x p l i c i t c o s t s are the f i r m ' s p a y r o l l , - 13 - payments f o r raw and semi-finished materials and payments f o r overhead costs of a l l kinds. I m p l i c i t costs: The i m p l i c i t costs of a firm are the costs of self-owned, self-employed resources. Examples of i m p l i c i t costs are the returns to labour provided by the owner himself ( i m p l i c i t wages) and the returns to the land and c a p i t a l , which are provided by the owner himself rather than hired from outside owners ( i m p l i c i t rent and i n t e r e s t ) . Margin of safety: Margin of safety refers to the excess of actual (or budgeted) sales over the break-even sales volume. Operating costs: The operating costs of a f i r m are the costs incurred by the f i r m i n conducting i t s regular major a c t i v i t i e s . They include the costs of goods sold, commercial costs, i n t e r e s t and depreciation and amortization. But, they exclude a l l other costs which are not subject to the controls exercised through everyday operating procedures. Hence, income taxes, losses from sales of plants and other property disposals, losses on f o r e i g n exchange and flood, f i r e and other extraordinary losses are excluded. Operating revenue: The operating revenue of a f i r m r e f e r s to the gross revenue or gross sales from the firm's regular major a c t i v i t i e s l e s s returns, allowances and cash discounts. Operating p r o f i t s : The operating p r o f i t s of a f i r m are the - lk - excess of the operating revenue over the operating costs. I f operating costs exceed operating revenue, the excess i s c a l l e d operating losses. Summary In th i s chapter, an attempt has been made to bring out the purpose of t h i s study, i t s l i m i t a t i o n s and i t s organ i s a t i o n . The hypothesis and n u l l hypothesis have also been discussed i n d e t a i l and the d e f i n i t i o n s of some of the more important terms i n t h i s thesis have been given. The nature of break-even analysis i s presented i n the next chapter. CHAPTER II THE NATURE OF BREAK-EVEN ANALYSIS Introduction The term, 'break-even' has become a part of the standard vocabulary of economists, accountants and managers i n general. Each of these three classes of people have contributed i n no small way to the increasing popularity of t h i s subject i n recent years. In f a c t , i t may be said that, today, the best discussions on break-even analysis are to be found i n economics, accounting and management books and journals. But, although a great deal of attention has been given to t h i s subject, there i s s t i l l some vagueness as to what the area involves. To many people, when break-even analysis i s mentioned, the f i r s t thing that comes to mind i s a simple cross-over chart, i n d i c a t i n g t o t a l sales revenue and t o t a l costs, with the cross-over point representing the break-even point. In r e a l i t y , break-even analysis i s more than the mere determination of the volume l e v e l at which revenue equals cost. Rather, i t exposes the e f f e c t on p r o f i t s r e s u l t i n g from the interplay of such factors as p r i c e s , costs, volume and product mix. Use of Break-Even Analysis To date, very l i t t l e has been done to determine - 1 6 - the extent to which f i r m s are u s i n g break-even a n a l y s i s . The study c a r r i e d out f o r the C o n t r o l l e r s h i p Foundation, I n c . i n 1 9 5 8 by two p r o f e s s o r s , Burnard Sord and Glenn Welsch of the U n i v e r s i t y of Texas, i s probably the o n l y p u b l i s h e d study r e l a t i n g to the e x t e n t to which break-even a n a l y s i s 1 i s used. I n t h i s study, p e r s o n a l i n t e r v i e w s were h e l d w i t h 3 5 l e a d i n g companies i n Canada, the D i s t r i c t of Columbia and 1 3 o t h e r s t a t e s i n the U n i t e d S t a t e s . I t was found t h a t f o r t y per cent of the companies d i d not prepare break-even a n a l y s e s , while t h i r t y - s e v e n per cent of the companies p r e  pared break-even a n a l y s e s a t r e g u l a r i n t e r v a l s (Table I ) . The remaining twenty-three per cent of the companies p r e  pared break-even analyses o n l y p e r i o d i c a l l y and as a p a r t of s p e c i a l s t u d i e s . I n the same study, q u e s t i o n n a i r e s were a l s o m a i l e d out to 3 8 9 o t h e r companies, out of which 3,hh responded. As Table I I shows, f i f t y per cent of the 31t-If respondents were making use of break-even a n a l y s e s . The study a l s o t r i e d to determine the frequency of p r e p a r a t i o n of break-even a n a l y s e s and the types o f break-even analyses used. The d e t a i l s are g i v e n i n Tables I and I I . The Development of Break-Even A n a l y s i s The concept of break-even a n a l y s i s was p r o b a b l y 1 . Burnard H. Sord and Glenn A. Welsch, Business  Budgeting. New York: C o n t r o l l e r s h i p Foundation, Inc., 1 9 f 8 7\"pp. 281-281+. - 1 7 - TABLE I Number and Percentages of Companies Interviewed Indicating Various Types and Frequencies of Break-Even Analysis  Preparation of Break-Even Analysis Prepare break-even analysis at regular i n t e r v a l s Prepare break-even analysis p e r i o d i c a l l y as a part of spe c i a l studies Do not prepare break-even analysis No. of Per Cent of Companies V5 Companies 1 3 8 lit 3 7 , 2 3  ho 1 0 0 Frequency of Preparation of Break-Even Analysis Prepare monthly Prepare semi-annually Prepare annually Prepare p e r i o d i c a l l y Per Cent of 2 1 No. of Companies using Companies B-E Analysis 3 1 9 _ 8 2 1 Ih J 1 0 0 Types of Break-Even Analysis Prepare f o r company as a whole Prepare f o r various d i v i s i o n s Prepare f o r plants Prepare f o r product l i n e s Prepare for branches or t e r r i t o r i e s Per Cent of 2 1 No. of Companies using Companies B-E Analysis 1 3 1 1 5 9 3 6 2 5? 2h h? Ih The number of companies does not t o t a l 2 1 and the percentages do not t o t a l 1 0 0 because some companies use more than one type of break-even analysis. Source: Burnard H. Sord and Glenn A. Welsch, Business Budgeting. New York: Controllership Foundation, Inc., 1 9 5 8 , p. 2 8 2 , Table 8 3 . - 1 8 - TABLE II Number and Percentage of Companies Answering Questionnaires Indicating Types and Frequency of Preparation of Break-Even Analysis as Reported by iMk Companies  Use of Break-Even Analysis Companies using break-even analysis Companies not i n d i c a t i n g the use of break-even analysis Frequency of Preparation Prepare monthly Prepare quarterly Prepare semi-annually Prepare annually Prepare as needed No i n d i c a t i o n as to frequency of preparation Types of Break-Even Analysis Prepare f o r company as a whole Prepare f o r various di v i s i o n s Prepare f o r plants Prepare f o r product l i n e s Prepare f o r sales branches No. of Companies 1 7 5 162 \\kk No. of Companies k5 7 1 1 0 6 5 1 kk No. of Companies 1 8 2 lk-7 1 0 6 13jf 2k Per Cent of ikk Companies 51 J\u00A3 1 0 0 Per Cent of 1 7 5 Companies using B-E Analysis 1 3 2 * 3 1 1 5 ..-31 1 0 0 Per Cent of 1 7 5 Companies using B-E Analysis 3 3 1 3 9 7 Less than one per cent. The number of companies does not t o t a l 3lfir- and the percentages do not t o t a l 1 0 0 because some companies use more than one type of break-even analysis. Source: Burnard H. Sord and Glenn A. Welsch, Business Budgeting, New York: Controllership Foundation, Inc., 1 9 5 8 , p. 2 8 2 , Table 8 3 . - 19 - c o n c e i v e d as a r e s u l t o f a t t e m p t s by u n i v e r s i t y t e a c h e r s and businessmen t o d e v e l o p t o o l s t o p r o v i d e a s c i e n t i f i c approach 2 t o b u s i n e s s . v e r y l i t t l e i s known about the e a r l y s t a g e s o f the development o f t h i s t o o l . Some w r i t e r s have t r i e d t o throw some l i g h t on t h i s a r e a but v i e w s t e n d t o c o n f l i c t . The f i r s t a t t e m p t t o s e p a r a t e c o s t s i n t o t h e i r f i x e d and v a r i a b l e components was made i n 1832 and the man who, s u p p o s e d l y , h o l d s t h e d i s t i n c t i o n o f h a v i n g made t h a t 4 a t t e m p t i s a c e r t a i n C h a r l e s Babbage. To the e x t e n t t h a t t h e s e p a r a t i o n o f c o s t s i s the b a s i s o f b reak-even a n a l y s i s , i t may be s a i d t h a t C h a r l e s Babbage made the f i r s t c o n t r i b u  t i o n t o t h e development o f b reak-even a n a l y s i s . But a n y t h i n g c l o s e t o t h e f o r m u l a s o r c h a r t s t h a t a r e used i n b r e a k - e v e n a n a l y s i s t o d a y , was n o t known t i l l 1897 when Henry Hess wrote on \"Time S a v i n g and I t s R e l a t i o n to P r o f i t s \" i n Volume XX (Dec. 16, 1897) o f t h e E n g i n e e r i n g Magazine. I n December, 1903, Henry Hess c o n t r i b u t e d a n o t h e r a r t i c l e , \" M a n u f a c t u r i n g : C a p i t a l , C o s t s , P r o f i t s , and D i v i d e n d s \" , t o t h e E n g i n e e r i n g  Magazine (Volume XXVI) and, i n t h i s a r t i c l e , he i n c l u d e d c h a r t s w h i c h a r e q u i t e s i m i l a r t o t h o s e used i n break-even 2. S o r d and W e l s c h , op. c i t . , p. 281. 3. Ned C h a p i n , \"The Development o f the Break-Even C h a r t : A B i b l i o g r a p h i c a l Note\", J o u r n a l o f B u s i n e s s , V o l . X X V I I I , No. 2, A p r i l 1955, p p . l*t8-14-9. Raymond V i l l e r s , \"Communications - The O r i g i n o f the Break-Even C h a r t \" , J o u r n a l o f B u s i n e s s . V o l . X X V I I I , No. h, O c t . 1955, PP. 290-297. K. V i l l e r s . i b i d . , p. 296. - 20 - analysis today, although he did not designate his presenta- t i o n as break-even charts. During the period just p r i o r to World War I, two other i n d u s t r i a l engineers, Walter Rautenstrauch and C. E. Knoeppel, were prominent i n the development of the break even chart. Rautenstrauch was the f i r s t to use the name, 6 \u2022Break-even charts'. This terminology i s , today, univer^- s a l l y accepted. I t might also be mentioned that i n Rauten strauch' s charts, the functional relationship between costs and volume was brought out, f o r the f i r s t time. Such a r e l a t i o n s h i p was never depicted i n the charts Henry Hess 7 used. The Break-Even Chart The break-even chart i s a portrayal i n graphic form of the r e l a t i o n s h i p of production,, costs and sales to p r o f i t . I t shows the amount of f i x e d and variable costs and the sales revenue at d i f f e r e n t l e v e l s of operation. Various names have been given to t h i s chart. I t i s sometimes known as a crossover chart, a p r o f i t r e a l i s a t i o n chart or a p r o f i t - graph. The break-even chart may be plotted i n several d i f f e r e n t forms, depending on the kind of information desired. 5. Chap i n , op. c i t . . p. 1^ 9. 6. V i l l e r s , l o c . c i t . 7. I b i d . . p. 296-297. - 2 1 - The d e t a i l s of these charts may vary but the underlying p r i n c i p l e s are a l l the same. Some are quite simple, con s i s t i n g of a l i n e or two, while others are quite complex, with many l i n e s and legends. In essence, they a l l i n t e r  r e l a t e sales, variable costs, f i x e d costs and volume l e v e l i n a form considered most h e l p f u l to the user. Since they are a l l b a s i c a l l y the same, they w i l l not be described here i n d i v i d u a l l y . Only the conventional break-even chart and the profit/volume chart w i l l be ex amined, since reference w i l l be made s p e c i f i c a l l y to them i n l a t e r chapters. In the conventional break-even chart (Exhibit I ) , the t o t a l cost l i n e , at the lower extremity, cuts the Y axis at the point where costs are f i x e d and volume (production or sales) i s equal to zero. From t h i s point, i t slopes upwards to the r i g h t . Revenue i s also represented by a l i n e a r l i n e which originates at the zero i n t e r c e p t i o n of the Y and X axes and slopes upwards to the r i g h t ; i t i s often presented as a 45 degree l i n e , with the horiz o n t a l and v e r t i c a l axes having the same scales and on the assumption that production i s equal to sales and s e l l i n g p r i c e i s f i x e d f o r a l l l e v e l s of sales. The point at which the t o t a l revenue l i n e crosses the t o t a l cost l i n e i s the break-even point and, at t h i s l e v e l of production and sales, the fir m allegedly w i l l have neither net p r o f i t nor net l o s s . A somewhat simpler graphic presentation of the * 23 *\u2022 EXHIBIT II A PROFIT/VOLUME CHART T r - \\ o u S a n d s \u00B0f Dollars 25 S a \\ e s V o l u m e - 24 - r e l a t i o n s h i p between p r o f i t s and volume i s the profit/volume chart. I t i s sometimes referred to as a profitgraph, a marginal income chart, or a profit-volume analysis graph. 8 I t i s sa i d to have been developed by C. E. Knoeppel. Although profit/volume charts are generally simpler than break-even charts, they are not always preferred to break even charts because they do not show the relationships between costs, revenue and volume. Nickerson, however, argues that since p r o f i t i s the residue of cost and revenue, profit/volume charts, therefore, r e a l l y r e f l e c t cost- 9 volume-revenue r e l a t i o n s h i p s . The profit/volume chart indicates the path of p r o f i t and consists of two areas, the p r o f i t area and the loss area, both of which are created by the horizontal axis which represents the t o t a l sales volume. The loss area i s composed of the f i x e d costs which i s marked o f f on the v e r t i c a l a x i s . The p r o f i t area indicates the amount of p r o f i t earned as the p r o f i t l i n e passes over the horizon t a l axis. The points of the p r o f i t l i n e are computed by 8. Knoeppel explained the reason f o r i t s development as follows: \"So f a r the f i n a n c i a l statement has been a fi n a n  c i a l t o o l rather than a management t o o l . I t i s a h i s t o r i c a l document and not i n the l e a s t prophetic. I t i s s t a t i c rather than dynamic. I t performs only a part of the function of which i t i s capable. Few accountants have crossed the l i n e between accounting and engineering, while many engineers have jumped the fence between the two\" - C. E. Knoeppel and Edgard C. Seybold, Managing f o r P r o f i t . New York: McGraw- H i l l Book Company, Inc., 1957, PP. 53-54* 9. Clarence B. Nickerson, Co s t Ac counting. Toronto: McGraw-Hill Book Company, Inc., 1954, p. 272. - 25 - subtracting from sales income the t o t a l costs indicated f o r each sales volume.^\u00B0 The break-even point i s the point at which the p r o f i t l i n e intersects the horizontal axis. The Break-Even Point Various d e f i n i t i o n s have been advanced f o r the break-even point. Generally, i t may be said that the \"break even point i s the volume l e v e l at which t o t a l revenue ex a c t l y equals t o t a l cost and neither p r o f i t s nor losses are made. Other d e f i n i t i o n s are merely v a r i a t i o n s . Mathematic a l l y , the break-even point can be determined by using the following equation: Fixed Costs Break-even point _ -j_ Variable Costs Sales To i l l u s t r a t e , the following budget data of a f i c t i t i o u s company, the ABC Company, may be used. 10. The slope of the p r o f i t l i n e i s also equal to the profit-volume (P/V) r a t i o , which i s the rate at which p r o f i t increases with increases i n volume and i s given by the formula: p Variable Costs V \" Sales or or _P Sales - Variable Costs V = Sales J?. Fixed Costs + P r o f i t s V = Sales The profit-volume r a t i o i s sometimes c a l l e d the marginal income r a t i o or variable p r o f i t r a t i o . - 2 6 - Annual P r o f i t Plan - ABC Company Fixed Variable Costs Costs Budgeted Sales $3,000,000. (200,000 units @ $ 1 5 . ) Budgeted Costs: Direct Material $500,000. Direct Labour 550,000. Factory Overhead $^50,000. 200,000. Administration Expenses ^25)000. ' 100,000. D i s t r i b u t i o n Expenses ^25.000. 150.000. $1 ,200,000. $ 1 , 5 0 0 , 0 0 0 . Total 2.700.000. Budgeted P r o f i t $ 300.000. If the above data i s applied to the break-even point equation given e a r l i e r , the r e s u l t w i l l be as follows: $1 .200.000. ft. m n o n Break-even point _ \u00B1 _ $1 , 5 0 0 v000. ^..^i^o^ovo. $3,000,000. = $2,^-000,000. Since the cost of each u n i t i s equal to $ 1 5 , there fore, r&gt; , ^ $2,i+OO,000. Break-even point _ \u2014 - \u2014 , \u2014 $ 1 5 . ' = 160,000 units I t i s claimed that the break-even point i s useful p a r t l y because i t i s a prerequisite to the determination of the margin of safety, which i s the excess of actual or budgeted sales over the break-even sales volume. Expressed as a percentage, i t i s equal to sales above the break-even - 27 - point divided by sales (actual or budgeted) mult i p l i e d by 100. The amount or the percentage indicates to what extent sales revenue may drop before losses begin. I t i s obvious that the higher the margin of safety, the better i s the p o s i t i o n of the firm. I t often pays management to determine the margin of safety at the average volume over a business cycle. A low margin often s p e l l s danger. The low margin may be due to the f a c t that the break-even point i s too high and since high f i x e d costs i s an important cause of high-break-even points, the remedy may be a reduction of the f i x e d costs over the long run. But, Bruce W i l l i s warns that the blame should not be put on f i x e d costs without a c a r e f u l s t u d y . ^ He suggests that i n e f f i c i e n t production, inadequate p r i c i n g and i n e f f e c t i v e s e l l i n g techniques may be the cause of the poor performance. Another usefulness of the break-even point follows from i t s very d e f i n i t i o n . As was stated i n Chapter I, the break-even point may also be defined as the point of time i n the budgetary period when losses turn into p r o f i t s . Hence, the break-even point may be used to indicate the point of time i n the budgetary period when contributions to p r o f i t s begin. I t may also be used to indicate the portion of the budgetary period that remains for the accumulation of the contributions to p r o f i t s . 11. Bruce C. W i l l i s , \"The Use of Break-Even Analysis i n Management,\" Canadian Chartered Accountant. Vo l . 