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A critical evaluation and test of break-even analysis as a technique for profit planning Lim, Say Chong 1965

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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.), U n i v e r s i t y of Malaya,  1963  A T h e s i s 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 t h e s i s as conforming t o the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 1965  In presenting the  this thesis i n p a r t i a l fulfilment of  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f •  B r i t i s h Columbia, I agree that available  the L i b r a r y  f o r r e f e r e n c e and s t u d y ,  mission f o r extensive  s h a l l make i t f r e e l y  I f u r t h e r agree that  per-  copying of this thesis f o r scholarly  p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by his  representatives.  cation  I t i s understood that  of t h i s thesis f o r f i n a n c i a l gain  w i t h o u t my w r i t t e n  s h a l l n o t be a l l o w e d  permission*  D e p a r t m e n t o f Commerce and B u s i n e s s The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a Date  copying or p u b l i -  A p r i l 30th 1965  Administration  ABSTRACT T h i s study p r o v i d e s a c r i t i c a l e v a l u a t i o n o f breakeven a n a l y s i s i n terms of i t s assumptions and uses and a l s o i n terms o f the economic theory o f the f i r m i n the s h o r t and l o n g r u n and under p e r f e c t and imperfect ditions.  I t also includes  competitive  a t e s t o f the h y p o t h e s i s  conthat  break-even a n a l y s i s can be b e t t e r than the percentage of s a l e s method as a technique f o r f o r e c a s t i n g the f u t u