73, Dec. 1958, p. 526. - 28 - A l t h o u g h t h e b r e a k - e v e n p o i n t m a y h a v e s o m e u s e  f u l n e s s , i t s d e t e r m i n a t i o n s h o u l d n o t b e o v e r - e m p h a s i s e d . I t s h o u l d a l w a y s b e r e m e m b e r e d t h a t i t d o e s n o t r e m a i n f i x e d a t a l l t i m e s , f o r a n y p a r t i c u l a r e n t e r p r i s e , b u t v a r i e s f r o m t i m e t o t i m e a s t h e f a c t o r s a f f e c t i n g i t u n d e r g o c h a n g e . H o w a r d S t e t t l e r , a p r o f e s s o r o f B u s i n e s s A d m i n i s t r a t i o n i n t h e U n i v e r s i t y o f K a n s a s s t a t e s t h a t : A l t h o u g h s t a t i s t i c a l c o n f i r m a t i o n i s n o t a v a i l a b l e , t h e r e a p p e a r s t o b e c o n  s i d e r a b l e j u s t i f i c a t i o n f o r c o n c l u d i n g t h a t m o s t p e o p l e w h o a r e f a m i l i a r w i t h b r e a k - e v e n c h a r t s a n d t h e a n a l y s i s o f b r e a k - e v e n i n f o r m a  t i o n a s s u m e t h a t t h e r e a s o n f o r s e e k i n g s u c h i n f o r m a t i o n i s t o d e t e r m i n e t h e b r e a k - e v e n p o i n t f o r a l l o r s o m e s e g m e n t o f a p r o f i t - m a k i n g e n t e r p r i s e . T r u e , b r e a k - e v e n a n a l y  s i s i s c a p a b l e o f l i v i n g u p t o i t s n a m e a n d s h o w i n g t h e v o l u m e l e v e l a t w h i c h e x p e n s e s a n d r e v e n u e s a r e e q u a l , b u t i f , a s c o n  t e n d e d , t h i s i s t h e o n l y u s e g e n e r a l l y m a d e o f s u c h i n f o r m a t i o n , t h e u s e i s n o t o n l y d e f i c i e n t , b u t m a y i n v o l v e a n a c t u a l d i s  s e r v i c e a s w e l l . ^ I t m u s t a l s o b e s t r e s s e d t h a t t h e b r e a k - e v e n p o i n t i s , a t b e s t , o n l y a n a p p r o x i m a t i o n b e c a u s e o f t h e m a n y r e  s t r i c t i v e a s s u m p t i o n s t h a t h a v e t o b e m a d e i n i t s c o m p u t a - 13 t i o n . U n d e r t h e c i r c u m s t a n c e s , e v e n t h e a p p r o p r i a t e n e s s o f t h e t e r m , ' b r e a k - e v e n p o i n t ' i s q u e s t i o n a b l e . T h e w o r d , \u2022 p o i n t ' , c a r r i e s t h e c o n n o t a t i o n o f g r e a t e x a c t n e s s . A b e t t e r t e r m m i g h t b e ' b r e a k - e v e n a r e a ' t o i n d i c a t e t h a t t h e 12. H o w a r d F . S t e t t l e r , \" B r e a k - E v e n A n a l y s i s : I t s U s e s a n d M i s u s e s \" , A c c o u n t i n g R e v i e w , V o l . 37, J u l y 1962, p . 460. 13. T h i s i s d i s c u s s e d i n C h a p t e r 3. - 29 - p r e c i s e l o c a t i o n o f t h e b r e a k - e v e n v o l u m e i s n o t k n o w n a n d c a n b e e s t i m a t e d o n l y r o u g h l y . C o s t B r e a k d o w n F r o m t h e d i s c u s s i o n s o f a r , i t m a y a l r e a d y b e e v i d e n t t h a t c o s t b e h a v i o u r c o n s t i t u t e s t h e c e n t r a l p r o b l e m i n b r e a k - e v e n a n a l y s i s . I f c o s t s c a n n o t b e c l a s s i f i e d a s f i x e d o r v a r i a b l e , n o b r e a k - e v e n c h a r t c a n b e c o n s t r u c t e d . T h i s c a n e a s i l y b e e x p l a i n e d . I f a l l c o s t s a r e v a r i a b l e , t h e r e c a n n o t b e a n y b r e a k - e v e n p o i n t s o l o n g a s t h e t o t a l r e v e n u e a n d t h e t o t a l c o s t s a r e r e p r e s e n t e d b y s t r a i g h t l i n e s , s t a r t i n g f r o m t h e i n t e r s e c t i o n o f t h e X a n d Y a x e s . T h e t w o l i n e s w i l l n e v e r i n t e r s e c t t o p r o v i d e a s i t u a t i o n w h e r e b y l o s s e s t u r n i n t o p r o f i t s o r w h e r e b y p r o f i t s t u r n i n t o l o s s e s . A t t h e s a m e t i m e , a l l c o s t s c a n n o t b e f i x e d b e c a u s e t h i s w o u l d b e a n u n r e a l i s t i c s i t u a t i o n . T h e r e f o r e , t o t a l c o s t s h a v e t o b e s e p a r a t e d i n t o t h e i r f i x e d a n d v a r  i a b l e c o m p o n e n t s . F i x e d c o s t s m a y b e d e f i n e d a s t h o s e c o s t s w h o s e a m o u n t i s n o t a t a l l i n f l u e n c e d b y t h e l e v e l o f a c t i v i t y i n t h e s h o r t - r u n a n d w i t h i n t h e e x p e c t e d r a n g e o f a c t i v i t y . O n t h e o t h e r h a n d , v a r i a b l e c o s t s m a y b e d e f i n e d a s t h o s e c o s t s , w h o s e a m o u n t i s a f u n c t i o n o f a c t i v i t y , i n c r e a s i n g o r d e c r e a s i n g i n t h e s a m e d i r e c t i o n a s a c t i v i t y . T h e c h a n g e i n t h e t o t a l v a r i a b l e c o s t s m a y o r m a y n o t b e p r o p o r t i o n a l t o t h e c h a n g e i n t h e l e v e l o f a c t i v i t y . H o w e v e r , i t i s - 30 - u s u a l l y a s s u m e d i n c o n v e n t i o n a l b r e a k - e v e n a n a l y s i s t h a t s t r a i g h t l i n e r e l a t i o n s h i p s e x i s t a n d , c o n s e q u e n t l y , i t i s n o t u n c o m m o n t o f i n d v a r i a b l e c o s t s b e i n g d e f i n e d a s t h o s e c o s t s w h i c h i n c r e a s e o r d e c r e a s e p r o p o r t i o n a t e l y w i t h i n - l i t c r e a s e s o r d e c r e a s e s i n v o l u m e . T h e a s s u m p t i o n o f l i n e a r i t y i s j u s t i f i e d i f t h e c h a n g e i n o u t p u t i s n o t t o o g r e a t - a s s u m i n g t h a t t h e r e i s n o c h a n g e i n t e c h n o l o g y a n d a d v e r t i s i n g a n d s a l e s p r o m o t i o n a r e a b s e n t . I f o u t p u t c h a n g e s a r e t o o l a r g e , t h e v a r i a b l e c o s t s m a y n o t b e l i n e a r ( c o n s t a n t p e r u n i t ) . T h i s c o u l d b e c a u s e d b y c h a n g i n g p r i c e s o r i n c r e a s i n g o r d i m i n i s h i n g r e t u r n s . T h i s f o l l o w s f r o m t h e f a c t t h a t , w i t h a l a r g e c h a n g e i n t h e d e m a n d f o r f a c t o r s o f p r o d u c t i o n , t h e p r i c e s o f t h e f a c t o r s o f p r o d u c t i o n m a y a l s o c h a n g e a n d t h i s m a y r e s u l t i n a c h a n g e i n t h e v a r i a b l e c o s t s p e r u n i t . F u r t h e r , t h e l e v e l o f e f f i c  i e n c y a t w h i c h v a r i a b l e r e s o u r c e s w o r k , m a y d i f f e r w h e n d i f f e r e n t a m o u n t s o f t h e m a r e u s e d w i t h g i v e n q u a n t i t i e s o f t h e f i x e d r e s o u r c e s . T h e i n c r e a s i n g o r d i m i n i s h i n g r e t u r n s t h a t r e s u l t m a y a l s o c h a n g e t h e a v e r a g e v a r i a b l e c o s t s . T h i s w i l l b e e x p l a i n e d i n g r e a t e r d e t a i l i n c h a p t e r I I I . I n o u r d e f i n i t i o n o f f i x e d c o s t s , r e f e r e n c e w a s m a d e t o t h e 1 s h o r t r u n ' w h i c h m a y b e d e f i n e d a s a p e r i o d o f t i m e w i t h i n w h i c h a f i r m c a n n o t a l t e r o r a d d o n t o i t e m s s u c h a s i t s c a p i t a l e q u i p m e n t a n d b u i l d i n g s . ' I t n o w b e c o m e s c l e a r t h a t t h e c l a s s i f i c a t i o n o f c o s t s i n t o f i x e d a n d v a r i a b l e Ih, P a u l Y a c o b i a n , \" A P r a c t i c a l E v a l u a t i o n o f B r e a k - E v e n A n a l y s i s \" , N . A . A . B u l l e t i n . V o l . kO, S e c . 1 , J a n . 1 9 5 9 , p . 2h. - 31 - categories i s possible only when the time period i s spec i f i e d . I f a s u f f i c i e n t l y long time period i s provided, almost a l l costs become variable through changes i n the scale of the firm's operations. The fixed-variable d i s t i n c t i o n i s gen e r a l l y also based on the assumption that volume w i l l move 15 within a ce r t a i n expected range of a c t i v i t y , because move ments outside t h i s range would be accompanied by changes i n the so-called f i x e d costs. Some writers, however, are not too happy about the c l a s s i f i c a t i o n of costs as f i x e d or variable. In most cases, the various writers are prepared to accept the idea that variable costs vary i n d i r e c t proportion to the rate of a c t i v i t y . I t i s the non-variable costs that have caused disagreement among the writers. In at l e a s t one case, the disagreement i s nothing more than a question of semantics. Gardner i s against the use of the word, 'fixed'. He argues that t h i s word i s psychologically u n f i t to describe costs 1 6 which do not vary with volume but, which vary with'time. He suggests that a better word for such costs would be 'stand- by' costs. 15. This i s the range of a c t i v i t y which management ex pects to handle with the equipment and organisation provided f o r i n the budget. 1 6 . Fred V. Gardner, P r o f i t Management and Control, New York: McGraw-Hill Book Company, Inc., 1955&gt; P\u00AB 2 8 . \" 1 7 . The same costs are also known as period costs or time costs since they are a function of time or capacity costs since they represent the costs of providing the capacity to do business. - 32 - Writing i n the Harvard Business Review i n 1951*, he state s : To me, the term f i x e d cost i s very unsatisfactory, because no cost i s r e a l l y f i x e d ; I prefer to l a b e l expenditures that continue regardlesSpOf production l e v e l as stand-by c o s t s . 1 \" This view seems to be i n l i n e with the advice given by Wally George about t h i r t e e n years e a r l i e r . In 19^1\u00BB George had given the following advice: Regard no costs as f i x e d or sacred. From t h i r t y to f i f t y percent of 'fixed cost' is.,generally subject to management control. 7 Apparently, Gardner i s only quarrelling with the choice of words. What he prefers to c a l l stand-by costs are e s s e n t i a l l y the same costs as those commonly referred to as f i x e d costs. There are, however, more serious disagree ments over the problem of non-variable costs. In one approach, i t has been suggested that the term, 'fixed costs' be replaced by the term, 'constant costs' to be made up of f i x e d costs and regulated costs. In t h i s case, f i x e d costs would r e f e r to costs which are f i x e d and beyond the control of management at a moment i n time (for example, the salary of sales- 18. Fred V. Gardner, \"Break-Even Point Control f o r Higher P r o f i t s \" , Harvard Business Review, Vol. XXXII, Sept.-Oct. 1 9 5 S P. l^ +T \"~\" 19. Wally E. George, \"How to Control Your Break-Even Point\", Factory Management and Maintenance. Oct. 19U-1, p. 87. 20. \"How to T e l l Where You Break-Even\", Fortune, February 19^ 9, P. 83. - 33 - men), w h i l e r e g u l a t e d c o s t s would r e f e r to cos ts w h i c h , though f i x e d , are n e v e r t h e l e s s s u b j e c t to the d i s c r e t i o n of manage ment ( f o r example, the bonus g i v e n to sa lesmen) . This k i n d of approach seems to agree w i t h the a d v i c e g i v e n by W a l l y George i n 1941. As of t o d a y , a g r e a t d e a l has a l r e a d y been w r i t t e n i n textbooks and j o u r n a l s about the i n a p p r o p r i a t e n e s s of the t e r m , ' f i x e d c o s t s ' . I n the years to come, there i s no doubt t h a t even more w i l l be w r i t t e n about i t . A d m i t t e d l y , i t i s not the i d e a l term to d e s c r i b e the k i n d of c o s t s to which i t r e f e r s . B u t , i t s c r i t i c s s h o u l d r e a l i s e t h a t i t , n o n e t h e l e s s , i s perhaps a b e t t e r term than any t h a t they can sugges t , to the ex tent t h a t i t has the advantage of w i d e l y e s t a b l i s h e d usage . I n the p a s t , many people were d i s s a t i s f i e d w i t h the c l a s s i f i c a t i o n of c o s t s i n t o f i x e d and v a r i a b l e . Today, many people are s t i l l d i s s a t i s f i e d w i t h t h i s c l a s s  i f i c a t i o n . I n the years to come, more people may j o i n the ranks of t h i s d i s s a t i s f i e d group. I t i s t r u e t h a t the c l a s s i f i c a t i o n of c o s t behaviour i n t h i s way i s f a r f rom be ing p e r f e c t ; b u t , i t i s a l s o t rue t h a t f o r y e a r s , c o s t s have been c l a s s i f i e d i n a s i m i l a r way f o r budget ing p u r  poses and a l t h o u g h the techniques used i n the s e p a r a t i o n were s imple ones , the u l t i m a t e r e s u l t s have been q u i t e s a t i s f a c t o r y . 2 ^ - There i s no doubt t h a t the a larm r a i s e d 2 1 . W i l l i a m J . V a t t e r , \"Account ing Measurements of I n  crementa l C o s t \" , J o u r n a l of B u s i n e s s , V o l . X V I I I , No. 1 , J a n . 1945, p p . 147-148. - 3^  - i s not a f a l s e one. But, the i n t e n s i t y of the excitement i s perhaps greater than i s warranted by the nature of the problem. In break-even analysis, i t i s assumed that i t i s reasonable to c l a s s i f y costs as f i x e d or v a r i a b l e . This brings us to the problem of semi-variable costs. Such costs vary with volume though not i n d i r e c t proportion to i t . They possess the c h a r a c t e r i s t i c s of both f i x e d and variable costs and are sometimes c a l l e d fixed-variable costs or semi fi x e d costs. Examples include items such as supervision, power and maintenance costs. In break-even analysis, one i s faced with the problem of separating these costs into t h e i r f i x e d and v ariable components. One way out of this problem i s to measure the v a r i a b i l i t y of these costs. Generally, there are three approaches to the measurement of cost v a r i a b i l i t y . They are: (a) The Accounting Approach - Inspection of accounts. (b) The S t a t i s t i c a l Approach- S t a t i s t i c a l analysis of h i s t o r i c a l costs. (c) The Engineering Approach- I n d u s t r i a l engineering studies. The accounting approach i s , by f a r , the simplest of the three. I t also requires the l e a s t time. By t h i s 22. J o e l Dean,\"Methods and P o t e n t i a l i t i e s of Break- Even Analysis\" i n David Solomons (ed*&gt;, Studies i n Costing. London: Sweet &amp; Maxwell, Ltd., 1952, pp. 232-233. - 3 5 - method, a c a r e f u l study has f i r s t to be made of the chart of accounts. On the basis of this study, costs which are either f i x e d or wholly variable, are then picked out, leav ing behind the so-called semi-variable costs. The s t a t i s  t i c a l technique and/or the engineering technique may then be applied to the semi-variable costs to separate t h e i r f i x e d and variable components. I t i s obvious that the accounting approach requires a thorough knowledge of the behaviour of the costs i n each of the accounts. Unless a f a i r l y complete knowledge of the operations and a c t i v i  t i e s of the enterprise i s obtained beforehand, the r e s u l t s arrived at, by using t h i s method, may be misleading. In any case, the very f a c t , that this approach requires the exercise of judgement, means that i t i s f a r from being an i n f a l l i b l e one. The s t a t i s t i c a l approach, involving the s t a t i s  t i c a l analysis of h i s t o r i c a l costs i s probably more thor ough and s c i e n t i f i c than the accounting method. But, unless computers are used, i t can also be more time consum ing and expensive. I t can be c a r r i e d out by using s t a t i s  t i c a l c o r r e l a t i o n techniques which r e l a t e each cost component to some measure of a c t i v i t y . The best example of t h i s approach i s the scatter chart technique under which the h i s t o r i c a l cost and volume (production or sales d o l l a r s as a measure of a c t i v i t y ) during each of several past months or years are plotted on a chart with volume as the horizon-- 36 - t a l axis and costs as the v e r t i c a l axis. Depending on the pattern formed by the grouping of the points plotted, a l i n e may then be f i t t e d through the points, either by the simple and p r a c t i c a l method of inspection or by the more s c i e n t i f i c method of l e a s t squares, to i l l u s t r a t e the usual behaviour 23 of the costs at various volumes (Exhibit I I I ) . The point (above the i n t e r s e c t i o n of the horizontal and v e r t i c a l axes), at which this l i n e cuts the v e r t i c a l axis, represents the f i x e d costs i . e . those costs not affected by any changes i n volume. A horizontal l i n e may then be drawn through this point to r e f l e c t the f i x e d costs. Another s t a t i s t i c a l technique i s the high-low points method. In t h i s method, the periods with the highest and lowest volumes are f i r s t selected. Then, the d i f f e r  ences i n the volumes of the two periods are related to the differences i n the costs of the two periods, to give the cost v a r i a b i l i t y pattern. This method i s almost as simple as the method of inspection, but i t i s very seldom used because i t i s extremely vulnerable to random variations i n costs. Unusually high or low cost figures may d i s t o r t the whole picture since only the extremes are considered i n t h i s method. 23. This i s explained i n greater d e t a i l i n chapter IV, which describes a study of 57 firms i n Worth America to determine the extent to which break-even analysis i s useful as a t o o l f o r forecasting operating p r o f i t s . In t h i s study, the s t a t i s t i c a l approach i s used to separate the costs and the l e a s t squares method i s used to f i t the l i n e through the points i n the scatter charts. - 37 * EXHIBIT III A SCATTER CHART T h o u s a n d s o f Dollars loot- So 0 4.0 - - Fixed Cost Lir-&gt;e ! t F(*edl C o s t s 1 &gt; 1 1 io 4-0 \u20AC&gt;o S O V o l u m e ( ^ QWS \u2014 \\r-\\ l l n o u \" s a \u00BB n c l s t &gt; o \\ \\ c \u00BB r s ) loo - 38 - The main d i f f i c u l t y with the s t a t i s t i c a l approach i s that h i s t o r i c a l cost data often show poor c o r r e l a t i o n with volume. This i s so mainly because costs often vary not s o l e l y because of volume but also because of many other f a c t o r s . These factors include changes i n plant, equipment, materials used, methods of manufacturing, personnel, work ing hours, factor p r i c e s and managerial p o l i c y . In study ing cost behaviour f o r purposes of break-even analysis, i t i s necessary to assume that these non-volume fac t o r s , which a f f e c t costs, w i l l remain constant. The engineering approach i s the only f e a s i b l e method, when h i s t o r i c a l data are unavailable or too un r e l i a b l e but I t can also be used f o r supplementing s t a t i s  t i c a l or accounting analysis when i t i s desired to project cost behaviour beyond the range of past output experience or when i t i s necessary to estimate the e f f e c t of major changes i n technology or plant size upon cost behaviour over a f a m i l i a r or unfamiliar output range. In essence, th i s method attempts to determine the physical inputs nec essary to achieve c e r t a i n levels of output and then con vert these to d o l l a r s at current or anticipated p r i c e s . The s u p e r i o r i t y of t h i s method l i e s i n the f a c t that i t attempts to work with r e l a t i o n s h i p s between various physical inputs and the volume of a c t i v i t y rather than with observed h i s t o r  i c a l patterns, which may be di s t o r t e d by cert a i n non-volume f a c t o r s . However, l i k e the s t a t i s t i c a l approach, i t also - 39 - can involve very high expenses. In addition, i t suffers from the drawback that the p r a c t i c a l f e a s i b i l i t y of i t s estimates cannot be pretested. These three approaches to the measurement of cost v a r i a b i l i t y are not necessarily mutually exclusive. In f a c t , i t i s often a good practice to use them to supplement each other. Summary Break-even analysis does not merely involve the determination of the break-even point. I t also shows the e f f e c t on p r o f i t s r e s u l t i n g from the inter p l a y of such fac tors as p r i c e s , costs and volume. Although there i s very l i t t l e agreement among writers regarding the development of break-even analysis, i t may generally be said that Charles Babbage, Henry Hess, Walter Rautenstrauch and C. E. Knoeppel were the pioneers. Henry Hess was responsible f o r the basic idea of the break-even chart but i t s u n i v e r s a l l y accepted terminology has been credited to Professor Rautenstrauch. The break-even chart Is b a s i c a l l y a portrayal i n graphic form of the relationship of production, cost and sales to p r o f i t , though i t may be pl o t t e d i n several d i f f e r  ent ways. In t h i s chapter, only the conventional break- even chart and the profit/volume chart have been presented. 2^. Dean, op. c i t . . p. 231. - ho - In the discussions on break-even charts, i n l a t e r chapters, reference w i l l be made mainly to these two charts. In any break-even chart, there must be a break even point, which may be defined as the volume l e v e l or point of time i n the budgetary period when losses turn into p r o f i t s . The break-even point Is useful because i t i s a prerequisite to the determination of the margin of safety, which i s a useful reference device f o r action. It i s also useful because i t indicates the point of time i n the bud getary period when contributions to p r o f i t s begin. However, i t must be r e a l i s e d that the break-even point i s not as exact as i t s name implies and that i t does not remain f i x e d at a l l times. Therefore, i t s usefulness should not be over emphasised. One of the most important steps i n break-even analysis i s the c l a s s i f i c a t i o n of costs as f i x e d or variable. Three approaches may generally be used. They are the account ing, s t a t i s t i c a l and engineering approaches. Of these three, the s t a t i s t i c a l method i s l i k e l y to give the most r e l i a b l e r e s u l t s i n terms of the data available and w i l l be used i n the t e s t , which w i l l be described i n chapter IV. From the fa c t s that are presented on break-even analysis i n this chapter, a c r i t i c a l evaluation of break-even analysis i s made i n the next chapter. CHAPTER III A CRITICAL EVALUATION OF BREAK-EVEN ANALYSIS Introduction In chapter I I , the nature of break-even analysis was given and some of the methods of separating the t o t a l costs of firms were presented. In th i s chapter, a c r i t i c a l evaluation of break-even analysis i s attempted i n terms of the economic theory of the f i r m i n the short and long run and under perfect and imperfect competitive conditions. The assumptions which are used i n break-even analysis and the uses to which break-even analysis may be put are also d i s  cussed. S t a t i c Analysis The r e l i a b i l i t y of break-even analysis i s dependent upon reasonably accurate portrayals of cost behaviour, which are affected by the inte r p l a y of a number of fa c t o r s . These f a c t o r s , as was discussed i n chapter I I , are constantly chang ing as management seeks to improve p r o f i t s . Break-even analysis attempts to arrest the motion of these dynamic forces by assuming that a l l of them, except volume, w i l l remain con stant during the period i n which the analysis w i l l be used. Hence, break-even analysis assumes a s t a t i c analysis, being a p i c t u r e of relationships which p r e v a i l only under one set of assumptions. - 42 - Since s t a t i c assumptions underlie the construction of break-even charts, c e r t a i n cautions have to be observed i n the use of these charts. To begin with, the positions of the l i n e s on the charts are r e l i a b l e only within the range of normal volume fluctuations i . e . , the relevant range which was 1 the basis f o r drawing the charts. Thus, i t would be more r e a l i s t i c i f the l i n e s on break-even charts were not extended back to the o r i g i n but instead were drawn as i l l u s t r a t e d i n Exhibit IV. The revenue-cost relationships may be v a l i d within the relevant range of volume but the same relationships are u n l i k e l y to p e r s i s t i f volume f a l l s outside the l i m i t s of the relevant range. An extreme reduction of volume may cause management to reduce many f i x e d costs. For example, executive s a l a r i e s may be reduced or excess plant and equipment may be sold to reduce depreciation, insurance and property taxes. By such actions, the break-even point i s lowered. A large increase i n volume has the opposite e f f e c t because costs which are f i x e d within the normal range of volume w i l l be increased. As examples, additional supervisors and clerks are often added and more machinery and equipment might be bought. 1. I t i s true that even within t h i s range, the effects of the dynamic forces may be f e l t , but as w i l l be pointed out l a t e r i n the chapter, research studies have shown that, within t h i s range, t o t a l v a r i a ble costs increase at a constant rate and prices are u n l i k e l y to change since firms tend to f e e l that t h e i r customers prefer stable p r i c e s . - h3 - EXHIBIT IV MODIFIED CONVENTIONAL BREAK-EVEN CHART loor- 8 0 y&gt; \u00AB 0 0 u 0 S O r C 0 0 U n IT &gt; J fl; 0 2 \"4 Total Rev/enUe Total Costs 2oh Relevfcint\" Range 2 0 4 0 S O 80 Volumne ( \" T h o u s a n d s of D o l o r s ) l o o - \u00A5* - A Short-Run Concept The s t a t i c s i t u a t i o n that break-even analysis assumes cannot e x i s t f o r long periods of time because the longer the period covered i n the projection, the l e s s r e l i a b l e i s the forecast of revenue and costs. In the short-run, i t may be true that there exists a unique functional relationship between the p r o f i t s of a f i r m and i t s volume and that, given the volume, the corresponding l e v e l of p r o f i t could be deter mined. But, t h i s Is progressively l e s s true as the time period increases because, r e a l i s t i c a l l y , p r o f i t i s dependent on a great many other f a c t o r s , apart from volume and, i n the long-run, dynamic forces continually work to s h i f t and modify these other factors as well as volume. I t , therefore, becomes clear that break-even analysis i s e s s e n t i a l l y a short-run con cept and i s more useful i n short-run, as opposed to long-run, f i n a n c i a l planning. In f a c t , i f a long-run concept i s attached to break-even analysis, i t s usefulness immediately becomes dubious. Professor Neuner states that: Break-even analysis and charts must be kept current and not attempt to r e f l e c t probable operating circumstances over a period longer than a year because not only the mixture of variable cost and income elements may change but also f i x e d costs gradually s h i f t over extended periods of time. d Linear and Curvi-Linear Charts There i s an i n t e r e s t i n g and perhaps deceptive resem- 2. John J . \u00A5. Neuner, Cost Accounting. Homewood, I l l i n o i s : Richard D. Irwin Company, 1957, p . 790. - K5 - blance between the l i n e a r and c u r v i - l i n e a r break-even charts. The basis f o r the construction of the l a t t e r stems from the cost-volume and revenue-volume functions of the economic theory of the firm, as i l l u s t r a t e d i n Exhibit \"V. Presented i n th i s form, the c u r v i - l i n e a r chart c l o s e l y resembles the l i n e a r chart, as described i n chapter I I , except f o r the nature of i t s t o t a l cost and t o t a l revenue functions. This w i l l be discussed i n d e t a i l l a t e r . Meanwhile, i t must be pointed out that where as the l i n e a r chart has only one break-even point, the c u r v i  l i n e a r chart reveals two break-even points, i . e . , two l e v e l s of output at which the firm's revenue just covers i t s costs so that net p r o f i t i s zero. These are the points B-^  and B 2 (Exhibit \u00A5 ) . Point B-^  i s analogous to the break-even point i n the l i n e a r chart and point B^ i s the l o g i c a l r e s u l t of the cu r v i - l i n e a r nature of the t o t a l cost and t o t a l revenue func tions. Another basic difference between the two analyses i s i n the point of maximum p r o f i t s . P r o f i t s may be defined as the excess of t o t a l revenue over t o t a l costs. I t i s clea r , therefore, that the large s t p r o f i t s , which a fir m could make, w i l l be earned when the v e r t i c a l distance between the t o t a l cost and the t o t a l revenue curves i s at i t s greatest. This i s indicated by MP at volume K, i n Exhibit 7. The l i n e a r break-even chart, on the other hand, shows p r o f i t maximised at f u l l capacity. This tends to give the impression that the c u r v i - l i n e a r analysis has a s l i g h t advantage over the EXHIBIT V CURVI-LINEAR BREAK-EVEN CHART l i n e a r analysis, since i t s p e c i f i e s the p r o f i t maximisation conditions. In other words, the c u r v i - l i n e a r approach appears to specify the p o s i t i o n within the p r o f i t area at which the f i r m should endeavour to operate. Linear break-even analysis, merely suggests that the business should operate above the break-even point and i t implies, what i s l o g i c a l l y untenable, that the p r o f i t area within the range of normal volume f l u c  tuations w i l l keep on widening as production volume expands. Di f f e r e n t concepts of p r o f i t s underlie the construc t i o n of the l i n e a r and c u r v i - l i n e a r charts. In the l a t t e r a d i s t i n c t i o n i s made between i m p l i c i t costs and e x p l i c i t costs and p r o f i t s are defined as the surplus or excess of t o t a l revenue over both types of costs. E x p l i c i t costs take the form of e x p l i c i t payments fo r resources bought outright or hired by the firm. The firm's p a y r o l l , payments f o r raw and semi-finished materials, payments of overhead costs of various kinds and payments into sinking funds and depreciation charges are examples of e x p l i c i t costs. They are the costs which accountants l i s t as expenses. Imp l i c i t costs, on the other hand, are those costs of self-owned, self-employed resources. The salary of a single proprietor, who sets aside no salary f o r himself but who takes the firm's p r o f i t s as payment f o r his services i s an excellent example. In accordance with the opportunity cost doctrine, the cost of the single proprietor's services i n producing his product i s the foregone al t e r n a t i v e product, which would have been produced, had he worked f o r - 43 - someone else i n .a s i m i l a r capacity. To the economist, a salary for the proprietor equal to the value of his services i n his next best a l t e r n a t i v e employment may be considered as a part of the firm's costs. I t i s an i m p l i c i t cost. In l i n e a r charts, however, i m p l i c i t cost i s i g  nored and a firm's t o t a l costs are considered to include only the e x p l i c i t obligations to resource owners. Under the circumstances, a firm's net income becomes the remainder of gross revenue aft e r operating and f i n a n c i a l expenses have been deducted. No consideration Is given to i m p l i c i t costs such as i n t e r e s t and dividend payments equal to what investors could earn had they invested elsewhere i n the economy. Separation of Costs In chapter I I , i t was stated that i n break-even analysis, i t i s necessary to separate t o t a l costs i n t o f i x e d costs and variable costs. Unless such a c l a s s i f i c a t i o n i s made, i t i s impossible to construct a break-even chart. But, i f as defined e a r l i e r , f i x e d costs equal those costs which remain f i x e d , i r r e s p e c t i v e of volume and variable costs equal those costs which vary i n d i r e c t proportion to volume, and i f costs can only be c l a s s i f i e d as f i x e d or var i a b l e , then there are bound to be some costs which are beyond c l a s s i f i  cation. Sidney Robbins states that, \"many costs and the components of these costs do not f a l l i nto neat black or white, f i x e d or variable categories, but are rather grey-. 1,9 - hued, partaking of the c h a r a c t e r i s t i c s of both types....\" J Some of these costs, popularly known as semi-variable costs, include costs f o r such items as supervision labour, power, maintenance, and accounting services. In break-even analysis, as indicated i n chapter I I , these costs are usually broken down into t h e i r f i x e d and variable components by either the accounting, s t a t i s t i c a l or engineering methods. None of these methods can produce com p l e t e l y accurate r e s u l t s but there i s also no reason to sus- h pect t h e i r a b i l i t y to produce s a t i s f a c t o r y r e s u l t s . Under the circumstances, the assumption made i n break-even analysis that a l l costs can be reasonably separated into t h e i r f i x e d and variable components should not provide any cause f o r alarm. What i s important i s recognition of the f a c t that i r r e s p e c t i v e of the method used i n the d i v i s i o n of the costs, the r e s u l t w i l l not be completely accurate and the more i n  accurate the d i v i s i o n of the costs, the more inaccurate w i l l the r e s u l t s of the break-even analysis be. Constant S e l l i n g Prices The presentation of t o t a l cost and t o t a l revenue 3. Sidney M. Robbins, \"Emphasizing the Marginal Factor i n Break-Even Analysis\", N.A.A. B u l l e t i n , V o l . V3, Oct. I96I, P. 59. William J . Vatter, \"Accounting Measurements of Incre mental Cost\", Journal of Business. Vol. XVIII, No. 1, Jan. 19^ 5, PP. 1H7-IWI - 50 - functions as straight l i n e s has often been questioned. The l i n e a r i t y of the t o t a l revenue curve implies a constant s e l l i n g p r i c e over the entire range of output. This i s not unusual i f conditions of pure competition are assumed. In a pure market, a l l competitors s e l l an i n s i g n i f i c a n t pro portion of the t o t a l output of a homogenous product and no single s e l l e r can, by his own e f f o r t s , influence p r i c e . Every s e l l e r must accept the same market p r i c e , determined as i t i s by the o v e r a l l i n t e r a c t i o n of supply and demand i n the market. In addition, every s e l l e r can s e l l a l l his out put at the market p r i c e . Unfortunately, such conditions of pure competition are rare or impossible to achieve i n the r e a l world. This, therefore, tends to suggest that the presentation of the t o t a l revenue function as a str a i g h t l i n e i s not v a l i d . Under any other market condition, other than pure competition, a fi r m can increase i t s sales volume only by lowering i t s s e l l i n g p r i c e , when a l l other determinants of demand - consumer incomes, consumer tastes and preferences, number of consumers and range of goods available to con sumers - remain unchanged and i f advertising and sales pro motion are assumed to be absent. In other words, the demand curve slopes downward to the r i g h t when the s e l l e r has any degree of monopolistic control over p r i c e , implying that for each possible s e l l i n g p r i c e , there i s a corresponding sales volume. Under such circumstances, the t o t a l revenue function - 51 - takes a c u r v i - l i n e a r form, as shown i n E x h i b i t V. Since i n almost a l l cases, producers f a c e c o n d i t i o n s of i m p e r f e c t o r m o n o p o l i s t i c c o m p e t i t i o n , one t h e r e f o r e tends to f i n d more ac c e p t a b l e the p r e s e n t a t i o n of the t o t a l revenue f u n c t i o n as c u r v i - l i n e a r r a t h e r than l i n e a r . However, i t must not be f o r g o t t e n t h a t over the range of s a l e s volume w i t h which most producers are f a m i l i a r , an unchanged p r i c e can be charged and hence i t i s p o s s i b l e to have a s t r a i g h t l i n e t o t a l revenue f u n c t i o n . By 'unchanged p r i c e ' , i t i s not i m p l i e d here t h a t t h i s i s the p r i c e which the market w i l l bear or that t h i s i s the p r i c e which can be h e l d i n d e f i n i t e l y i n a s s o c i a t i o n w i t h s a l e s volume i n c r e a s e s . Assuming t h a t non-price inducements are absent, once s a l e s volume has i n c r e a s e d beyond the l e v e l a t which the s e l l i n g p r i c e i s j u s t r i g h t to enable the producer to c l e a r a l l h i s output w i t h the giv e n market demand, any f u r t h e r i n c r e a s e i n output must n e c e s s a r i l y be s o l d a t a lower p r i c e . I t i s o n l y when the p r i c e charged, w i t h i n the normal s a l e s volume range, i s below the demand curve f a c e d by the producer t h a t i t i s p o s s i b l e to have an unchanged p r i c e . But, sooner or l a t e r , the demand curve i s bound to make i t s i n f l u e n c e f e l t . This can be i l l u s t r a t e d . In E x h i b i t VI, p r i c e I s measured along the v e r t i c a l a x i s and s a l e s volume along the h o r i z o n t a l a x i s . I f OP i s the p r i c e and DD the demand curve and i f the f i r m i s o n l y concerned w i t h the range of s a l e s volume MN, then the p r i c e OP can be charged throughout t h a t range. So - 52 - EXHIBIT VI THE LIMITS OF CONSTANT PRICES O H Nl Q 5&lt;a|es Voluw - \\e - 53 - long as the demand does not change, the fi r m can charge a constant p r i c e , OP and s e l l any output up to the l e v e l OQ. Obviously, f o r quantities less than OQ, the firm could have charged a higher p r i c e and s t i l l s e l l the whole of i t s out put. For example, f o r quantity OM, the f i r m could have charged OP-^ . But, i t i s not unusual to f i n d a f i r m f i x i n g i t s p r i c e at OP even though i t i s w i l l i n g to s e l l only OM quantities, with the given demand curve DD. This i s so because firms tend to f e e l that t h e i r customers prefer stable prices and hence once pr i c e i s set and shown to be p r o f i t  able, i t i s l i k e l y to be retained u n t i l some major change 5 i n conditions causes an inroad into the desired p r o f i t goal. Since PP and DD, i n Exhibit VI, have to Intersect somewhere, i t therefore follows that the t o t a l revenue curve cannot con tinue i n d e f i n i t e l y as a straight l i n e but, sooner or l a t e r , must f a l l quite steeply. Beyond the sales volume OQ, the pric e l i n e PP i s above the demand l i n e DD and any desired increase i n sales must therefore necessarily be preceded by a reduction i n p r i c e s . From the above i t may l o g i c a l l y be concluded that, i n the vast majority of non-agricultural, i n d u s t r i a l enterprise situations, which are characterised by conditions of imperfect or monopolistic competition, the l i n e a r break-even chart i s incorrect on the revenue side, except f o r small range of sales volume over which i t i s 5. Robert F. L a n z i l l o t t i , \"Pricing Objectives i n Large Companies\", American Economic Review, VOL. XLVIII, No. 5\u00BB Dec. 1958, p. 937. - 5k - possible to have an unchanged p r i c e . Total Cost and Constant Unit Variable Costs The l i n e a r break-even chart also carries the assumption that cost-volume relationships are usually char acterised by straight l i n e s and since the f i x e d cost com ponent i s always taken as given, i t therefore follows that i t i s the shape of the variable cost function that determines the shape of the t o t a l cost function. I f thi s i s the case, then to draw a l i n e a r t o t a l cost function from zero to 100 percent of productive capacity i s to suggest that variable cost per unit i s constant f o r a l l volumes of a c t i v i t y up to f u l l capacity and that marginal cost i s also constant and equal to variable cost per un i t , as i l l u s t r a t e d i n Exhibit VII. A l i n e a r t o t a l cost function also suggests, as the same Ex h i b i t shows, that t o t a l cost per unit declines con tinuously over the entire volume range up to f u l l capacity and i s always higher than variable costs per unit or marginal costs. Diseconomies of scale are supposedly non-existent. This disturbs economists because i t c o n f l i c t s with the economic theory of the firm. Economists have generally drawn the t o t a l cost function as a curve which r i s e s f i r s t at a declining rate and then at an accelerating rate, as i l l u s  trated i n Exhibit VIII. They believe that, as the volume of output of a f i r m increases from zero l e v e l to 'optimum1 - 55 - E X H I B I T V I I C O N S T A N T A V E R A G E V A R I A B L E C O S T 7o 5oh x-&gt; 0 4o| u 3oh 2 o h loh o r M^r-&lt;^\\v-\\o\\ CosV AsVer-cacje Var\\ot&gt;\\e Cost 2 0 30 AO S O G O Vol ( O u t p u t ) Sol- E X H I B I T V I I I ECONOMISTS' COST CURVES 7\u00B0h - 57 - volume l e v e l , u n i t variable costs w i l l most l i k e l y f a l l s l i g h t l y (assuming that factor prices remain constant), since the variable factors w i l l produce somewhat more e f f i c i e n t l y near the firm's 'optimum' volume l e v e l than at very low volume l e v e l s . The increased e f f i c i e n c y may be due to increased s p e c i a l i s a t i o n . But, as the f i r m approaches i t s 'optimum' volume l e v e l , economists argue that a further increase i n the volume of output w i l l most c e r t a i n l y increase u n i t var iable costs quite sharply. Economists point out that an increased volume of output can only come from the use of more of the variable factors of production or from obtaining harder work or greater output from the e x i s t i n g ones. The f a c t that more of the variable f a c t o r s have to be used to a f i x e d amount of the f i x e d f a c t o r s , w i l l lead to overcrowding and bad organisation. Moreover, the f a c t that existing factors have to be used more i n t e n s i v e l y w i l l mean that workers tend to suffer from overstrain and that machines tend to break down more frequently. Hence, economists envisage unit variable cost curves as f a l l i n g s l i g h t l y from zero volume to a volume l e v e l j u s t short of the 'optimum' volume l e v e l and r i s i n g sharply from there onwards, as i l l u s t r a t e d i n E xhibit IX. Unit variable cost curves, according to economists, are un l i k e l y to remain constant.7 6. The 'optimum' volume l e v e l i s the volume l e v e l at which a l l the factors of production used by the f i r m are being employed i n the 'right' or 'optimum' proportions with each other. At this volume l e v e l , the average cost of the f i r m i s therefore at a minimum. 7. I t may be added that sales promotion e f f o r t s may also work to destroy the l i n e a r i t y of cost curves. - 59 - Meticulous s t a t i s t i c a l i n v e s t i g a t i o n by J o e l Dean, R. A. Lester, R. H. Whitman and others, however, do not seem 8 to support the arguments of the economists. In an a r t i c l e i n an N.A.C.A. b u l l e t i n , John Kempster mentioned that: In the economic research which has been done on cost, one of the important points which has been at stake i s the question of whether unit variable costs f a l l and then r i s e with expanding output or are constant i n t h e i r v a r i a b i l i t y . Putting i t another way, t h i s i s the same question as whether t o t a l variable costs would be expressed as a curve or a straight l i n e i n diagrammatic presentations. Some what contrary to theory, the research investigations of economists have concluded, i n general, that unit variables are con stant throughout the relevant ranges of volume, that i s , t o t a l variable costs i n  crease at a constant r a t e . \" Summarising from the above discussion, i t may be said that since f i x e d costs remain f i x e d at a l l volumes, i t i s the variable cost function that determines the shape of the t o t a l cost function. In the l i n e a r break-even analysis, the t o t a l cost function i s drawn as a straight l i n e , giving the impression that u n i t variable costs remain constant at a l l volumes. This i s contradictory to the economic theory of the f i r m . In economic analysis, u n i t variable costs are described as having a 'TJ ' shape. The research investigations of some economists, however, support the impression of constant 8 . J . Johnston, S t a t i s t i c a l Cost Analysis, New York: McGraw-Hill Book Company, Inc., I960 , pp. I 36 - I68 . 9. John H. Kempster, \"Break-Even Analysis - Common Ground f o r the Economist and the Cost Accountant\", N.A.C.A, B u l l e t i n . Feb. 15, 1949, p. 712. - 60 - u n i t variable costs given i n l i n e a r break-even analysis, f o r relevant ranges of volume. Production Equals Sales So f a r , various assumptions i n break-even analysis, r e l a t i n g to the t o t a l cost and revenue functions, have been made. To t h i s l i s t , may be added the further assumption that sales and production are synchronised and there i s no s i g  n i f i c a n t amount of production for inventory or no substantial amount of sales from inventory. A l l f i x e d costs incurred by the f i r m are, therefore, considered as period costs and charged against the revenue r e a l i s e d i n the same period. This assumption i s obviously not e n t i r e l y true. At times, firms produce more than what they can s e l l , as a r e s u l t of which inventories are b u i l t up and, at other times, they may produce less than what they can s e l l and consequently, inventories are depleted. In f a c t , i n practice, firms s e l  dom f i n d that t h e i r sales exactly equal t h e i r production. In many periods, however, firms may f i n d that the difference between sales and production i s not very s i g n i f i c a n t and t h i s i s the p o s i t i o n that i s generally taken i n discussions on break-even analysis. One writer stated that: Inventories, though, are usually very small i n comparison to t o t a l pro duction and, f o r p r a c t i c a l purposes, are ignored i n comparing sales at various l e v e l s of production....The l e a s t probable error, then, i s obtained by disregarding the inventory problem i n determining sales - 6 1 - at any volume and to consider a l l produc t i o n immediately s a l e a b l e . 1 U Glenn A. Welsch i s of the opinion that \"produc t i v i t y and inventory change are frequently of l i t t l e con sequence within any one period\" but added that \" i n case of lack of synchronization between production and sales, i t i s important that adjustment be made for the increase or decrease i n i n v e n t o r y \" . 1 1 However, t h i s tends to weaken the usefulness of break-even analysis. As G. R. Crowning- sh i e l d puts i t : The adjustments that are required i n the break-even analysis, when sales and produc t i o n volumes do not coincide, take away one of the p r i n c i p a l merits of the break-even analysis, i t s s i m p l i c i t y . If synchroniz ati o n within reasonable l i m i t s cannot be presumed, the usefulness of the analysis may be destroyed and some other device w i l l have to be substituted for i t . 1 2 Since conventional break-even analysis assumes that production equals sales, therefore, no p r o v i s i o n i s made f o r the d e f e r r a l of f i x e d costs i n inventories. This i s consistent with the procedure known i n accounting as d i r e c t costing, variable costing or marginal costing, where- 1 0 . W. L. F i l l , \"The Break-Even Chart \" j The Accounting  Review. Vo l . 2 7 , A p r i l 1 9 5 2 , p. 2 0 3 . 1 1 . Glenn A. Welsch, \"The Construction and Uses of Break- Even Analysis\", C o n t r o l l e r . Y o l . 2 1 , Oct. 1 9 5 3 , p . k65. 1 2 . Gerald R. Crowningshield, Cost Accounting,: P r i n c i  ples and Marginal Applications\". . Boston: Houghton M i f f l i n Company, 1 9 6 2 , p. ^ 0 3 . - 62 - by only variable costs are included i n inventories. But, t h i s i s not consistent with normal cost accounting proced- 1^  ures. J In accounting theory, i f an inventory arises from current production, that portion of f i x e d costs, which i s u t i l i s e d to produce the goods going into inventories, i s deferred i n the inventories. To use d i r e c t costing i n inventory valuation i s to assume that the wage of a worker who operates a machine i n producing goods i s a product cost while a proportionate part of the cost of the machine i s not a product cost. From the conventional break-even analysis, i t may be implied that even i f production i s not equal to sales, a l l f i x e d costs w i l l s t i l l be charged against the revenue of the same period. Under such circumstances, expenses are not properly matched against revenue because the concept of break-even analysis implies that revenue equals expenses i n  curred i n r e a l i s i n g revenue, at the break-even l e v e l of a c t i v i t y . If production i s greater than sales and a l l f i x e d costs are funnelled through the p r o f i t and loss statement 13. The Committee on Accounting Concepts and Standards of the American Accounting Association e x p l i c i t l y states that: \"...the cost of a manufactured product i s the sum of the a c q u i s i t i o n costs reasonably traceable to that product and should include both d i r e c t and i n d i r e c t f a c t o r s . \" \"Accounting and Reporting Standards f o r Corporate F i n a n c i a l Statements: 1957 Revision\", The Accounting Review. Vol. XXXII, Oct. 1957? P\u00BB 539. Two members of the Committee dissented from this p ortion of the statement. Gordon Shillinglaw states that\"...there are two divergent points of view as to which cost elements should be assigned to products. The most widely held view i s that product cost should include a share of a l l manufacturing costs\". However he adds that d i r e c t costing has been winning increasing support i n recent years. Shillinglaw, Gordon, Cost Accounting: Analy  s i s and Control, Homewood, I l l i n o i s : Richard D. Irwin, Inc., 1961, p. 291. - 63 - f o r the period, then i t means that, at the break-even l e v e l of a c t i v i t y , revenue f o r the period equals the expenses incurred i n r e a l i s i n g t h i s revenue plus the expenses i n  curred i n r e a l i s i n g the revenue of l a t e r periods, when the inventories from current production are sold. This tends to d i s t o r t the picture of the p r o f i t a b i l i t y of the business fo r the current period as well as f o r those periods i n the future, whose sales include inventories from p r i o r produc t i o n . Although conventional break-even analysis elimin ates t h i s problem by assuming that production equals sales, i t i s wise to be aware of the existence of th i s problem. The greater the difference between production and sales, the more serious i s the problem. In f a c t , i n firms i n which there exists a s i g n i f i c a n t difference between production and sales, i t may be advisable not to consider the use of break-even analysis. Sales Mix The synchronization of production and sales i s , however, not the l a s t of the basic assumptions of break-even analysis. An executive, who intends to make use of break even analysis, i s also faced with the problem of product mix or sales mix. This problem arises so long as the f i r m i s a multi-product firm and i f , i n addition, the various products have d i f f e r e n t margins of return over variable - 6h - costs. This becomes clear when we consider the fact that, i n a firm, i f the t o t a l sales revenue i s made up of the revenue of products with high margins over variable costs, the break-even point w i l l be lower than i f t o t a l sales revenue i s composed of the revenue of low margin items. This being the case, each time the sales mix changes, the break even point and the p r o f i t pattern w i l l also change. Hence, other things being equal, management i s generally considered to be making a good move, profitwise, i f i t t r i e s to i n  crease the sales of a hi g h - p r o f i t margin product at the expense of a l e s s p r o f i t a b l e item. The sales mix i s , therefore, an important f a c t o r i n break-even analysis. With a given t o t a l cost function and a given t o t a l revenue function, an increase i n t o t a l sales, from a sales volume above the break-even volume, may not produce the expected increase i n p r o f i t s , i f there i s a change i n the sales mix. The increase i n p r o f i t s may be greater or le s s than what i s expected, depending on whether the change i n sales mix i s from the higher margin products to the lower margin products or the reverse. To overcome t h i s problem, the users of break-even analysis assume a given mix or that the sales mix w i l l remain constant as sales volume changes. This assumption, however, presents a serious l i m i t a t i o n when the composition of demand f o r the products of the f i r m changes. To avoid t h i s assumption and to make break-even - 6 5 - analysis more usef u l , various writers have advanced many possible solutions to t h i s problem. Perhaps, the approach which has received the greatest attention, i s the one which requires a separate c a l c u l a t i o n or graph f o r each product. Fixed costs, therefore, have to be appropriately allocated to the various products and this i s where the d i f f i c u l t y l i e s with t h i s method. I t has already been mentioned e a r l i e r that the separation of costs as f i x e d costs or variable costs i s fraught with d i f f i c u l t i e s . The job of a l l o c a t i n g f i x e d costs among the various products i s even more t r y i n g . Some costs may be common costs, the a l l o c a t i o n of which i s just not p r a c t i c a b l e . This means that the sum of the i n d i v i d u a l break-even points w i l l not equal the break-even point f o r the f i r m as a whole. The assumption of a constant sales mix, made i n conventional break-even analysis, i s thus necessary only i n a multi-product firm; but then the single-product f i r m i s , today, a d i s t i n c t r a r i t y i n the r e a l world of business. None l^f. Paul May recommends the use of a p r o f i t polygraph - P. A. May \" P r o f i t Polygraph f o r Product Mix Evaluation\", N.A.C.A. B u l l e t i n . Vol. 37, Sec. 1, Nov. 1955, pp. 307-318. Richard Conway suggests the method of sequential con si d e r a t i o n on a single chart or the use of multi-dimensional analysis - R. W. Conway, \"Breaking out of the Limitations of Break-Even Analysis\", N.A.C.A. B u l l e t i n . Vol. 38, Sec. 1, June 1957, pp. 1265-1272. J o e l Dean suggests the use of a family of product-mix l i n e s - J o e l Dean, Managerial Economics, Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , Inc., 1951, p. 335. These methods may produce more accurate r e s u l t s but, usually t h i s i s achieved at the expense of the advantages of break-even analysis, such as, ease of understanding, inexpen- siveness and quickness i n preparation. - 66 - of the methods, which have been advanced to overcome the l i m i t a t i o n s of this assumption, seems to be completely s a t i s f a c t o r y . Each has i t s weaknesses and consequently, the problem of adjusting break-even analysis to the dynamic s i t u a t i o n of changing product mix i s as serious now as i t was when break-even analysis was f i r s t used more than f i f t y years ago. Today, as f a r as the problem of sales mix goes, users of break-even analysis can do l i t t l e more than recog nise the f a c t that generally, the usefulness of break-even ana l y s i s , f o r the firm as a whole, decreases as the number of products sold by the f i r m increases, c e t e r i s paribus. This, however, may not necessarily be true i f the sales mix of the multi-product f i r m changes so slowly over time that when break-even analysis i s used for short-term forecasting, the d i s t o r t i o n i n the r e s u l t s caused by the assumption of a constant sales mix, may be only n e g l i g i b l e . Further, some multi-product firms price t h e i r products i n such a way as to provide on a l l products sold, a constant return over variable costs, i n which case, the problem of changes i n sales mix does not even a r i s e , because i n such a s i t u a t i o n , assuming that the sales volume and f i x e d costs remain the same, a change i n the sales mix w i l l not cause a s h i f t i n the break even point. This, however, presupposes the use of cost-plus p r i c i n g as opposed to the marginal cost p r i c i n g of the econo mists. Such a presupposition may be v a l i d . Some writers claim that cost-plus p r i c i n g i s the common method of p r i c i n g . 15. Ibid., p. 'ifitf-if5 7 . - 67 - This has been confirmed i n some studies. H a l l and Hitch, i n a study undertaken before the outbreak of World War I I , indicated that about s i x t y - f i v e per cent of firms i n mon o p o l i s t i c competition and seventy-five per cent of monopo- 16 l i s t i c and o l i g o p o l i s t i c firms adopt cost-plus p r i c i n g . Planning and Control I t has been mentioned before that break-even analy s i s i s usefu l for f i n a n c i a l planning and control. This arises mainly from the f a c t that break-even analysis i s capable of depicting graphically the relationships between cost, volume, revenue and p r o f i t . Hence, i f management i s faced with several a l t e r n a t i v e courses of action, break-even analysis i s capable of bringing out f o r the benefit of manage ment, the probable e f f e c t s on cost, volume and revenue and ultimately on p r o f i t of each of the d i f f e r e n t courses of action. This w i l l help management i n i t s decision-making and planning. In planning, f o r instance, break-even analysis may also show whether e f f o r t s would be better directed toward 16. R. L. H a l l and C. J . Hitch, \"Price Theory and Business Behaviour\", Oxford Economic Papers, No. 2, Hay 1939, Table 6, p. 26. In another study of 20 companies i n the United States, over a period of years i n the 1950's, Professor L a n z i l l o t t i found that target return on investment p r i c i n g was the most frequently used method of p r i c i n g . He also found that the most frequent use of t h i s method was i n the p r i c i n g of new products, and that some companies, which used this method f o r the i r new products, employed cost-plus p r i c i n g for t h e i r other products. L a n z i l o t t i , op. c i t . , p. 923-932. - 68 - the reduction of f i x e d costs or of variable costs or whether the e f f o r t s should be exerted to increase volume. If the fixed costs of a firm constitute a very high proportion of t o t a l costs, then i t must operate at a substantial percentage of capacity to cover such costs but, once the break-even volume i s reached, p r o f i t s increase at a very rapid rate, with increases i n volume. On the other hand, i f the t o t a l costs of a firm are made up mainly of variable costs, then a r e l a t i v e l y low volume i s s u f f i c i e n t to cover f i x e d costs but, even a f t e r the break-even volume has been reached, p r o f i t s w i l l not increase at a f a s t rate. On the f i n a n c i a l side, i f a firm has a high percentage of f i x e d costs, an increase i n volume may not cause a serious demand for cash but, i f the firm has a high percentage of variable costs, an increase i n volume i s l i k e l y to cause an increase i n variable costs and eventually a drain on cash. In control, break-even analysis i s useful f o r detecting any insidious upward creep of costs, which might otherwise go unnoticed. I t can also be used to compare actual and planned performances and to show the l o g i c a l points of attack to e f f e c t improvement. A common error made by manage ment i s to overemphasize the importance of volume as a deter minant of p r o f i t s . Some management people may assume that an increase i n volume w i l l automatically increase p r o f i t s . A c t u a l ly, this happens above the break-even point only i f prices remain unchanged and only i f variable costs are kept - 69 - under co n t r o l . Unfortunately, an increase i n volume very often i s accompanied by an increase i n costs, which i s f r e  quently large anough to more than o f f s e t the b e n e f i c i a l volume e f f e c t . Break-even analysis comes i n handy here since i t i s capable of bringing to the attention of management the p r o f i t determinant that has been responsible for o f f s e t t i n g the volume e f f e c t . With t h i s b r i e f introduction to the uses of break even analysis, we can now go on to examine more s p e c i f i c areas of management planning and control, i n which break even analysis Is capable of playing a s i g n i f i c a n t r o l e . P r i c i n g P o l i c i e s P r i c i n g a product i s one of the most delicate prob lems of management. A poor p r i c i n g p o l i c y may lead a business into bankruptcy. Many factors influence the p r i c i n g decisions of management but the most important factor i s probably cost. Some firms adopt the p o l i c y of s e l l i n g some of t h e i r minor products below cost, i n order to a t t r a c t customers. There i s , however, hardly any profit-making f i r m which can aff o r d to s e l l consistently below cost. In order to be successful, firms have to recover not only their costs but also a p r o f i t that i s adequate to maintain the incentive f o r t h e i r continued operation. Break-even analysis can provide some help to man agement i n the establishment of p r i c e s . Break-even charts - 70 - can be drawn to show the e f f e c t on p r o f i t s of d i f f e r e n t price l e v e l s . These charts may then be compared with one drawn under e x i s t i n g conditions to show the volume of sales that would be necessary to achieve the same l e v e l of p r o f i t s . A higher p r i c e , ceteris paribus, has the e f f e c t of r a i s i n g the profit/volume r a t i o and accelerating the recovery of f i x e d costs. Hence, a lower volume of sales would b e \" s u f f i c i e n t to a t t a i n the p r o f i t objective. Conversely, a lower price would lower the profit/volume r a t i o and reduce the rate of recovery of f i x e d costs. Attainment of the p r o f i t objective, i n t h i s case, would require a higher volume of sales. The usefulness of break-even analysis, i n p r i c i n g decisions, arises mainly from the f a c t that i t can ably show the cost-volume-revenue structure of a business. But, one should never overestimate the usefulness of break-even analysis i n p r i c i n g decisions because the e f f e c t on p r o f i t s of a change i n price depends not only on the cost-volume- revenue structure of the business but also on the e f f e c t on volume of the change i n p r i c e , that i s , on the price elas t i c i t y of demand. In actual f a c t , i n any p r i c i n g decision, the l a t t e r would appear to be, as important as, i f not more important than the former. Unfortunately, break-even analy si s does not, i n any way, t e l l us what the price e l a s t i c i t y of demand f o r a product i s l i k e . C a p i t a l Expenditures Capital expenditures usually involve large sums - 71 - of money. Firms, very often, have to resort to outside sources of funds to finance t h e i r c a p i t a l expenditures. An unwise investment decision by management may put an end to the operation of a business. Therefore, management has to be extremely c a r e f u l i n every investment decision that i t makes. This requires management to have a good idea of, among other things, the changing relationships of cost, volume, revenue and p r o f i t s . Break-even analysis i s usefu l i n decisions involving c a p i t a l expenditures since i t i s extremely capable of bringing out these re l a t i o n s h i p s . If a firm i s thinking of making an investment, i t can make use of break-even analysis to compare i t s p o s i t i o n under the two alternative situations; (a) i f the investment i s undertaken and (b) i f the investment i s not undertaken. The difference i n the p r o f i t s under the two sit u a t i o n s , a f t e r adjustments f o r present values, may then be compared with the cost of c a p i t a l . On the basis of this and other relevant evidence, a decision may be made as to whether the investment ought to be undertaken. In looking at i t s p o s i t i o n under the two s i t u a t i o n s , the fi r m should recognise the chang ing cost-volume-revenue relationships and the resultant e f f e c t upon p r o f i t , caused by variations i n the volume of business. Occasionally, firms have made the error of computing cost and revenue estimates on the basis of maximum u t i l i s a t i o n of pro posed productive f a c i l i t i e s or on the basis of a c e r t a i n 17 'representative', 'normal' or 'average' volume of business. 17. John 1. t&gt;. Tse, P r o f i t Planning through Volume-Cost  Ana l y s i s . New York: The Macmillan Company, I960, p. 21. - 72 - An i m p l i c i t assumption i s then made that the unit cost and p r o f i t w i l l remain the same at a l l other l e v e l s of operation, as they would at the maximum or representative volume of business. This tends to d i s t o r t the picture and lead to un sound decisions because the changing cost-volume-revenue relationships are ignored. Break-even analysis, by making management aware of the changing cost-volume-revenue r e l a t i o n s h i p s , tends to guide management to more r e a l i s t i c thinking. With th i s method, management can obtain a clear perception of costs, revenue and p r o f i t s or losses to be expected under actual operating con diti o n s and not under some imaginary or deceptive s i t u a t i o n . The use of break-even analysis does not mean that management's judgement can now be completely eliminated and decisions can be made s o l e l y on an objective basis. But, break-even analysis can help management to make better and more i n t e l l i g e n t decis ions about c a p i t a l expenditures. Make or Buy Problems Many firms have faced the problem of having to decide whether i t i s more p r o f i t a b l e to make or to buy compon ent parts that are used i n the firm's assembled products. A decision of t h i s nature requires consideration of a number of fa c t o r s . For instance, the firm may have to consider the need f o r an assured supply, continuity of delivery and maintenance of product qu a l i t y . I f i t i s assumed that the firm need not - 73 - have to worry about these p o l i c y f a c t o r s , then the answer to the make or buy problems would probably revolve around the question of costs. This means that proper cost information would be required so that the cost of making can be compared with the cost of buying. If a f i r m has unused productive capacities i n the short-run, the cost of making may be based on the a d d i t i o n a l costs that i t w i l l have to incur i f the orders were kept i n the company. In the long-run, however, the firm's cost of making should include d i r e c t materials, d i r e c t labour, the variable costs involved, a share of f i x e d costs and a p r o f i t f i g u r e . Break-even analysis i s useful i n the comparison of the cost of making and the cost of buying since i t can show the e f f e c t s on p r o f i t s , at d i f f e r e n t volume l e v e l s , of the two alternatives and thereby help management to make i t s decision. Cost Control Cost control i s one of the most important aspects of the management of a business. Operating p r o f i t s , as de fi n e d i n chapter I, are equal to operating revenue minus operating costs. But, management does not have too much control over operating revenue since there i s a l i m i t to the amount that a business can s e l l and s e l l i n g prices are, to a large extent, established by competition. Hence, the - 7h - profit-making capacity of a business depends l a r g e l y on the e f f i c i e n c y with which costs are controlled. One of the ways i n which cost control can be achieved i s through the use of f l e x i b l e budgets, which \" r e f l e c t the amount Of- cost that i s reasonably necessary to 18 achieve each of several s p e c i f i e d volumes of a c t i v i t y . \" For purposes of cost control, the predetermined costs are based on standards set f o r materials, labour and expenses. These predetermined costs may then be compared with actual costs and the differences, c a l l e d variances, may be analysed. From the analysis of the variances, management may introduce measures to check the unfavourable trends and departures from the predetermined costs. In t h i s way, f l e x i b l e budgets a i d i n the control of costs. There i s a greal deal of s i m i l a r i t y between f l e x  i b l e budgets and break-even charts. In f a c t , i t may be said that whereas f l e x i b l e budgets are tabular variable income statements, break-even charts are graphic variable income 19 statements. ' The construction of break-even charts i s very often based on the data of f l e x i b l e budgets; and just as f l e x  i b l e budgets are usefu l f o r cost control, so are break-even charts. For purposes of cost control, the predetermined costs and the actual cost may be plotted on a break-even chart to 18. Shillinglaw, op. c i t . , p. 217. 19. Adolf Matz, Othel J . Curry and George W. Frank, Cost  Accounting, C i n c i n n a t i : South-Western Publishing Company, 1952, p. 678. - 75 - bring out the variances and on the basis of the analysis of these variances, corrective actions may be taken by management. Summary In t h i s chapter, i t has been shown that break-even analysis can be used i n decision-making involving make or buy problems and i n problems related to c a p i t a l expenditures, cost control and p r i c i n g decisions. These are, by no means, the only uses to which break-even analysis can be put. In f a c t , break-even analysis has been used i n the solving of many other problems concerning a l t e r n a t i v e s , which involve cost, volume and p r o f i t r e l a t i o n s h i p s . I t was also pointed out, i n this chapter, that i n using break-even analysis, many r e s t r i c t i v e assumptions have to be made. The assumptions include the following: (a) A l l costs can be reasonably separated into their f i x e d and variable components and whereas f i x e d costs remain f i x e d at a l l volumes, variable costs vary i n d i r e c t proportion to volume. (b) S e l l i n g prices remain constant at a l l volumes. (c) Production equals or clos e l y follows sales and a l l f i x e d costs incurred i n a period are, therefore, deducted from that period's revenue. (d) There i s only one product or i f several products are being produced and sold, the sales mix w i l l remain cons tant. These assumptions are more v a l i d f o r some firms than f o r others. In those firms i n which these assumptions are very u n r e a l i s t i c , break-even analysis i s v i r t u a l l y useless, unless - 76 - the firms are w i l l i n g to make adjustments to overcome the l i m i t a t i o n s that are inherent i n these assumptions. CHAPTER IV TEST OF BREAK-EVEII ANALYSIS Introduction There are many ways of forecasting the operating p r o f i t s of firms. Some of these techniques are rather naive. An example i s the environmental analysis method. The essen t i a l idea here i s to discover a functional r e l a t i o n s h i p between a f i r m 1 s p r o f i t s and one or more indicators of national a c t i v i t y - such as, disposable income or any re l i a b l e index of i n d u s t r i a l production - on the assumption that the well-being of a firm, as measured by i t s p r o f i t s , i s d i r e c t l y determined by business conditions i n the t o t a l economy. A modification of t h i s technique i s the c o r r e l a t i o n analysis method, whereby a functional relationship i s f i r s t determined between a firm's p r o f i t s and some i n t e r n a l var iable f a c t o r , f o r example, the sales of the firm. On the basis of th i s r e l a t i o n s h i p , forecasts of the firm's p r o f i t s may then be made. In t h i s study, t h i s technique w i l l be c a l l e d the percentage of sales method. I t i s obvious that the accuracy of the p r o f i t forecast, by th i s method, depends d i r e c t l y on: (a) the extent to which the firm's p r o f i t s are t r u l y r e l a t e d to the independent v a r i a b l e , sales and (b) the accuracy of the forecast made f o r the independent var i a b l e . - 78 - A more sophisticated way of forecasting p r o f i t s involves the use of the break-even technique. Break-even analysis - i t s nature and i t s pros and cons - needs no further comment here. The purpose i n t h i s chapter Is to te s t the hypothesis and the n u l l hypothesis, as d e t a i l e d i n chapter I. Source of Data The data f o r the t e s t are taken from Moody's 1 I n d u s t r i a l Manuals. As indicated i n chapter I, the s t a t i s  t i c a l approach (least squares method) i s used to separate the t o t a l costs of the f i r m into f i x e d costs and variable costs, since i n terms of the data a v a i l a b l e , i t i s l i k e l y to give more r e l i a b l e r e s u l t s than the accounting or engin eering methods. Included i n the universe of firms are only those firms i n Moody's I n d u s t r i a l Manuals, which have had losses at some time or other over the period covered i n the study. This i s so because preliminary studies to t h i s test showed that, i n the case of those firms, which had never suffered any losses, i t was not possible to separate t h e i r t o t a l costs into t h e i r f i x e d and variable components, by the s t a t i s t i c a l approach. In this t e s t , the year chosen f o r the forecast i s 1956. Any other year could have been chosen so long as i t i s a past year; otherwise, i t would not be possible to 1. Detailed i n chapter I. - 79 - compare the f o r e c a s t p r o f i t s w i t h the a c t u a l p r o f i t s , to d e t e r  mine the accuracy of the f o r e c a s t s . F o r the t e s t , i n order to measure c o s t v a r i a b i l i t y , the behaviour of c o s t s of each f i r m i n the sample i s s t u d i e d f o r a maximum p e r i o d of t e n y e a r s , from 1946 to 1955. As i n d i c a t e d i n chapter I, Moody's I n d u s t r i a l Manuals from 1946 to 1958 are used to o b t a i n the 2 d a t a . A c l o s e examination of the Manuals f o r t h i s p e r i o d showed t h a t 589 f i r m s c o u l d be i n c l u d e d i n the u n i v e r s e . F o r e c a s t i n g Operating P r o f i t s A. Break-Even Method In f o r e c a s t i n g the o p e r a t i n g p r o f i t s of the sample f i r m s by the break-even method, the f o l l o w i n g assumptions are made : 3 (a) A l l c o s t s can r easonably be c l a s s i f i e d as f i x e d or v a r i a b l e . (b) S e l l i n g p r i c e s remain constant a t a l l volumes. (c) P r o d u c t i o n and s a l e s are synchronised and (d) The s a l e s mix remains c o n s t a n t . The o p e r a t i n g p r o f i t s of f i r m s a t any g i v e n volume l e v e l i s equal to the o p e r a t i n g revenue minus the o p e r a t i n g 2. There i s a time l a g i n Moody,'.s I n d u s t r i a l Manuals. The data of some companies appear i n the manuals one or two years a f t e r the end of t h e i r f i s c a l y ear. 3. The need f o r these assumptions have been d i s c u s s e d i n chapter I I I . T h e i r v a l i d i t y v a r i e s among the sample f i r m s . F o r most of the sample f i r m s , the f i r s t t h ree assumptions are q u i t e v a l i d . The f o u r t h assumption, however, i s not v a l i d f o r almost a l l the f i r m s but has to be made i n order to c a r r y out the t e s t . - 80 - costs at that volume l e v e l . In t h i s study, the forecast volume l e v e l i s given and i s equal to that at which the actual operating p r o f i t s are r e a l i s e d . The operating revenue i s also given and i s equal to the volume l e v e l , on the assump t i o n that production and sales are synchronised. Therefore, i n order to forecast the operating p r o f i t s , i t i s only nec essary to determine the operating costs. The determination of the operating costs, at a given volume l e v e l , can be attempted i n many ways. The accounting, engineering and s t a t i s t i c a l approaches have already been explained i n chapter I I . The s t a t i s t i c a l approach, with the scatter chart technique and the method of l e a s t squares, i s used here. The reason f o r t h i s has been discussed i n chapter I. By t h i s method, the operating cost' figures of a l l the sample firms are co l l e c t e d for as many as possible of the years between 19*+6 and 1955 ( i n c l u s i v e ) . These figures are then p l o t t e d on scatter charts with sales volume as the hor i z o n t a l axis and operating costs as the v e r t i c a l axis. The idea here i s to achieve an estimate of the c o r r e l a t i o n between costs and sales volume. S h i l l i n g - law advises that the s t a t i s t i c a l approach \"must be regarded as f i r s t approximations. If there are strong common-sense reasons f o r doubting that the r e s u l t i n g cost-volume pattern i s reasonable, then the conclusion of the s t a t i s t i c a l analy- s i s should be supplemented by the a p p l i c a t i o n of judgement.\" h. Gordon' Shiilinglaw, Cost Accounting: Analysis and  Control. Homewood, I l l i n o i s : Richard D. Irwin, Inc., 196l, P. 235. - 81 - In t h i s study, those cost figures which show.an 'abnormal' 5 r e l a t i o n s h i p to sales volume are eliminated. Once th i s stage has been reached, a l i n e of best f i t may be established through the remaining p l o t t e d points 6 by the method of l e a s t squares. The formula f o r a straight l i n e trend i s y = a + bx. The l e a s t squares method provides two simultaneous equations which when solved determine the values of the constants, a and b i n the equation of the s t r a i g h t l i n e t r e n d . 7 These two simultaneous equations are as follows: \u2022\u00A3y = Na + b ^ x \u00A3xy - a-^x + b i : x 2 where: - sigma, sum of, summation. N = No. of items, years or pl o t t e d points of the data under consideration. x = Value of the independent v a r i a b l e , f o r example, the sales volume i n t h i s study. y = Value of the dependent variable, f o r example, the operating, costs i n t h i s study. 5. A cost figure i s considered to have an abnormal re l a t i o n s h i p to sales volume i f i t l i e s some distance away from the trend that other cost figures seem to be e s t a b l i s h  i n g . Judgement i s , of course, involved here. 6. For a technical explanation of t h i s s t a t i s t i c a l pro cess, reference may be made to Frederick E. Croxton and Dudley J . Cowden, Applied General S t a t i s t i c s . 2nd Ed.; Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , Inc., 1955, PP- 263-275. 7. Fortran Programming i s used to a s s i s t i n a r r i v i n g at the values of the constants, a and b. See Appendix VI. - 82 - Since, i n t h i s study, x represents the sales volume and y, the operating costs, once the values of a and b have been derived, the operating costs of any firm, f o r any sales volume, may be estimated merely by substituting x, i n the formula y = a + bx, with the value of the given sales volume. When the operating costs, at the given sales volume, have been determined, a forecast of the operating p r o f i t s , at that sales volume, can be made by subtracting the opera tin g costs from the given operating revenue. B. Percentage of Sales Method The percentage of sales method of forecasting operating p r o f i t s i s very much simpler than the break-even method. By the percentage of sales method, f o r each sample firm, the operating p r o f i t s as a percentage of the sales volume i s determined f o r as many as possible of the years between 19^6 and 1955 ( i n c l u s i v e ) . The mean average of these 8 percentages i s then determined. The ultimate purpose here, 8. The mode i s not used here because, f o r most of the sample firms, the same percentage d i d not appear more than once. There i s no s p e c i a l reason to prefer the median. Simpson and Kafka state that \"the arithmetic mean i s the most commonly used and best known of the averages, and i s preferred unless precluding circumstances are present, such as extreme values at either end of the ser i e s , or open-end classes or varying class i n t e r v a l s or unless we d e f i n i t e l y wish to e s t a b l i s h the most frequent value or some other p o s i t i o n a l average.\" George Simpson and F r i t z Kafka, Basic  S t a t i s t i c s . Hew York: W. W. Norton and Company, Inc., 1957\u00BB p. 171. In thi s study, the precluding circumstances are either absent or are very i n s i g n i f i c a n t . - 83 - as i n the case of break-even analysis, i s to compare the forecast operating p r o f i t s with the actual operating p r o f i t s , therefore, i t i s assumed that the sales volume i n the forecast year, 1956, i s given and Is equal to the sales volume at which the actual operating p r o f i t s are r e a l i s e d i n 1956. Once the sales volume i s known, a forecast of the operating p r o f i t s can be made by applying to the given sales volume, the average percentage of p r o f i t s as a percentage of sales f o r the years 1946 to 1955. The Sample Before making a decision on the firms to be In cluded i n the sample, a decision has to be made on the number of firms to be included i n the sample. For t h i s purpose, i t i s necessary to state the desired degree of accuracy. In t h i s study, i t i s asserted with a p r o b a b i l i t y of 0.95 that the estimated mean w i l l be within $0.10 of the true mean. The confidence i n t e r v a l i s a r b i t r a r i l y f i x e d , depending on what i s f e l t to be reasonable, under the c i r  cumstances. In t h i s case, consideration was given to the 9 _ f a c t that the sample mean of the exploratory study, X^, i s only $0.26m. (Table I I I ) . The t-table (Appendix II) shows that f o r a 95 percent degree of confidence, with 9 degrees of freedom (n -1 ) , the standard error of the mean 9. This i s explained i n the next page. - 8 if - 1 \u00B0 i s equal to 2 . 2 6 2 . From t h i s , the following formula, may be used to determine the size of the sample: 2 . 2 6 2 ( - J c ) = $ 0 . 1 0 m where 6 = standard deviation of the universe (population) and n = size of the sample. In order to determine the standard deviation of the universe, a s t a r t has to be made with an exploratory study of some firms, picked at random from the universe. In t h i s case, 1 0 firms are used f o r the exploratory study. The basic p r i n c i p l e behind random sampling i s that every f i r m i n the universe must have an equal chance of being chosen. To achieve t h i s , use can be made of prepared tables of random numbers. F i r s t l y , a l l the 5 8 9 firms i n the universe are l i s t e d i n alphabetical order and numbered from 1 to 5 8 9 . A decision i s then made to use Kendall and Smith's \"Tables of Random Sampling Numbers, Tracts f o r Computers No. XXIV\" 1 1 (Appendix I ) . To avoid any p o s s i b i l i t y that the choice of a s t a r t i n g point might be nonrandom, i t i s a r b i t r a r i l y decided, before examining the Random Number Tables, to s t a r t picking 1 0 firms from Row 1 2 j and columns 6 , 7 and 8 of the random numbers shown on page 1 5 of the tables. This would give the numbers: 1 0 . John S. Freund and Frank J . Williams, Modern Business  S t a t i s t i c s . Englewood C l i f f s , N.J.: Pren t i c e - H a l l , Inc., 1 9 5 8 , p. 1 9 3 . 1 1 . M. G. Kendall and B. B. Smith, Tables of Random Sampling  Numbers. Tracts f o r Computers No. XXIV. Cambridge: Cambridge U n i v e r s i t y Press, 1 9 5 1 . - 8 5 - 3 7 7 339 218 043 1 5 7 144 4 5 1 4 9 8 0 7 0 5 2 5 S i n c e t h e u n i v e r s e i s made up o f 5 8 9 f i r m s , any number e x c e e d i n g 5 8 9 i s i g n o r e d . I n t h e same way, any number w h i c h appeared more t h a n once i s a l s o i g n o r e d a f t e r i t had appeared f o r t h e f i r s t t i m e . T h i s happened i n the case o f t h e number, 043. Once t h e f i r m s f o r the e x p l o r a t o r y s t u d y have been p i c k e d , t h e s t a n d a r d d e v i a t i o n of t h e u n i v e r s e X ( 6 ) can be d e t e r m i n e d by u s i n g t h e f o r m u l a : 6 - J \u2014x  where: 6 = s t a n d a r d d e v i a t i o n o f t h e u n i v e r s e = sigma, sum o f , summation X^ = d i f f e r e n c e between a c t u a l and f o r e c a s t p r o f i t s X^ = mean of t h e d i f f e r e n c e i n p r o f i t s n = s i z e o f t h e sample i n t h e e x p l o r a t o r y s t u d y _ 2 Table I I I shows t h a t \u00A3(X&amp; - X d ) = $ 0 . 9 1 2 7 m . T h e r e f o r e , the s t a n d a r d d e v i a t i o n o f t h e u n i v e r s e , 6 i s e q u a l t o : ^ ( X d - X d ) _ / $o &gt; 9 1 27m n - 1 J 9 '$0.1014m. = $0.3184m. E a r l i e r , t h e f o r m u l a f o r the s i z e o f t h e sample - 86 - had been given as: 2.262 ( T = T ) = $0.10m. where: 6 = standard deviation of the un i v e r s e and n = size of the sample This i s the same as: n = ( - jO.lOm\" v 27262 Since, i t has already been found that 6 = $0.318^111. Therefore, n = ($0.3l8Um ^ 1\u00B0/^ )2 = ftQ.^18^2 = 7.20362 = 51.88 This means that a random sample of size , 52 w i l l s u f f i c e to give the desired degree of accuracy. But Simpson and Kafka advises that \"the use of a formula to obtain an estimate of sample size does not give us more than a rough approximation. In pr a c t i c e , i t i s advisable to take the sample estimate as a bare minimum to be increased f o r 12 safety.\" Therefore, following the advice of Simpson and Kafka, f i v e more firms are added to the 52 firms to give a sample siz e of 57 firms. Once the number of firms to be included i n the 12. Simpson, op. c i t . , p. Wf. TABLE I I I Computation o f the Standard D e v i a t i o n of the U n i v e r s e ($ Amounts i n M i l l i o n s ) Volume D i f f e r e n c e Slope Between or of V a r i  F o r e  A c t u a l and Sales F i x e d Trend able T o t a l c a s t A c t u a l F o r e c a s t Name o f Revenue Costs L i n e Costs Costs P r o f i t s P r o f i t s P r o f i t s Company (x) Pf = P a - P f x d \" ^ d - N2 (a) (b) (bx) (a+bx) x-(a+bx) Pa = * d \u2022 (Xd-Xd) Auto S o l e r \u2022 Company (ga.) $2.02 $0 . 0 9 0.81 $1.64 $ 1 . 7 3 $0 . 2 9 $0 . 3 7 $0.08 -$0.18 $0 . 0 3 2 4 \u2022 B o l s a C h i c a O i l 0 0 Corp. (Del.) 1.20 0 . 06 0 . 9 3 1.12 1.18 0.02 0.20 0.18 - 0.08 0 . 0 0 6 4 ^ Diamond T.Motor 1 Car Co. (111.) 4 5 . 4 3 0.02 0 . 97 44-. 07 1+4.09 1.3k 2. kO 1 . 0 6 0 . 8 0 o.64oo Dauega S t o r e s Corp.(N.J.) 24.64 2 . 2 4 0 . 9 0 22.19 24.42 0.22 0.1k 0 . 0 6 -0.20 0.0400 Globe American Corp. (Ind.) k.39 1.42 0 . 7 6 3-3k if. 76 (0 . 3 7 ) (0 . 2 8 ) 0.09 -0.17 0 .0289 Mohawk L i q u e r 4 . 3 4 0 . 28 0 . 5 5 0.0841 Corp. (Mich.) 5.07 0 . 7 9 0 . 7 0 3 . 5 5 0 . 7 3 0.29 New England Box o .6o 0.84 (0.01) 0 . 0 6 0 . 0400 Co. (Mass.) k.Ok 3 . 3 9 3 . 9 9 0 . 0 5 -0.20 Ronson Corp.(N.J . ) 3 1 . 9 5 7 . 9 1 0 . 6 5 20 . 77 28 .68 3.27 3 . 0 7 0 . 2 0 -0 . 0 6 0 .0036 Standard Commer c i a l Tobacco Co.Inc.(Del.) if. 87 0 . 0 6 0 . 9 ^ 4 . 5 8 k.6k O .23 0 . 0 4 0 . 1 9 -0 . 0 7 0 . 0049 12th S t r e e t 0.0324 Store (111.) 3 . 8 5 0 . 9 1 0 . 8 0 3 .08 3 . 9 9 (0.1*0 (0 . 0 6 ) 0.08 -0.18 Zi51 0 .9127 The sum of the d i f f e r e n c e s between a c t u a l and f o r e c a s t p r o f i t s (^X^) = $ 2 . 5 5 m. Ther e f o r e , the mean o f the d i f f e r e n c e s (Id) = $ 2 . 5 5 \" 1 0 = $ 0 . 2 6 m. In determining the differences between actual and forecast p r o f i t s ( p - p f ), signs are ignored because we are only interested i n the magnitude of tfie d i f f e r  ence and not i n the d i r e c t i o n of the differences. CO CO sample i s known, the firms can be drawn at random from the universe o f 589 a l p h a b e t i c a l l y l i s t e d firms. Here, again, use can be made of Kendall and Smith's \"Tables of Random Sampling Numbers, Tracts f o r Computers No. XXT?\"\"1\"3 (Appen dix I ) , following the same procedure as that used to obtain the firms f o r the exploratory study. Method o f Analysis In order to determine whether break-even analysis or the percentage of sales method can provide a better f o r e  cast o f operating p r o f i t s , a comparison must f i r s t be made of the forecasts of the two methods with the actual operating p r o f i t s . A comparison of the forecast of the percentage o f sales method with the actual operating p r o f i t s i s given i n Table IV and a comparison o f the forecast o f break-even analysis with the actual operating p r o f i t s i s given i n Table V. The method which gives a smaller difference be tween forecast operating p r o f i t s and actual operating p r o f i t s should be the more accurate method. Table V shows that, f o r the 57 firms shown i n the sample, the difference between the forecast operating p r o f i t s and actual operating p r o f i t s , by the percentage o f sales method, t o t a l s $24.27m. This gives a mean difference o f $0.4257m, that i s $24.27m divided by 14 57. Table V shows that the difference between the forecast 13. Kendall, i o c . c i t . 1 4 . The mean i s used instead of the mode or the median because i t i s l e a s t subjected to sampling v a r i a t i o n . This was discussed i n chapter I. TABLE IV DIFFERENCE BETWEEN ACTUAL AND FORECAST PROFITS - PERCENTAGE OF SALES METHOD ($ Amounts i n M i l l i o n s ) Av.Percentage Difference of P r o f i t s Between as a Per Sales Fore Actual and centage of Volume cast Actual Forecast Name of Company Sales i n 1 9 5 6 P r o f i t s P r o f i t s P r o f i t s (a) (b) P f = 6 a x 1 0 0 Pa ( P a-P f ) 1 Baush Machine Tool Co. 9.84 2 B e l l Company - 0 . 5 5 3 Bishop and Babcock Manufacturing Co. 3 . 6 9 4 Brown-McLaren Manufacturing Co. 3 . 4 4 5 Carpenter (L.E.) &amp; Co. - 2 . 5 2 6 Chief Consolidated Mining Co. 0 . 7 4 7 Cleveland-Sandusky Brewing Corp. 5 . 7 6 8 Consolidated R e t a i l Stores, Inc. 2 . 5 9 9 Cooper Tire and Rubber Co. 3 . 1 3 1 0 Curtis Lighting, Inc. 2 . 0 1 1 1 Dixon (Joseph) Crucible Co. 3 . 2 0 1 2 E. &amp; B. Brewing Co. Inc. 1 . 3 5 1 3 Flagg-Utica Corp. - 1 . 1 7 14 F l o t i l l Products, Inc. 1 . 7 3 1 5 Flour M i l l s of America, Inc. 0 . 4 4 16 Gerotor May Corp. - 5 \u00AB 5 5 1 7 Gum Product, Inc. - 4 U - 3 1 8 Hathaway Bakeries, Inc. \u00A7 . 8 l 1 9 H i l l e r Helicopters 4 . 3 9 2 0 Jacob Ruppert 0 . 0 3 2 1 Jeannette Glass Co. 5 . 6 9 2 2 Jessop S t e e l Co. 3 .06 2 3 Lanston Industries, Inc. 1 0 . 2 1 24 Longchamps, Inc. 2 . 1 6 2 5 Macmillan Petroleum Corp. 2 . 6 3 h . 0 3 6.64 5 . 7 2 1 . 6 2 3 ^ 5 0 . 5 6 1 . 3 8 21 . 0 4 3.73 12.65 0 . 9 2 17.18 21.41 48 . 5 5 1.3^ 2.10 1 8 . 8 9 9 . 8 3 4 7 . 5 7 5.18 24.85 2.91 7.73 14 . 1 6 . 3 9 ( 0 . 0 4 ) 0 . 2 1 0 . 0 5 ( 0 . 0 9 ) 0 . 0 0 0 . 0 8 0 . 5 5 0 . 7 4 0 . 0 8 0.41 0 . 0 1 ( 0 . 2 0 ) 0 . 3 7 0 . 2 1 ( 0 . 0 7 ) ( 0 . 0 9 ) 0 . 5 3 0 . 4 3 0 . 0 1 0 . 3 0 0 . 7 6 0 . 3 0 0 . 1 7 0 . 3 7 . 4 4 ( o ! 2 8 ) ( 0 . 1 5 ) ( 0 . 1 0 ) ( 0 . 4 3 ) ( 0 . 0 7 ) 0 . 0 2 ( 1 . 7 7 ) 1 . 0 7 0 . 1 5 O .98 0 . 0 5 0.64) 1 . 9 2 6 . 9 7 ( 0 . 2 5 ) 0 . 1 3 ( 1 . 0 0 ) 0 . 3 2 ( 0 . 1 9 ) 0 . 4 4 3 . ^ 7 ( 0 . 0 2 ) ( 0 . 0 2 ) 0 . 5 3 10 .05 0.24 0 . 3 6 0 . 1 5 0 . 3 4 0 . 0 7 0 . 0 6 2 . 3 2 0 . 3 3 0 . 0 7 0 . 5 7 0 . 0 4 0.84 1 . 5 5 O . 7 6 0 . 1 8 0 . 2 2 1 . 5 3 0 . 1 1 0 . 2 0 0.14 2 . 7 1 0 . 3 2 0 . 1 9 0 . 1 6 Name of Company Av. Percentage of P r o f i t s as a Per centage of Sales (a) 26 Maguire Industries, Inc. - 3.82 27 Mandel Brothers, Inc. 0.05 28 Merrimac Hat Corp. 2.26 29 Michigan Bakeries, Inc. 1.72 30 Morgan's, Inc. - 2 .24 31 National Research Corporation - 1.49 32 Nelson (N.O.) Co. 1.5^ 33 Oceanic O i l Co. 17.35 34 0 ' S u l l i v a n Rubber Corp. ^\u202235 35 Peck, Stow &amp; Wilcox Co. 6.03 36 P l a s t i c Wire &amp; Cable Corp. 5.29 37 Plume and Atwood Manufacturing Co. 0.67 38 Powdrell &amp; Alexander, Inc. 3.67 39 Queen Anne Candy Co. 4.17 40 Reis (Robert) &amp; Co. 0.86 4 l Reymer &amp; Brothers, Inc. 1.82 h2 Richmond Cedar Works 2.16 43 Rochester &amp; Pittsburgh Coal Co. 2.35 hh Rock-Ola Manufacturing Co. 0 .41 U-5 Rudy Manufacturing Co. 0.75 ho Sandura Co. - 0.75 47 Scranton Lace Co. 5.3^ 48 Seneca F a l l s Machine Co. - 5 . H 49 Shasta Water Co. 2.26 50 Sherman Products, Inc. 3.71 51 Sidney Blumenthal &amp; Co. 2 .14 52 Stylon Corp. 6.02 Sales Volume i n 1956 (b) Fore cast P r o f i t s Pf = 6  a x TOO Actual P r o f i t s Pa Difference Between Actual and Forecast P r o f i t s ( p a-P f ) $2.50 1(0.10) 31.55 0.02 3.04 0.07 8.38 0 .14 4.76 (0.11) 7 .14 (0.11) 15.62 0.24 1.85 0.32 6.35 2 .51 0.28 0.15 11.43 0.61 10.16 0.07 4.75 0.17 2.73 6.11 4.83 0 .04 1.73 0.03 1.51 0.03 45.76 1.08 5.97 0.02 9.03 0.07 8.67 (0.07) 6.05 6.32 2.44 (0.37) 2.32 0.05 5 .84 0.22 20.23 0.43 6.45 0.39 $0.08 $0.18 (O.36) O.38 0.15 0.08 0.27 0.13 0.05 0 .16 0.49 0.60 (0.09) 0.33 0.58 0.26 0.08 0.20 0.29 0 .14 1.1+8 0.87 0.00 0.07 0.73 0.56 0.08 0.03 0.06 0.02 (0.01) 0 .04 (0.19) 0.22 1.87 0.79 0.73 0.71 1.05 0.98 1.00 1.07 (6.09) o .4 i (0.06) 0.31 0.04 0.01 0.5s 0.36 0 .27 0.16 0.90 0.51 Name of Company Av.Percentage of P r o f i t s as a Per centage of Sales Sales Volume i n 1 9 5 6 Fore cast P r o f i t s Actual P r o f i t s Difference Between Actual and Forecast P r o f i t s (a) (b) Pf = 6  a x V5b~ Pa ( Pa-Pf ) 5 3 Unexcelled Chemical Corp. 5H- V i c t o r Products Corp. 55Wayne Screw Products Co. 56 Wilson Brothers 5 7 Yolande Corp. - 3.29 6 . 3 7 7 . 1 6 1 . 6 3 2.64 11 . 0 4 5.42 1 . 1 8 19.55 2.19 $(o .03) 0 . 3 5 0 . 0 8 0 . 3 2 0 . 0 6 $ ( 0 . 1 7 ) ( 0 . 2 2 ) ( 0 . 0 6 ) 0.14 (0.09) $0 .14 0 . 5 7 0.14 0 . 1 8 o.i? 24.27 i ro TABLE V DIFFERENCE BETWEEN ACTUAL AND FORECAST PROFITS - BREAK-EVEN METHOD ($ Amounts i n M i l l i o n s ) 1 (x) 2 (a) 3 (b) 4 (bx) 5 (a+bx) *6-x-(a+bx) P a 8 ( p a-P f ) 1 Baush Machine Tool Co. $4.03 2 B e l l Co. ' 6.64 3 BishoD and Babcock Manufactur ing Co. 5'72 4 Brown-McLaren Manufacturing Co. 1.62 5 Carpenter (L.E.) &amp; Co. 3.45 6 Chief Consolidated Mining Co. 0.56 7 Cleveland Sandusky Brewing Corp. I .38 8 Consolidated R e t a i l Stores, Inc. 21.04 9 Cooper Tire and Rubber Co. 23.74 10 Curtis Lighting, Inc. 3.73 11 Dixon (Joseph) Crucible Co, 12.65 12 E &amp; B Brewing Co. Inc. 0.92 13 Flagg-Utica Corp. 17.18 14 F l o t i l l Products, Inc. 21.41 15 Flour M i l l s of America, Inc. 48.55 16 Ge rotor May Corp. 1 .34 17 Gum Products, Inc. 2.10 18 Hathaway Bakeries, Inc. 18.89 19 H i l l e r Helicopters 9.83 20 Jacob Ruppert 47.57 21 Jeannette Glass Co. 5.18 22Jessop S t e e l Co. 24.85 23 Lanston Industries, Inc. 2.91 24 Long champs, Inc. 7.73 25 MacMillan Petroleum Corp. 14 .16 26 Maguire Industries, Inc. 2.50 27 Mandel Brothers, Inc. 31.55 28 Merrimac Hat Corp. 3 .04 10.35 3.40 0.19 0.20 0.53 0.37 0.25 10.42 0.24 0.24 1.31 0.09 5.24 2.30 1.70 0.64 0.07 1.85 1.48 3.86 1.11 5.21 0.34 0.85 2.04 0.23 ^.99 0.65 0.7M- O.67 0.93 0.78 0.88 0.71 0.75 0.62 0.94 0.86 0.83 0.89 0.69 0.80 0.97 O.78 0.96 0.93 0.77 0.90 0.66 0.68 0.90 0.87 0.82 0.91 0.85 O.89 $2.98 4.45 5.32 1.26 3.04 0 .40 1 .04 13.04 22.32 3.21 10.50 0.82 11.85 17.13 47.09 1.05 2.02 17.57 7.57 42.81 3 .42 16.90 2.62 6.73 11.61 2.28 26.82 2.71 $3.33 7.85 1 .46 3.57 0.77 1.29 23.46 22 .56 3 A 5 11 .81 0.91 17.09 48.79 1.69 2.09 19.42 9.05 46.67 4.53 20.11 2.96 7.57 13.65 2.51 31.81 3.36 $0.70 (1.21) 0.21 0.16 (0.12) (0.21) 0.09 (2 .42) 1.18 0.28 0 .84 0.01 0.09 1.98 (0.24) (0.35) 0.01 (0.53) 0.78 0.90 0.65 4 .7^ (0.05) 0.16 0.51 (0.01) (0.26) (0.32) $0.44 (0.28) (0.15) (0.10) (0.43) (0.07) 0.02 (1.77) 1.07 0.15 0.98 0.05 0 .64 1.92 0.97 (0.25) 0.13 (l .oo) 0.32 (0.19) 0.44 3.47 (0.02) (0.02) 0.53 0.08 (O.36) 0.15 10.26 0.93 O.36 0.26 0.31 0 .14 0.07 0.65 0.11 0.13 0 .14 o.o4 0.55 0.06 1.21 0.10 0.12 0.47 0 .46 1.09 0.21 1.27 0.03 0.18 0.02 0.09 0.10 0.47 1 - 2 3 ^ 5 (x) (a) (b) (bx) (a+bx) 6 7 P f = x-(a+bx) Pj 8 ( P a - P f &gt; 29 M i c h i g a n B a k e r i e s , Inc. $ 8 . 3 8 30 Morgan's Inc. 4.76 31 N a t i o n a l Research C o r p o r a t i o n 7.14 32 Nelson (N.O.) Company 1 5 . 6 2 33 Oceanic O i l Company 1 . 8 5 3 4 0 ' S u l l i v a n Rubber Corp. 6 . 3 5 35 Peck, Stow &amp; Wilcox Co. 2.51 36 P l a s t i c Wire and Cable Corp. 1 1 . 4 3 37 Plume &amp; Atwood Manufacturing Co. 10.16 38 P o w d r e l l &amp; Alexander, I nc. 4 . 7 5 39 Queen Anne Candy Co. 2 . 7 3 40 Reis (Robert) &amp; Co. 4 . 8 3 41 R@ymer &amp; Broth e r s Inc. 1.73 42 RiehiDnd Cedar Works 1 .51 43 Rochester &amp; P i t t s b u r g Coal Co. 4 5 . 7 6 4 4 Rock-Ola Manufacturing Co. 5 .97 45 Rudy Manufacturing Co. 9 . 0 3 46 Sandura Company 8 . 6 7 47 Scranton Lace Co. 6 . 0 5 48 Seneca F a l l s Machine Co. 2 . 4 4 49 Shasta Water Co. 2.32 50 Sherman Products, Inc. 5.84 51 Sidney Blumenthal &amp; Co. 2 0 . 2 3 52 S t y l o n Corp. 6 . 4 5 53 U n e x c e l l e d Chemical Corp. 1.04 5 ^ V i c t o r Products Corp. 5 .42 55 Wayne Screw Products Co. 1 .18 56 W i l s o n B r o t h e r s 19 *55 57 Yolande Corp. 2 . 1 9 10.52 0 . 6 5 0 . 0 2 1 .26 0 . 3 4 0 . 1 2 0 . 2 9 0 . 4 3 1 .3\"i 1 .22 0 . 6 9 1 .52 0 . 3 4 0 .27 7 .48 1 .79 0 . 1 9 0 . 7 5 1 .25 0 .31 0 .21 0.3*+ 3.60 0 . 4 9 0 .11 1 . 1 5 0 .18 0 . 1 9 0 .91 0 . 9 0 0.79 1 .00 0.92 0 . 5 1 0.93 0.87 O .83 0.83 0.68 0 . 7 2 0 . 7 0 0.84 0.99 0.79 0.61 0 . 9 1 0.84 0.75 0.71 0 . 9 0 O .78 0.81 0.73 0.99 0.79 0.78 I . 0 3 0.64 $7.54 3.76 7.14 14.37 0.94 5.91 2.18 9.49 8.43 3 .23 1.97 3.38 1.45 1.49 3 6 . 1 5 3.64 8.22 7.28 4.54 1.73 2.09 4.56 16.39 4.71 1.03 4.28 0 . 9 2 20.14 1.40 $ 8 . 0 6 4.41 7 . 1 6 1 5 . 6 3 1 .28 6 . 0 3 2 . 4 7 9 . 9 2 9 . 7 7 4 . 4 5 2 . 6 6 4 . 9 0 1 . 7 9 1 . 7 6 ^ 3 . 6 3 5 A 3 8.41 8 . 0 3 5 . 7 9 2.04 2 . 3 0 4 . 9 0 1 9 . 9 9 5 . 2 0 1.14 5 . 4 3 1 . 1 0 2 0 . 3 3 2 . 3 1 $ 0 . 3 2 o .35 ( 0 . 0 2 ) ( 0 . 0 1 ) 0 . 5 7 0 . 3 2 o .o4 1 .51 0 . 3 9 0 . 3 0 0 . 0 7 ( 0 . 0 7 ) ( 0 . 0 6 ) ( 0 . 2 5 ) 2 . 1 3 0 . 5 4 0 . 6 2 0.64 0 . 2 6 o .4o 0 . 0 2 0 . 9 4 0 . 2 4 1 . 2 5 ( 0 . 1 0 ) ( 0 . 0 1 ) 0 .08 ( 0 . 7 8 ) ( 0 . 1 2 ) |o. 27 $ 0 . 0 5 0 . 0 5 0 . 3 0 0 . 4 9 0 .51 ( 0 . 0 9 ) 0 .08 0 .58 0 . 0 1 0 .08 0 . 2 4 0 . 2 9 0 . 2 5 1.48 0 . 0 3 0 . 0 0 0 . 3 9 0 . 7 3 0 . 4 3 0 . 08 0 . 0 1 0 . 0 6 0 . 1 3 ( 0 . 0 7 ) 0 .01 1 ( 0 . 1 9 ) 0 . 0 6 vO I . 8 7 0 . 2 6 0 . 7 3 0 . 1 9 1 1 . 0 5 0 . 4 3 1 . 0 0 0 . 3 6 ( 0 . 0 9 ) 0 . 3 5 ( 0 . 0 6 ) 0.46 0 . 0 4 0 . 0 2 0 .58 0 . 3 6 0 . 2 7 0 . 0 3 0 . 9 0 0 . 3 5 ( 0 . 1 7 ) 0 . 0 7 ( 0 . 2 2 ) 0 . 2 1 ( 0 . 0 6 ) 0.14 0.14 0 . 9 2 ( 0 . 0 9 ) 0.03 1 6 . 5 1 See Note next page. NOTE: Column 1 = Volume or Sales Revenue 2 = Fixed Costs 3 = Slope of the Trend Line h = Variable Costs 5 = Total Costs 6 = Forecast P r o f i t s 7 = Actual P r o f i t s 8 = Difference between Actual and Forecast P r o f i t s . - 9 6 - operating p r o f i t s and the actual operating p r o f i t s , by the break-even method, fo r the 57 sample firms, t o t a l s $ 1 6 . 5 1 m . The mean difference, i n t h i s case, i s $ 0 . 2 8 9 6 m , that i s , $ 1 6 . 5 1 m divided by 5 7 . On the basis of the r e s u l t s shown i n Tables IV and V, one would be tempted to conclude that the break-even method produces more accurate forecasts than the percentage of sales method. This, however, would be a rather hasty conclusion unless one subjects the r e s u l t s to a test of s i g n i f i c a n c e to determine whether the difference i n the r e s u l t s of the two methods was brought about by chance f a c t o r s . For example, i t may be possible that, i f the sam ple of 57 firms had been picked from a d i f f e r e n t page i n the Tables of Random Numbers, the difference i n the r e s u l t s might have been i n favour of the percentage of sales method or there might not have been any difference i n the r e s u l t s . Therefore, a conclusion regarding the accuracy of the two methods should be arrived at, only a f t e r a test of s i g n i f i c a n c e has been c a r r i e d out. For t h i s t e s t , l e t the symbol, p^ represent the mean difference obtained by the percentage of sales method and p 2 , the mean difference ob tained by the break-even method. I t i s already known that P x i s equal to $ 0 . 4 2 5 7 m and p 2 i s equal to $ 0 . 2 8 9 6 m . As discussed i n chapter I, the best way to go about deter mining whether there i s a s i g n i f i c a n t difference between the two means i s to set up the n u l l hypothesis that p-^  i s - 97 - equal to p 2 and i s also equal to the mean of the universe (' \"Tr ). The r e j e c t i o n of the n u l l hypothesis w i l l mean that there i s a s i g n i f i c a n t difference between the two means, while acceptance of the n u l l hypothesis w i l l mean that there' i s no s i g n i f i c a n t difference between the two means. In order to do t h i s , i t i s necessary to determine the value of z, where z i s the r a t i o of P i ~ P 2 to an estimate of the standard error of the difference between the two sample means. The standard error of the difference between the sample means i s : P l - P 2 where: 6 P 1 - P 2 6 6 f r n In this study, ^ i s not known. I f i t i s known, i t would be better to tes t p^ against ^ and p 2 against ft , rather than to examine the sign i f i c a n c e of Pi-Pg. Since, 2 2 '6 +6 P i ?2 - + n l n 2 = The standard error of the d i f f e r  ence between p^ and p 2 = the standard error of = the standard error of p 2 = mean of the universe = 1 - TT = size of the sample - 98 - i s n o t known, an e s t i m a t e , p, has t o be made f o r i t , based on the i n f o r m a t i o n i n the two samples. Thus: n = P l + P2 ). 4257m + 1 0 .2896m 2 2 * $ 0 . 3 5 7 6 5 m . Under the c i r c u m s t a n c e s , the e a r l i e r f o r m u l a ; o. P l ~ P 2 J n x n 2 now becomes: P l - P 2 V n x n 2 T h i s i s t h e same a s : 6 p i - p 2 = J FC1-F) + s i n c e : p x = $ 0 . 4 2 5 7 m P 2 .= $ 0 . 2 8 9 6 m P\" = $ 0 . 3 5 7 6 5 m and n^ = n 2 = 5 7 - 99 - Therefore: 6 p l \" P 2 * ( 1 ~ P ) ^ + = i | 0 ' 3 5 7 6 5 m ( 1-^\u00B0-35765m) (57- + =ii0O5765m X |0.64235m x ^7 = /|oT2297l+m x $0.03508m =J$o.00806m = $o.08978m P 1-P 2 = $0.4257m - $0.2896m = $0.1361m Since: z - P l \" P 2 A. 6 p l * p 2 Therefore: z = l o ^ ^ l m = 1 ' 5 1 5 6 The determination of the z value, however, alone w i l l not indicate whether the difference between the sample means i s s i g n i f i c a n t or not, unless and u n t i l the c r i t e r i o n of significance has been established. In chapter I, i t was explained that a l e v e l of significance of 0.01 should be used and i t was also pointed out that since, at t h i s l e v e l of significance the value of z i s 2.667, the n u l l hypothesis should therefore be accepted i f z ^ 2.667 and should be rejected i f z &gt; 2.667. I t has already been shown that, i n th i s study the value of z i s equal to 1.5156. Under the circumstances, the n u l l hypothesis should be accepted and the hypothesis should be rejected. On thi s basis, a con cl u s i o n may be drawn that there i s no difference between break-even analysis and the percentage of sales method as a technique for forecasting the future operating p r o f i t s of - 1Q0- f i r m s . B u t , i t must be p o i n t e d o u t t h a t t h i s c o n c l u s i o n does n o t h o l d a t a l l l e v e l s o f s i g n i f i c a n c e . From t h e t - t a b l e i n Appendix I I , i t may be f o u n d t h a t , f o r 57 degrees o f freedom, a t the 0.10 l e v e l o f s i g n i f i c a n c e , the z v a l u e i s e q u a l t o 1.673 and a t t h e 0.20 l e v e l o f s i g n i f i c a n c e , the z v a l u e i s e q u a l t o 1.297* By i n t e r p o l a t i o n , 1.516 becomes t h e v a l u e o f z a t t h e 0.14 l e v e l o f s i g n i f i c a n c e . T h i s means t h a t i f a c r i t e r i o n o f s i g n i f i c a n c e o f more t h a n 0.14 l e v e l o f s i g n i f i c a n c e i s u s e d , t h e d i f f e r e n c e between the two sample means w i l l be s i g n i f i c a n t and t h e n u l l h y p o t h  e s i s t h a t Pi=P2 w i l l have t o be r e j e c t e d and the h y p o t h e s i s t h a t pi_&gt; p 2 w i l l have t o be a c c e p t e d . On t h e o t h e r hand, i f a c r i t e r i o n o f s i g n i f i c a n c e o f l e s s t h a n 0.14 l e v e l o f s i g n i f i c a n c e i s u s e d , t h e r e v e r s e w i l l be t r u e . Summary I t was s t a t e d i n c h a p t e r I t h a t t h e h y p o t h e s i s i s t h a t b r e a k - e v e n a n a l y s i s can be b e t t e r t h a n t h e p e r c e n t a g e o f s a l e s method as a t e c h n i q u e f o r f o r e c a s t i n g the f u t u r e o p e r a t i n g p r o f i t s o f f i r m s and the n u l l h y p o t h e s i s i s t h a t t h e r e i s no d i f f e r e n c e between break-even a n a l y s i s and the p e r c e n t a g e o f s a l e s method as a t e c h n i q u e f o r f o r e c a s t i n g t h e f u t u r e o p e r a t i n g p r o f i t s o f f i r m s . I f t h e r e s u l t s o f t h e f o r e c a s t s o f break-even a n a l y s i s and t h e p e r c e n t a g e o f s a l e s method are n o t sub-- 101 - jected to a test of si g n i f i c a n c e , the conclusion may be drawn that the former produces more accurate forecasts of operating p r o f i t s than the l a t t e r since the mean of the difference between forecast operating p r o f i t s and actual operating p r o f i t s a r r i v e d at by the former i s smaller than that a r r i v e d at by the l a t t e r . The n u l l hypothesis would, therefore, be rejected and the hypothesis would be accepted. But, a conclusion of this nature would be somewhat dubious since chance factors could have caused the difference i n the means obtained by the two methods. A test of significance would c e r t a i n l y lend greater v a l i d i t y to the conclusion. But, unfortunately, the r e s u l t s of tests of si g n i f i c a n c e , depend to a large extent on the c r i t e r i o n of significance chosen. I t was Shown that i f a l e v e l of significance of greater than 0.14 i s chosen, then the difference i n the means obtained by the two methods would turn out to be s i g n i f i c a n t . This would mean a r e j e c t i o n of the n u l l hypothesis and acceptance of the hypothesis. On the other hand, i f a l e v e l of s i g n i f i  cance of les s than 0.14 Is chosen, the difference i n the means obtained by the two methods would turn out to be not s i g n i f i c a n t . This would permit the acceptance of the n u l l hypothesis and the r e j e c t i o n of the hypothesis, as they have been stated. The choice of the l e v e l of significance depends on the type of error that i s to be avoided. In chapter I, - 102 - i t was argued that type error I should be minimised and that a l e v e l of significance of 0.01 should be used. With t h i s argument, the n u l l hypothesis should be accepted and the conclusion i s that there i s no difference between break even analysis and the percentage of sales method, as a technique f o r forecasting the future operating p r o f i t s of firms. CHAPTER V SUMMARY AND CONCLUSION i Summary Break-even analysis i s a management ai d , which shows the e f f e c t of changes i n the l e v e l of a c t i v i t y on costs, revenue and p r o f i t s , assuming that other things are equal and break-even charts are graphic presentations of cost-volume-profit r e l a t i o n s h i p s . In every break-even chart, there i s a break-even point which shows the volume l e v e l at which t o t a l revenue exactly equals t o t a l costs. Break-even charts, however, can also be constructed such that the break even point shows the point of time i n the budgetary period when losses turn into p r o f i t s . These break-even points are useful i n the sense that they are prerequisites to the deter mination of the margin of safety and also because they indicate the portion of the budgetary period that remains for the accumulation of the contributions to p r o f i t s . But, t h e i r usefulness should not be overemphasised, since they do not remain fi x e d f o r long but keep on changing as the fac tors a f f e c t i n g them undergo change. Besides, they are not as exact as t h e i r name seems to suggest. I t i s claimed that break-even analysis can be used by management f o r various purposes. They include p r o f i t projections, cost control, p r i c e determination and - 104 - decision-making involving make or buy problems and c a p i t a l expenditure problems. But i n putting break-even analysis to these uses, various assumptions have to be made. These assumptions are as follows: (a) A l l costs can be reasonably separated into t h e i r f i x e d and variable components and whereas f i x e d costs remain f i x e d at a l l volumes, variable costs vary i n d i r e c t proportion to volume. (b) S e l l i n g prices remain constant at a l l volumes. (c) Production equals or closely follows sales and a l l f i x e d costs incurred i n a period are, therefore, deducted from that period's revenue. (d) There i s only one product or i f several products are being produced and sold, the sales mix w i l l remain con stant. A t e s t was ca r r i e d out to determine the us e f u l  ness of break-even analysis as a technique f o r forecasting p r o f i t s . In t h i s t e s t , break-even analysis was compared with the percentage of sales method. For t h i s test, no adjustments were made to the data, which were taken from Moody's In d u s t r i a l Manuals. I t was found that, at the 0.01 l e v e l of si g n i f i c a n c e , there was no difference i n the accur acy of the forecasts of the tv/o techniques. The hypothesis that break-even analysis can be better than the percentage of sales method as a technique f o r forecasting the future operating p r o f i t s of firms was, therefore, rejected. Conclusion Break-even analysis may be relevant f o r various - 1 0 5 - managerial economic problems. But, i n using break-even analysis many r e s t r i c t i v e assumptions have to be made. The v a l i d i t y of these assumptions varies with firms. In some firms, (a) The t o t a l costs may be predominated by the cost of items whose prices fluctuate widely. (b) There may be a great difference between production volume and sales volume i n any given budgetary period of time. (c) Advertising and sales promotion may be very important and highly s h i f t a b l e . (d) Many products may be produced and sold. These products may have d i f f e r e n t margins of return over variable costs and the sales mix may vary greatly. (e) The product design or technology may change continuously over short periods. For such firms, the r e s t r i c t i v e assumptions are obviously very u n r e a l i s t i c . I f break-even analysis i s used, the r e s u l t s obtained w i l l be so inaccurate that they w i l l be v i r t u a l l y useless. Under the circumstances, management must either t o t a l l y abandon the break-even device or make adjustments to overcome the l i m i t a t i o n s of the assumptions. Fortunately, not a l l firms are faced with these two a l t e r  natives. In some firms, even without adjustments, the assumptions are quite r e a l i s t i c and more accurate fore casts can be made. In the te s t i n t h i s t h e s i s , i t was found that the percentage of sales method i s as r e l i a b l e as break-even an a l y s i s , as a technique f o r forecasting p r o f i t s . But, i t - 106 - must be emphasised that i n the te s t , i n forecasting p r o f i t s by the break-even method, no adjustments were made to the data. Hence, any conclusion drawn, based on the te s t , has to be r e s t r i c t e d to situations i n which no adjustments are made. On the basis of t h i s study, i t may be concluded that management should use the percentage of sales method instead of break-even analysis to forecast p r o f i t s , i f i t i s not prepared to adjust i t s data to recognise the effects of changes i n the determinants of p r o f i t s , other than volume. On the other hand, i f management i s prepared to make the adjustments, i t i s only possible to state, as f a r as t h i s study i s concerned, that the forecasts by the break even technique w i l l now be more accurate than i f adjust ments were not made; but i t i s not possible to state whether they w i l l be better than those by the percentage of sales method. Further, i f adjustments are to be made, management must also r e a l i s e that some of the advantages of break-even analysis, p a r t i c u l a r l y s i m p l i c i t y and quickness of prepar ation, have to be s a c r i f i c e d . Hence, i f the managerial s t a f f i s pressed f o r time or i f the funds of the firm are l i m i t e d , i t may be advisable not to use break-even analysis altogether. The increase i n the accuracy, as a r e s u l t of the adjustments, may not j u s t i f y the increase i n expense, time and e f f o r t that would be required, though i t i s recog nised that other managerial functions such as planning, - 107 - p r i c e - s e t t i n g and preparation of budgets also require the analysis of cost behaviour and adjustments so that the add i t i o n a l expense, time and e f f o r t i n making the adjust ments, may not be very great. On the whole, i t may be said that t h i s study has a negative approach i n the sense that i t merely shows the circumstances under which break-even analysis should not be used. But, i t does not, i n any way, suggest the circum stances under which i t would be worthwhile to use the technique. With the co-operation of some firms, further research may be ca r r i e d out to determine the usefulness of break-even analysis, i f adjustments are made. - 1 0 8 - BIBLIOGRAPHY A. BOOKS Anderson, David R. P r a c t i c a l C o n t r o l l e r s h i p , Homewood, I l l i n o i s : R i c h a r d D. Irwin, Inc., 1 9 5 4 . Anthony, R. N. Management A c c o u n t i n g : Text and Cases. Homewood, I l l i n o i s : R i c h a r d D. Irw i n , Inc., 1 9 5 6 . Bierman, H a r o l d . M a n a g e r i a l Accounting, New York: The M a c M i l l a n Company, 1 9 5 9 . C r o w h i n g s h i e l d , G e r a l d R. 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APPENDIX I TABLE OF RANDOM SAMPLING NUMBERS Twenty-Third Thousand 1-- 4 5 - 8 9-\u202212 1 28 0 7 3 0 0 2 k3 2 46 8 0 6 6 58 1 3 64 3 04 9 0 1 7 0 3 3 2 0 1 4 1 0 63 6 1 17 17 7 9 5 3 6 2 6 0 7 9h 49 6 0 3 8 7 32 59 3 6 7 1 8 K5 7 6 8 6 1 0 3 0 8 3 9 0 1 8 0 V- 2 3 85 9 9 1 0 3 . 4 7 8 5 78 1 0 7 0 7 5 1 1 2 6 7 1 0 0 1 1 1 6 2 5 8 1 6 1 0 5 68 1 2 8 2 9 6 53 7 7 72 40 1 3 1 0 18 8 3 3 9 5 4 V&gt; 14 9 5 5 2 5 2 18 ? 2 6 1 1 5 2 0 7 1 1 9 8 7 3 ^ 8 9 1 6 14 3 7 9 5 9 0 K5 64 17 7 0 57 x 3 1 0 ^3 57 68 1 8 1 6 3 1 57 1 6 4 4 1 9 8 8 48 41 4 4 8 5 5 2 2 0 2 3 3 1 08 29 1 9 8 6 2 1 9 0 4 4 9 0 ^3 4 2 48 2 2 0 9 1 8 24 51 1 7 14 2 3 6 7 9 0 64 98 8 0 9 1 2 4 84 42 3 0 7 0 6 9 2 3 2 5 8 9 3 6 08 56 1 7 7 7 1 3 - 1 6 0 6 4 7 1 6 9 6 2 0 58 6 2 14 2 2 3 0 9 2 7 6 0 7 38 9 4 84 8 1 7 0 64 1 0 7 6 4 2 98 6 9 1 9 3 5 4 3 0 2 0 1 8 8 0 4 0 3 0 2 3 2 7h 3 3 4 5 1 1 64 57 1 5 8 8 9 9 6 1 4 3 6 1 51 7 3 9h 1 3 17- - 2 0 2 1 --24 68 07 7 5 98 7 9 41 0 5 51 1 1 18 6 6 5h 6 5 0 9 7 3 04 19 2 3 9 3 0 6 78 0 5 3 6 9 0 4 4 2 2 6 3 56 1 1 3 3 3 1 3 1 3 7 2 3 84 3 3 6 2 7 2 1 6 3 8 2 1 9 0 2 6 * 3 13 2 6 24 3 6 8 8 2 5 2 4 0 1 14 0 6 6 6 3 0 7 5 68 9 9 1 7 5h 8 6 ^3 1 5 04 27 1 3 7 9 2 6 4 9 9 7 0 1 7 6 7 5 9 0 6 7 08 5 * 9 2 7 0 0 2 2 9 2 3 2 9 7 4 5 2 84 3 5 59 7 5 6 1 1 9 6 2 1 2 8 1 9 2 1 6 43 3 ^ 8 2 2 5 - 2 8 2 9 - 3 . 2 3 3 - 3 6 3 7 - 4 0 81 2 2 5 2 4 2 9 3 0 1 6 6 7 9 74 7 3 3 9 0 9 64 4 5 3 3 9 5 1 3 7 9 14 7 0 6 6 4 5 24 53 8 9 3 1 4 9 9 5 8 1 9 2 9 1 0 8 57 68 3 1 1 2 48 9 3 84 5 5 7 9 5 2 0 7 4 7 2 5 9 9 7 5 2 7 3 7 p i 29 4 4 4 8 0 7 5 5 8 8 5 0 25 5 9 5 4 0 0 5 9 84 7 7 2 3 2 9 1 6 89 0 2 4 4 5 4 4 3 V P 8 7 6 9 7 7 K5 8 1 6 6 9 1 5 2 7 9 0 2 5 9 6 2 9 7 0 9 8 7 51 7 0 7 5 9 2 6 5 46 28 3 7 0 9 14 7 7 53 0 4 8 8 1 0 9 4 3 ^ 38 3 6 3 1 64 6 1 1 6 1 1 78 7 7 8 3 1 0 3 7 P r 8 9 6 1 7 7 2 6 7 1 9 1 6 7 0 3 64 1 9 8 2 1 6 9 0 57 9 9 1 1 7 2 3 9 9 9 51 6 9 6 6 0 0 1 0 2 3 5 9 1 2 9 7 4 9 4 9 9 1 46 8 7 0 6 27 2 0 6 6 23 3 4 8 2 hh 7 5 3 0 6 5 7 5 1 1 0 2 3 9 41 56 0 0 1 2 7 1 7 9 3 8 7 3 14 7 1 31 43 8 0 3 3 3k 67 59 9+ k5 1 3 8 8 81 6 0 9 6 24 3 4 0 4 1 5 8 3 2 4 1 2 I 5 6 9 10 11 12 ll ll 17 18 19 20 21 22 i 2 5 1-4 65 99 91 93 60 31 89 76 31 93 *+9 95 14 03 08 40 61 52 49 74 43 09 76 51 58 86 37 81 89 07 92 12 16 31 87 14 66 18 88 99 36 42 69 30 09 24 5-8 05 25 27 47 75 41 42 80 81 18 91 68 16 42 33 20 76 52 96 14 43 78 69 27 13 36 25 20 38 07 07 33 56 | 5 43 89 96 77 56 15 44 68 63 64 88 02 71 10 24 75 9-12 79 76 25 39 82 92 \u00A5 P 89 89 25 51 38 76 90 83 07 49 90 02 24 8 5 69 18 60 03 45 09 05 96 29 09 77 52 80 02 42 60 86 18 49 91 42 21 00 72 99 12 99 09 Twenty-fourth Thousand 13-16 17-20 21-24 25-28 29-32 33-36 37-40 15 67 67 95 09 98 35 10 66 35 63 86 92 82 25 87 M 53 50 85 32 60 95 20 21 65 31 56 28 5k- 31 73 58 09 28 72 11 20 07 91 61 99 77 13 84 20 57 08 80 89 38 73 H4 47 49 63 19 74 67 64 27 03 11 M8 41 52 50 09 32 15 37 10 69 68 58 35 83 95 13 41 06 70 83 88 85 97 h-7 31 18 3^ 66 24 21 02 68 14 64 47 41 96 67 82 51 3; 5 61 7h 89 46 51 01 6 99 85 91 _ S7 56 85 09 M + 84 07 68 65 29 66 44 56 65 05 82 86 66 87 36 89 05 79 85 06 51 06 68 83 18 77 20 11 18 51 10 67 79 5h 97 73 71 55 25 30 17 25 21 01 31 02 41 21 12 87 10 83 07 97 15 10 81 33 15 11 86 82 43 88 80 61 57 51 3^ 83 29 87 43 76 08 31 13 13 69 75 20 51 24 91 02 06 66 81 53 32 25 65 00 81 24 69 98 56 28 44 21 22 70 7h 03 4 6 65 13 89 91 95 25 09 09 15 07 49 7h 78 52 80 68 26 38 17 36 12 02 h) P 06 82 01 5^ 21 10 00 05 33 74 65 96 53 70 78 64 60 74 07 99 46 66 56 46 77 79 82 26 19 16 81 13 84 39 1 H H Source s M. G. Kendall and B. B. Smith, Tables of Random Sampling Numbers. Tracts fo r Computers N o. XXIV. Cambridge: Cambridge University Press, 1951, p. 15. - 116 - APPENDIX II VALUES OF t FOR GIVEN DEGREES OF FREEDOM (n) AND AT SPECIFIED LEVELS OF SIGNIFICANCE LEVEL OF SIGNIFICANCE n ,\u2014 i , , , U y n 0.10 0.05 0.02 0.01 0.20 1 3.078 2 1.886 3 1.638 4 1-533 5 1.476 6 1.U40 7 1.415 8 1.397 9 1.383 10 1.372 20 1.325 ?\u00B0 1.310 40 1.303 6o 1.296 100 I.289 00 I.282 6.314 12.706 31.821 63.657 1 2.920 4.303 6.965 9.925 2 2.353 3.182 4.541 5.841 3 2.132 2.776 3.747 4.604 4 2.015 2.571 3.365 4.032 5 1.943 2.447 3.143 3.707 6 1.895 2.365 2.998 3.^ 99 7 1.860 2.306 2.896 3.355 8 1.833 2.262 2.821 3.250 9 1.812 2.228 2.764 3.169 10 1.725 2.086 2.528 2.845 20 1.697 2.042 2.457 2.750 1.684 2.021 2.423 2.704 1.671 2.000 2.390 2.660 60 1.658 I.98O 2.358 2.617 120 1.645 1.960 2.326 2.576 00 Source: Frederick E. Croxton and Dudley J . Cowden, Applied Gen  e r a l S t a t i s t i c s . New York: Pre n t i c e - H a l l , Inc.,1955, PP. 750-751, Appendix I. APPENDIX III OPERATING REVENUE (In millions of do l l a r s ) Name of Company 1 9 5 5 195 -^ 1 9 5 3 1 9 5 2 1951 1 9 5 0 19^9 1948 19^7 1946 1 Auto-Soler Co. 1.56 1.76 2.68 2.33 2 . 3 2 1.17 0 . 0 8 1.08 1.14 1 . 0 7 2 Balsa Chica O i l Corp. 0.97 0 . 8 9 O .76 0 . 7 1 0.78 0.87 O . 6 9 1.76 0.58 0.48 3 Bausa Machine Tool Company 1 . 8 0 3 . 5 2 3.88 5.66 3.61 1.87 I . 6 3 2 . 0 7 1 . 2 6 1 . 3 1 4 B e l l Company 8 . 2 0 1 1 . 5 2 14.53 14.85 16.68 15.9h 13 .44 _ 5 Bischop &amp; Babcock Mfg. 3A7 Co. 8.75 h.99 7 . 2 0 6 . 2 2 3 . 1 6 2.98 4 . 2 4 7.17 2.35 6 Brown McLaren Mfg. Co. 1 . 1 2 1 . 2 9 2 . 4 0 1 .91 1.55 1.18 0 .65 O . 8 3 O . 8 2 0.69 7 Carpenter (L.E.) &amp; Co. 6.65 h.95 4.48 5.96 7.14 3 . 3 1 2 . 0 2 2.58 2 . 1 1 3 . 9 0 8 Chief Consolidated Mining Co. 1 . 0 6 1 . 3 6 0 . 9 1 1.33 1.35 1.59 I . 6 3 1 . 9 8 1 . 1 9 0 . 9 5 9 Cleveland-Sandusky 1.45 1.42 1 . 2 8 Brewing Corp. 1.35 1 . 2 7 1.72 1 . 2 7 1 . 1 2 1 . 4 5 1 . 2 8 1 0 Consolidated Ret a i l Stores Inc. 26 .49 25 .75 2 8 . 1 3 3 0 . 0 2 2 9 . 7 2 29 .24 3 1 . 5 1 35.65 31 .59 3 1 . 6 2 1 1 Copper Tire and Rubber Co. 2 3 . 6 3 1 5 . 0 3 2 2 . 9 5 1 7 . 0 6 17.71 1 3 . 2 7 5.94 7.77 1 1 . 0 8 1 1 . 0 2 1 2 Curtis Lighting 2.64 2.55 1.87 O .98 3 . 0 4 2 . 6 0 I . 6 9 2.74 2.58 2 .21 1 3 Davega Stores Corp. 2 3 . 8 2 24 .75 2 6 . 3 8 2 6 . 3 1 28 .84 2 4 . 3 6 24 .75 2 3 . 3 1 2 1 . 1 0 \u2014 14 Diamond Motor Car Co. 37.93 25 .83 8 2 . 1 1 79.93 5 0 . 0 6 2 7 . 0 9 2 1 . 2 8 37.47 41.68 2 2 . 6 9 1 5 Dixon (Joseph) Crumble Co. 11.63 1 0 . 0 0 IO . 3 8 9 . 6 2 11 .55 9 . 0 1 7 . 2 4 8 . 8 0 1 0 . 0 4 9 . 9 ^ 1 6 E &amp; B Brewing Co.Inc. 1 . 2 8 1 . 6 1 1.57 1.37 . 7 0 O .76 0 .79 0 . 5 6 0 . 9 7 1 . 3 2 1 7 Flagg U t i c a Corporation 1 7 . ^-2 1 5 . 9 2 1 8 . 2 3 13-41 - - \u2014 - \u2014 1 8 F l o t i l l Products Inc. 17 .23 1 8 . 1 9 1 7 . 0 0 1 3 . 2 6 1 5 . 1 1 14 .29 8 . 6 2 8.46 \u2014 _ 1 9 Flour M i l l s of America, Inc. 37.55 3 8 . 6 3 62 .93 108.14 93.64 80 .58 1 1 5 . 3 0 97 .29 54 .70 28 .08 2 0 Gerotor May Corpor 1.84 4 . 3 0 a t i o n 1 . 3 0 4.88 4 . 8 1 2.35 1.97 1.66 2 . 5 8 1 . 8 8 2 1 Globe America Corpor 8 . 7 1 8.39 a t i o n 4.85 6 . 8 0 7 . 5 0 7.59 5.66 1 0 . 0 6 6 . 0 7 1.88 Name of Company 1 9 5 5 195^ 1 9 5 3 1 9 5 2 1 9 5 1 1 9 5 0 1 9 ^ 9 1948 1 9 4 7 1 9 4 6 2 2 Gum Products Inc. 2 . 1 1 2 . 2 9 2 . 0 2 1 . 9 5 2 . 4 9 2 . 2 0 2 . 5 8 4 .32 2 3 Hathaway Bakeries, Inc. 2 2 . 7 3 2 3 . 9 4 2 6 . 3 0 2 7 . 6 2 27.88 2 7 . 3 0 2 6 . 1 9 2 5 . 8 0 2 2 . 1 1 1 9 . 7 8 24 H i l l e r Helicopters 7 . 7 4 6 . 3 5 1 0 . 3 7 14.40 6.66 - 2 5 Jacob Rupert 4 9 . 1 2 5 2 . 5 1 5 7 . 2 2 4 9 . 8 3 3 8 . 8 1 3 0 . 3 1 2 5 . 8 0 3 9 . 7 6 4 3 . 7 3 3 8 . 6 3 2 6 J e a n n e t t e Glass Company 5 . 1 4 4 . 6 2 4 .66 4 . 3 3 4-. 41 3 . 4 2 2 . 7 1 2 . 8 2 3 . 7 3 5 . 5 2 2 7 Jessop Steel Co. 1 6 . 4 0 1 1 . 3 8 1 5 . 5 8 1 6 . 5 3 1 5 . 2 3 8 . 3 2 6 .44 8 . 8 9 1 1 . 3 3 1 1 . 2 5 28 Lanston Industries Inc. 2 . 9 8 4 . 0 0 3 - 5 8 3 . 1 4 3 . 3 3 3 . 1 3 3 . 8 8 3 . 6 6 2 . 1 0 2 . 4 6 2 9 Longchamps Inc. 7 - 7 8 7 . 9 9 8 . 7 7 7 . 7 8 7-66 7 . 9 0 8 . 2 9 8 . 2 0 3 0 MacMillan Petroleum Corp. 1 3 . 7 1 1 4 . 0 1 1 6 . 4 0 1 5 . 9 5 14-.20 1 1 . 8 4 9 . 4 8 1 1 . 0 5 9 . 6 3 9 . 0 0 3 1 Maguire Industries,Inc. I.98 I . 7 6 2 . 1 4 2 . 3 3 2 . 9 6 2 . 7 0 2 . 6 8 3 . 6 O 3 2 Mandel Brothers Inc. 3 2 . 1 7 3 0 . 7 0 3 0 . 5 5 3 2 . 0 4 3 4 . 2 9 3 3 . 9 8 3 5 . 6 3 3 6 . 3 3 3 5 . 0 7 2 7 . 4 8 3 3 Merrimac Hat Corp. 2 . 6 0 5 . 9 9 6 . 9 5 7 . 2 5 7 . 6 8 8 . 7 8 8 . 5 8 8 . 8 0 1 1 . 9 3 1 3 - 5 5 3 4 Michigan Bakeries,Inc. 7 . 7 6 7 . 2 6 6 . 0 9 5 . 5 1 4 . 8 4 4 . 2 5 3 . 9 2 4 . 3 3 3 5 Mohawk Liquer Corp. 3 . 9 1 3 . 6 1 3 - 7 2 3 . 2 2 2 . 9 2 2 . 5 2 2 . 9 6 2 . 7 5 1 . 7 5 3 . 8 0 3 6 Morgan's Inc. 4 . 4 3 3 . 3 1 3 . 2 9 2 . 2 2 1 . 3 0 2 . 2 8 2 . 8 9 3 . 9 5 4 . 0 2 3 . 0 7 3 7 National Research Corp. 4 . 2 3 H-.63 3 . 5 3 H-.12 2 . 8 2 1 . 2 9 1 . 4 1 1 . 1 6 O . 9 7 1 . 3 2 38 Nelson (N . 0 . ) \"Company 1 7 - 7 2 1 5 . 6 4 2 . 6 8 2 . 9 9 H-.19 4 . 3 0 2 . 8 1 4 . 2 9 3 9 New England Box Company 4.04 3 . 6 6 5 . 5 5 6 . 5 5 7 . 1 9 6 . 7 5 5 . 2 6 6 . 6 9 7 . 3 6 6 . 1 2 40 Oceanic O i l Company 1 . 8 8 2 . 0 5 1 . 0 9 0 . 8 1 0 . 9 1 - 41 0 \u00BB S u l l i v a n Rubber Corp. 6 . 4 8 6 . 6 l 6 . 8 4 6 . 6 1 6 . 2 9 5 . 9 2 3 . 9 7 3 . 0 3 4 . 3 8 6 . 2 0 42 Peck Stow &amp; Willox Co. 2 . 2 0 4 . 3 3 5 . 0 0 5 . 0 0 5 . 0 9 4 . 1 3 4 . 0 8 5 . 1 3 4 3 P l a s t i c Wire and Cable Corp. 8 . 5 1 6 . 2 0 8 . 5 7 9 . 4 0 6 . 0 6 2 . 9 2 2 . 0 3 2 . 3 1 3 . 0 5 2 . 2 1 4 4 Plume &amp; Atwood Mfg.Co. 9 . 6 3 9 . 1 4 1 0 . 5 1 8 . 2 7 1 0 . 0 6 8 . 8 2 5 . 4 6 6 . 7 3 6 . 7 0 4 5 Powdrell &amp; Alexander Inc.6 . 1 9 7 . 5 1 1 2 . 8 9 1 5 . 9 5 1 7 . 8 3 2 1 . 6 2 1 8 . 3 1 2 3 . 0 6 21.89 2 0 . 5 7 46 Queen Anne Candy Co. 2 . 8 4 3 . 2 7 3 . 5 1 3.5*+ 3 . 0 7 3 . 1 5 3 . 0 5 2 . 0 3 2 . 9 2 3 . 3 4 4 7 Reis (Robert) &amp; Co. 4 . 6 5 H-.23 4 . 8 2 4 .41 4 . 8 4 4 . 6 9 4 . 4 9 6 . 1 6 7 . 5 9 9 . 0 9 48 Reymer &amp; Brothers Inc. 2 . 2 5 2 . 1 0 2 . 6 8 2 . 9 0 2 . 4 l 2 . 3 7 2 . 5 9 2 . 4 7 2 . 4 6 2 . 2 2 4 9 Richmond Cedar Works 1 . 6 5 1 . 6 8 2 . 8 7 2 . 46 2 . 8 5 2 . 2 7 2 . 7 5 -Name of Company 1 9 5 5 1 9 5 4 1 9 5 3 5 0 Rochester &amp; Pittsburg Coal Co. 3 8 . 1 0 3 1 . 8 0 41.95 51 Rock Ola Mfg. Corp. 4 . 8 l 4 . 7 6 3 - 2 8 5 2 . Ronson Corporation 28 .95 24 .42 26.48 5 3 Rudy Mfg. Company 3 . 6 2 3 . 2 6 3 \u00AB 5 6 5 4 Sandura Company 4 . 7 6 3 . 5 6 3 .84 5 5 Scranton Lace Company 6.41 5 . 8 2 6 . 6 5 5 6 Seneca F a l l s Machine C o . 1 . 6 0 3.46 4 . 0 7 57 Shasta Water Company 2.65 1.93 0 . 5 4 58 Sherman Products, Inc. 4 . 3 1 3 . 5 6 3 . 7 3 59 Sidney Blumenthal &amp; Co. Inc. 2 2 . 7 ^ - 18 .49 24 .19 6 0 Standard Commercial Tobacco Inc. 5-39 3 . 5 6 12 .84 6 1 Stylon Corp. 6 . 0 5 3 - 9 0 2 . 1 6 6 2 1 2 t h Street Store 3 . 7 7 3 . 6 5 4 . 1 2 6 3 Unexcelled Chemical Corp. 1 . 2 1 4 . 6 8 8 . 4 5 64 V i c t o r Products Cor poration 6 . 0 6 6 . 6 3 8.40 6 5 Wayne Screw Products Co. 1 .64 1 . 1 1 1 . 8 2 6 6 Wilson Brothers 2 0 . 3 9 1 9 . 5 1 2 1 . 1 0 6 7 Yolande Corporation 2 . 2 3 2 . 2 9 2 . 7 8 1 9 5 2 1 9 5 1 1 9 5 0 1 9 4 9 1 9 4 8 1 9 4 7 1 9 4 6 42 .76 3 . 7 9 28 .46 2.14 5 . 3 5 7 . 0 2 3 . 7 2 0 . 4 7 3 A 3 12 .46 1 . 2 5 4 . 5 7 6 . 3 5 7 . 8 2 1 . 6 8 2 1 . 1 1 2 . 2 6 4 7 . 8 8 4 . 1 5 3 ^ . 6 3 2 . 2 1 4 . 4 3 6 . 9 7 2 .64 0 . 7 7 2 . 2 6 2 . 3 5 2 . 1 5 4 . 8 2 3 . 6 0 8 .49 1.96 24 .09 2 . 8 2 4 5 . 7 7 5 . 2 2 3 2 . 5 0 2 . 7 6 7 . 1 3 6 . 6 0 1 . 1 0 0 . 7 6 1 . 0 3 2 5 . 9 6 3 1 . 3 4 2 1 . 8 5 3 . 1 5 5T08 2 . 7 2 9 . 5 9 1.32 2 1 . 8 8 2 . 7 3 5 . 1 5 3 2 . 1 3 I . 8 7 4.92 6 .84 0 . 7 5 0 . 8 9 1 . 7 5 1 5 . 8 9 4 . 4 9 5 . 2 7 2 . 3 8 8 .14 0 . 9 9 1 6 . 7 3 2 . 8 5 VI2 2 8 . 8 2 2.65 3.86 9 . 0 8 O . 6 3 0 . 9 2 2 . 5 1 21 .85 3..26 5^65 3.85 10.81 1.21 16 .42 3.47 8 . 1 2 1 8 . 1 8 2 . 3 6 7 . 1 0 0 . 7 7 1 . 1 2 2 . 1 2 2 1 . 9 4 6 . 6 6 5^74 4 . 8 3 1 0 . 0 7 1 . 3 0 I 6 . 9 6 3 . 5 4 3 . 9 5 1 1 . 0 0 1 . 3 9 5T26 0 . 1 3 1 . 1 3 1 . 1 5 2 2 . 2 6 1 6 . 1 3 5 . 3 7 6 . 1 6 5 . 7 0 1.03 1 3 . 2 8 2 . 8 5 APPENDIX IV OPERATING COSTS ( i n millions of d o l l a r s ) Name of Company 1 9 5 5 1954 1 9 5 3 1 9 5 2 1 9 5 1 1 9 5 0 1 9 4 9 1948 1947 1946 1 Auto Soler Company 1.55 2.24 1 . 9 6 2 . 0 1 1 . 0 9 0.84 0.97 0.89 0.84 2 Balsa Chica O i l Corp. 1.08 0.96 0.74 0 . 7 2 0.68 1.08 0 . 7 2 0 . 8 0 0.57 ,0.39 3 Baush Machine Tool Company 1.77 3 . 0 8 3.10 4.54 2 . 9 6 1.61 1 . 5 5 1.93 1 . 3 1 1.88 4 B e l l Company 9.49 1 3 . 1 2 14 . 1 6 15.69 1 5 . 9 0 1 3 . 7 2 1 2 . 1 3 - \u2014 _ 5 Bishop &lt;&amp;f Babcock Mfg.Co, . 8.29 5 . 0 7 6.67 5.97 3-53 3- 2\u00A3 2 . 8 3 3.79 7 . 0 7 2.37 6 Brown McLaren Mfg. Co. 1 . 2 3 1.36 2 . 1 1 1.59 1 . 2 8 1.08 0 . 6 7 0.84 0.81 0 . 6 8 7 Carpenter (L.E.) &amp; Co. 6.42 4 . 8 2 4.33 5.88 6 . 8 3 3 . 2 8 2.21 2.81 2.77 3.67 8 Chief Consolidated Mining Co. 1 . 2 2 .35 1 . 1 5 1.18 1 . 6 2 1.57 1 . 4 0 1.75 1.14 0.85 9 Cleveland-Sandusky 1.46 1 . 1 8 Brewing Co. 1.41 1 . 2 6 1 . 1 5 1.61 1 . 2 6 1 . 2 2 1 . 0 9 1 . 0 7 1 0 Consolidated R e t a i l Stores Inc. 2 8 . 2 1 25.97 27.68 29.42 2 8 . 0 3 2 8 . 1 9 30.20 33.34 29.43 2 9 . 0 4 11 Cooper Tire and Rubber Co. 2 2 . 7 1 14.84 21.93 16.77 16.65 1 2 . 1 6 6 . 2 2 7 . 8 0 IO . 7 6 9.92 1 2 Curtis Lighting 2 . 7 1 2.57 2 . 0 7 1.08 2 . 8 8 2.44 1 . 6 1 2.45 2.34 1.93 1 3 Davega-Stores Corp. 2 4 . 2 0 2 5 . 0 1 26.21 2 6 . 1 6 27.47 23.35 23.57 21.57 19 . 0 1 14- Diamond T. Motor Car.Co, .37.71 2 6 . 3 2 8 0 . 2 5 77 . 6 1 48 . 2 2 26.59 2 1 . 0 9 35.68 3 8 . 6 3 21.46 1 5 Dixon (Joseph) Crumble Co. 10.76 9.4o 10.04 9.56 11 . 0 0 8 . 6 1 7 . 2 8 8.67 9.84 9.37 16 E &amp; B Brewing Co. Inc. 1.30 1.4o 1.29 8.87 0 . 5 0 I . 0 9 1 . 0 2 0.86 1.90 0.80 17 Flagg U t i c a Corporation 16.88 16.09 1 8 . 1 0 14.56 mm _ \u2014 _ \u2014 18 F l o t i l l Products 5 Inc. 15.87 17.46 1 6 . 9 6 13.57 13.44 1 2 . 1 7 9 . 0 7 9 . 7 2 \u2014 \u2014 1 9 Flour M i l l s of America, Inc. 38.34 39.20 6 8 . 0 2 107.85 92.79 79 . 3 6 : 1 1 3 . 3 0 93.47 50.44 28.88 2 0 Gerotor May Corp. 1 . 7 1 2 . 2 2 4 . 0 9 4 . 3 6 4.41. 4 . 2 5 2.06 2.04 2.66 2 . 0 0 2 1 Globe America Corp. 6 . 0 2 7 . 2 1 8 . 1 2 6.88 7.53 6 . 6 3 5 . 2 7 9 . 2 6 6 . 2 1 2 . 5 0 Name of Company 1 9 5 5 1 9 5 4 1 9 5 3 2 2 Gum Products Inc. I . 9 8 2 . 1 7 1 . 9 0 2 3 Hathaway Bakeries Inc. 2 3 . 2 1 24 . 2 6 2 5 . 0 2 24 H i l l e r Helicopters 7 . 7 7 6.46 9 . 7 0 2 5 Jacob Ruppert 4 9 . 0 2 5 1 . 5 9 5 6 . 1 6 2 6 Jeannette Glass Company 4 . 7 6 4 . 3 0 4 . 2 2 2 7 Jessop Steel Co. 1 4 . 6 7 1 1 . 1 9 14.06 28 Lanston Industries,Inc. 3.14 4 . 4 5 3 . 2 0 2 9 Longchamps Inc. 8 . 0 2 7.64 8 . 6 1 3 0 MacMillan Petroleum ' Corp. 1 3 . 5 5 1 3 . 9 5 1 6 . 4 5 3 1 Maguire Industries,Inc. 1 . 9 4 1 . 6 6 2 . 1 6 3 2 Mandel Brothers Inc. 3 2 . 7 7 3 1 . 9 1 3 1 . 8 5 3 3 Merrimac Hat Corp. 2 . 6 9 5 . 8 2 6 . 8 2 3 4 Michigan Bakeries,Inc. 7 . 5 2 7 . 2 0 6 . 1 3 3 5 Mohawk Liquer Corp. 3 . 7 1 3.43 3.44 3 6 Morgan's Inc. 4 . 3 1 3.3* 3 . 2 8 3 7 National Research Corp. 4 . 7 3 4 . 5 4 3 . 5 3 3 8 Nelson (N . 0 . ) Company 1 7 . 5 6 1 5 . 8 5 2 . 7 2 3 9 New England Box Company 3 . 8 3 3 . 6 7 5 . 4 4 4 0 Oceanic O i l Company 1.40 1 . 2 8 0 . 9 1 41 0 ' S u l l i v a n Rubber Corp. 6 . 4 3 6 . 2 7 6 . 5 3 42 Peck Stow &amp; Wilcox Co. I . 9 6 4 . 5 2 4 . 5 1 4 3 P l a s t i c Wire and Cable Corp. 7 - 7 6 5 . 5 9 7 . 5 7 4 4 Plume &amp; Atwood Mfg. Co. 9 . 9 1 9 . 0 8 9 . 8 6 4 5 Powdrell &amp; Alexander Inc. 5 . 8 9 8 . 5 6 1 3 . 5 5 46 Queen Anne Candy Co. 2 . 7 2 3 . 1 2 3 . 2 5 4 7 Reis (Robert) &amp; Co. 4 . 5 5 4.23 4 . 8 2 4 8 Reymer &amp; Brothers Inc. 2 . 2 5 2.28 2 . 6 7 4 9 Richmond Cedar Works 1 . 6 6 I . 3 9 3 . 2 3 5 0 Rochester &amp; Pittsburg Coal Co. 3 7 . 7 1 3 2 . 4 3 4 0 . 5 4 51 Rock Ola Mfg. Corp. 4 . 4 4 4 . 4 9 3 . 8 1 1 9 5 2 1 9 5 1 1 9 5 0 1 9 4 9 1 9 4 8 1 9 4 7 1 9 4 6 2 . 4 0 2 6 . 7 0 12.42 4 8 . 5 6 3 . 9 9 1 3 . 8 3 2 . 7 0 7 . 7 1 1 5 . 3 4 2 . 0 6 3 3 . 1 1 7 . 1 2 5 . 6 6 3 . 2 0 2 . 2 3 3 . 9 7 2 . 7 3 6.41 O .87 6 . 2 4 4.40 7 . 9 4 8 . 2 6 1 6 . 9 8 3 . 2 6 4.41 2 . 7 5 2 . 5 5 2 . 1 9 2 6 . 9 2 6 . 1 1 3 9 . 0 6 4 . 3 5 1 2 . 5 6 2 . 6 0 7 . 4 5 13.41 2.72 3 3 . 7 8 7.48 4 . 7 9 2 . 8 3 1 . 7 6 2 . 4 0 3 . 9 1 6.84 0 . 6 2 5 . 8 2 4 . 5 1 5.23 9 . 2 6 17.64 2 . 8 7 4.84 2.42 2 . 5 9 2 . 5 3 2 5 . 9 2 3 2 4 6 3 . 4 9 7 . 7 4 2 . 4 7 7.46 1 1 . 6 5 2 . 9 4 3 4 . 0 2 8 . 5 2 4 . 1 5 2 . 3 9 2 . 4 7 1 . 3 3 2 . 6 1 6.41 5 ? 4 4 3 . 8 9 2 . 7 9 8 . 5 4 2 0 . 6 7 2 . 8 5 4 . 6 9 2 . 3 8 2 . 2 1 3 . 0 7 2 5 . 0 5 2 8 . 0 3 2 . 8 0 7 . 2 9 2 . 7 0 7 . 9 3 9 . 6 0 3 . 4 7 3 5 . 0 5 8.41 3 . 7 1 2 . 9 2 3 . 0 6 1 . 3 4 2 . 1 9 5.27 4 . 0 0 4 . 1 3 2 . 1 1 6 . 2 3 1 8 . 6 0 2 . 9 2 4 . 4 9 2 . 5 8 2 . 6 1 4 . 7 3 24 . 3 0 3 9 . 7 6 2.84 9 . 5 1 2 . 3 8 7 . 9 7 10.40 4.41 3 5 . 4 7 8 . 7 9 4 . 0 6 2 . 6 1 3 . 7 1 1 . 1 8 2 . 5 6 6 . 1 6 2 . 8 9 4 . 6 7 2 . 3 4 6 . 6 2 2 0 . 3 7 2 . 1 0 6 . 1 6 2 . 3 6 21.24 1 8 . 3 9 4 2 . 8 5 3 5 . 8 0 3 . 3 1 4 . 1 7 1 2 . 0 3 1 1 . 5 6 1 . 5 5 1 . 8 3 , 9 . 0 6 8 . 4 5 3 3 . 3 6 2 6 A 5 1 1 . 5 9 1 2 . 0 2 2 . 1 1 3 . 0 9 3 . 6 2 2 . 8 1 1 . 1 7 1 . 3 8 6 A 4 5 A 7 4 . 1 2 5 ^ 8 0 3.29 2 . 0 5 6 . 4 3 - 1 7 . 9 9 14 . 8 7 3 . 1 0 2 . 9 7 7 . 5 9 9 . 0 9 2 . 2 9 1 . 9 5 41 . 4 0 4 5 . 3 4 43 . 2 2 4 . 1 3 4 . 7 4 5 . 3 4 4.84 5.46 6.59 3.68 Name of Company 1 9 5 5 1 9 5 4 1 9 5 3 1 9 5 2 1 9 5 1 1 9 5 0 1949 1 9 4 8 1947 1946 5 2 Ronson Corporation 2 6 . 3 5 5 3 R u d y Mfg. Company 3 . 7 2 5 4 Sandura Co. 4 . 5 9 5 5 Scranton Lace Company 6 . 3 6 5 o Seneca F a l l s Machine Co. 1 . 8 9 57 Shasta Water Company 2.64 58 Sherman Products, Inc. 3 . 8 9 59 Sidney Blumenthal &amp; Co. 24 . 3 0 6 0 Standard Commercial Tobacco Co. 4 . 9 2 6 1 Stylon Corp. 4 . 7 8 6 2 1 2 t h Street Store 3 . 8 6 6 3 Unexcelled Chemical Corp. 1 . 4 4 64 V i c t o r Products Corp. 6 . 2 9 6 5 Wayne Screw Products Co. 1 . 6 6 6 6 Wilson Brothers 2 0 . 1 1 6 7 Yolands Corporation 2 . 2 7 24.97 24.97 3 0 . 2 1 3 . 0 3 3 . 3 7 2 . 1 9 3.89 4 . 2 1 5.48 5 . 9 8 6.46 6 . 9 6 2.91 3 . 1 3 2 . 8 6 1 . 8 5 0.9+ 0.48 3 . 3 1 3 . 2 2 3 . 0 1 1 9 . 7 8 2 3 . 9 2 2 5 . 3 0 3 . 2 6 1 1 . 8 9 1 1 . 4 5 3.48 2 . 1 3 1 . 3 0 3 . 7 8 4 . 2 3 4 . 7 2 4 . 6 1 8 . 9 7 6 . 5 2 7 . 0 1 8 . 0 9 7 . 2 2 1 . 1 3 1 . 6 9 1.41 1 9 . ^ 4 2 0 . 9 6 2 1 . 0 7 2 . 3 7 2 . 7 7 2 . 3 4 2 8 . 4 9 2 6 . 0 5 23.74 2 . 2 3 2.79 1 . 9 3 4 . 9 1 6 . 6 2 5.00 6 . 9 0 6.23 6 . 3 2 2 . 0 3 0 . 9 8 0.75 0.80 0.80 0.80 1.84 1 . 2 9 1 . 9 0 28.65 19.59 16.01 2 . 3 5 3 . 0 1 4 . 2 9 2.00 4.77 5 . 0 4 5 . 2 0 3.71 2.71 2.45 7.67 8.77 7.89 1.64 1 . 2 1 0 . 9 0 2 3 . 8 6 21.11 16.86 2.86 2.72 2.81 19.85 12.59 3 . 6 2 2.44 2.18 1 . 5 2 3 . 2 3 7.85 6 . 0 1 4.53 0 . 6 9 0 . 8 0 0 . 4 3 0 . 8 2 1.08 1 . 0 5 2.06 1 . 7 0 1.43 21 . 1 5 21.33 19.98 3 . 5 1 6 . 2 5 15.65 5A1 5T48 5^06 4.47 4.86 5.39 9.68 8.44 4.54 1.07 1.10 0.86 15.96 16.46 12.53 3.14 3.11 2.41 APPENDIX V OPERATING PROFITS (i n millions of dol l a r s ) Name of Company- 1955 195^ 1953 1952 1951 1950 1949 1948 19V7 1946 1. Auto Soler Company 0.13 0.21 0.44 0.37 0.31 0.08 o.o4 0.11 0.25 0.23 2 Balsa Chica O i l Corp. -0.11 -0.07 0.02 -0.01 0.10 -0.19 -0.03 -0.04 0.01 0.09 3 Baush Machine Tool Co. 0.03 0.44 0.78 1.12 0.65 0.26 0.08 0.14 -0.05 .0.32 4 B e l l Company -1.29 -1.60 0.37 -0.84 0.78 2.22 1.31 - \u2014 \u2014 5 Bishop &amp;\"Babcock Mfg.Co, . 0.46 -0.08 0.53 0.25 -0.06 -^ 0.09 0.15 0.45 1.10 -0.02 6 Brown McLaren Mfg. Co. -0.11 -0.07 0.39 O.32 0.29 -0.10 -0.02 0.01 0.01 0.01 7 Carpenter (L.E.) &amp; Co. 0.23 0.13 0.15 0.08 0.31 Q...03 -0.19 -0.23 -0.06 0.23 8 Chief Consolidated Mining Co. -0.16 0.01 -0.24 0.15 -0.27 0.02 0.23 0.23 0.05 0.10 9 Cleveland Sandusky 0.04 -o.o4 Brewing Corp. 0.09 0.10 0.12 0.11 0.01 -0.10 0.36 0.21 10 Consolidated R e t a i l Stores, Inc. -1.72 -0.22 0.45 0.60 0.89 1.05 1.31 2.31 2.16 2.58 11 Cooper Tire and 1.06 Rubber Co. 0.93 0.19 1.02 , 0.89 1.11 -0.28 -0.23 0.32 1.10 12 Curtis Lighting -0.13 -0.02 -0.02 -0.10 0.16 0.16 0.08 0.29 0.24 0.28 Davega Stores Corp. -0.38 -0.26 0.17 0.15 1.37 1.01 1.18 1.74 2.09 - 14 Diamond Motor Car 1.84 Company 0.22 -0.49 1.86 2.32 0.50 0.19 1.79 3.05 1.23 15 Dixon (Joseph) Crumble 0.60 0.34 -0.04 Co. 0.87 0.06 0.55 0.40 0.13 0.20 0.57 16 E &amp; B Brewing Co.Inc. -0.02 0.21 0.28 0.50 0.20 -0.33 -0.23 -0.30 0.07 0.52 17 Flagg U t i c a Corporation 0.54 -0.17 0.13 -1.15 - - - - \u2014 18 F l o t i l l Products, Inc. 1.36 0.73 0.04 -0.31 1.67 2.12 -0.45 -1.26 \u2014 \u2014 19 Flour M i l l s of America,Inc. -0.79 -0.57 -3.09 0.29 0.85 1.22 2.00 3.82 4.26 -0.80 20 Gerotor May Corp. -0.41 -0.38 -0.41 0.21 0.52 o.4o 0.10 -0.09 -0.38 -0.08 -0.12 21 Glove America Corp. -0.17 0.59 0.62 0.86 0.96 0.39 0.80 -0.14 -0.62 22 Gum Products Inc. 0.13 0.12 0.12 -0.45 0.30 \u2022-0.33 -0.49 - o.4l \u2014 \u2014 23 Hathaway Breweries,Inc. -0.42 -0.32 O.38 0.92 0.96 1.38 1.14 1.50 0.87 1.39 Name of Company 1955 1954 1953 24 H i l l e r Helicopters 25 Jacob Rupert 26Jeannette Glass Company 27 Jessop Steel Co. 28 Lanston Industries, Inc. 29 Longchamps Inc. 30 MacMillan Petroleum Corp. 31 Maguire Industries, Inc. 32 Mandel Brothers, Inc. 33 Merrimac Hat Corp. 34 Michigan Bakeries, Inc. 35 Mohawk Liquer Corp. 36 Morgan 1s Inc. 37 National Research Corp. 38 Nelson (N.O.) Company 39 New England Box Company 40 Oceanic O i l Company 41 0'Sullivan Rubber Corp. 42 Peck Stow &amp; Wilcox Co. 43Plastic Wire &amp; Cable Corp. 44 Plume &amp; Atwood Mfg. Co. 45 Powdrell &amp; Alexander Inc. 46 Queen Anne Candy Comoany 47 Reis (Robert) &amp; Co. 48 Reymer &amp; Brothers, Inc. 49 Richmond Cedar Works 50 Rochester &amp; Pittsburg Coal Co. 51 Rock Ola Mfg. Corp. 52 Ronson Corporation 53 Rudy Mfg. Company 54 Sandura Company -0:03 -0.11 0.67 0.10 0.92 1.06 0.38 0.32 0.44 1.73 0.19 1.52 -0.16 -0.45 0.38 -0.24 0.35 0.16 0.16 0.06 -0.05 o.o4 . 0.10 -0.02 -0.60 -1.21 -1.30 -0.09 0.17 0.13 0.24 0.06 -o.o4 0.20 0.18 0.28 0.12 -0.07 0.01 -6.5O 0.09 0.00 0.16 -0.21 -0.04 0.21 -0.01 0.11 0.48 0.77 0.18 0.05 0.34 0.31 0.24 -0.19 O.49 0.75 0.61 1.00 -0.28 0.Q6 0.65 0.30 -1.05 -0.66 0.12 0.15 0.26 0.10 0.03 -0.02 0.00 0.18 0.01 -0.01 0.29 -0.36 0.39 -0.63 1.41 0.37 0.27 -0.53 2.60 -0.55 1.51 -0.10 0.23 0.19 0.17 -0.33 -0.37 1952 1951 1950 1949 1948 1947 1946 1.98 1.27 0.34 2.70 0.44 0.07 0.61 0.27 -1.07 O.13 -0.15 0.02 -0.01 0,15 0.26 0.14 \u20220.06 0.37 0.60 1.46 0.01 \u20221.03 0.28 -0.23 0.15 .0.09 1.36 \u20220.34 \u20221.75 \u20220.05 \u20220.13 0.55 -0.25 0.06 2.67 0.73 0.21 0.79 0.24 0.51 0.20 0.05 0.09 -0.46 0.42 1.28 0.35 0.29 0.47 0.58 O.83 0.80 0.15 0.20 -0.12 -0.01 0.26 2.54 \u20220.59 6.14 \u20220.02 \u20220.48 -1.85 -0.07 0.58 0.66 0.44 0.19 -0.24 -o.o4 0.26 0.10 0.13 -0.19 -0.04 1.69 0.34 0T48 0.28 0.13 0.28 0.95 0.30 -0.08 -0.01 0.06 2.55 \u20220.12 6.45 \u20220.03 0.51 -2.23 2* ~ 0.00 0.88 2.83 -0.09 -0.02 0.42 1.35 -0.85 -0.62 -0.70 -0.31 1.18 1.28 0.55 0.63 O.36 0.23 \u2014 _ -0.12 0.65 0.57 0.55 -0.79 -0.81 - 0.58 0.86 1.71 1.31 0.17 0.01 0.34 1.53 0.21 0.27 -o.o4 0.14 -0.36 0.71 -0.17 0.2^  0.40 0.26 -0.07 0.02 -0.20 -0.06 0.62 1.73 - - \u2014 -0.01 0.53 0.92 0.65 rO.03 0.14 0.26 o.4o -0.05 0.46 \u2014 -0.83 -0.03 -0.24 0.16 -0.77 0.11 0.27 \u2014 -0.29 2.69 3.90 5.70 0.13 -0.07 -0.18 0,37 -0.19 -0.30 0.67 1.53 0.01 0.11 0.17 0.27 0.14 \u2014 \u2014 \u2014 0.31 0.06 1.53 0.27 8.39 8.97 5.59 3.38 -0.06 0.21 0.18 -0.13 -0.08 0.63 - -Name of Company 1 9 5 5 1 9 5 4 1 9 5 3 1 9 5 2 1 9 5 1 1 9 5 0 1 9 4 9 1948 1 9 4 7 1 9 4 6 5 5 Scranton Lace Company 0 . 0 5 5 o Seneca F a l l s Machine Co. - 0 . 2 9 57 Shasta Water Company 0 . 0 1 58 Sherman Products, Inc. 0.42 59 Sidney Blumenthal &amp; Co\u2022 l n c . 6 0 Standard Commercial Tobacco Co. 0 . 4 7 6 1 Stylon Corp. 1 . 2 7 6 2 1 2 t h Street Store - 0 . 0 9 6 3 Unexcelled Chemical Corp - 0 . 2 3 64 V i c t o r Products Corp. - 0 . 2 3 6 5 Wayne Screw Products Co. 0 . 0 4 6 o Wilson Brothers 0 . 2 5 6 7 Yolands Corporation - 0 . 0 4 \u2022 0 . 1 6 0 . 5 5 0 . 0 8 0 . 2 5 0 . 1 9 0 . 9 4 0 . 0 0 0 . 5 1 0 . 0 6 0 . 8 6 \u2022 0 . 0 1 0 . 4 2 0 . 3 0 0.42 \u2022 0 . 1 3 0 . 0 7 \u2022O.38 - 0 . 0 2 0 . 0 7 \u2022 0 . 0 8 0 . 9 5 0 . 0 3 \u2022 0 . 1 1 \u2022 0 . 5 2 0 . 3 1 0 . 1 3 0 . 2 0 0 . 0 1 1 . 0 1 \u2022 0 . 0 5 - 0 . 1 5 - 0 . 1 7 0 . 6 0 0.27 o.o4 - 0 . 0 8 0 . 0 7 0 . 6 1 \u2022 0 . 0 3 0.42 - 1 . 5 6 - 1 . 2 9 0 . 2 7 0 . 6 6 2 . 6 9 0 . 0 0 0 . 1 5 0 . 0 5 \u2022 0 . 1 1 0 . 8 2 0 . 3 2 0 . 2 3 \u2022o.o4 0 . 3 7 0 . 1 2 0.04 0 . 2 6 0 . 5 2 0 . 0 0 0 . 0 9 - 0 . 1 5 1 . 2 3 - 0 . 0 6 0 . 1 0 0 . 4 5 1 . 0 9 - 0 . 0 3 0.04 0.42 0 . 7 3 - 0 . 3 0 0 . 0 8 - 0 . 2 8 2 . 2 6 - 0 . 2 2 0 . 7 0 0 . 6 1 2 . 2 8 0.14 0 . 2 0 - 0 . 2 5 0.41 0.48 0 . 0 4 0 . 0 1 0 . 8 2 0 . 1 1 0 . 7 7 0 . 0 1 0 . 0 7 - 0 . 0 7 0 . 2 5 0 . 0 9 - 0 . 1 3 0.04 0.24 - 0 . 6 2 1.13 0.14 0.46 0 . 3 3 0 . 2 6 - 0 . 0 3 I . 6 3 0 . 2 0 0 . 5 0 0 . 4 3 0 . 3 1 0 . 7 7 1 . 1 6 0 . 1 7 0 . 7 5 0 . 4 4 - 126 - APPENDIX VI As was mentioned i n chapter IV, f o r t r a n program ming was used to a s s i s t i n a r r i v i n g at the values of the constants, a and b i n the equation of the straight l i n e trend, y = a + bx. The data were submitted to the UBC computing centre i n the manner shown i n the Fortran Coding Form i n the next page. The output of data i s as given i n Tables IV and V i n chapter IV. UBC Computing Centre Programmer F O R T R A N C O D I N G F O R M D a t e _ _ Page of STATEMENT c NO. c 0 N T FORTRAN STATEMENT &gt;&gt; IDENTIFICATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 1 9 5 5 1 \u2022 5 6 1 \u2022 4 0 \u2022 1 1 9 5 4 1 \u2022 7 6 1 \u2022 \u2022? 0 \u2022 2 1 1 9 5 5 2 \u2022 6 8 2 \u2022 2 4 0 \u2022 4 4 1 9 2 2 \u2022 1 \u2022 9 6 0 \u00AB 7 1 9 5 1 2 \u2022 2 2 \u2022 0 1 0 \u2022 1 1 9 5 0 1 \u2022 1 7 1 \u2022 0 9 0 \u2022 0 8 1 9 4 9 0 \u2022 8 0 0 \u2022 8 4 0 \u2022 0 4 1 9 4 8 1 \u2022 0 8 0 \u2022 9 7 0 \u2022 1 l 1 9 4 7 1 \u2022 1 4 0 \u2022 8 9 0 \u2022 2 1 9 4 6 1 \u2022 0 7 0 * 8 4 0 \u2022 2 E N D S A L \u2022 C 0 S T P R 0 P I T A U T 0 S 0 L E R rt 0 \u2022 \\ \u2014 \u2014 I "@en
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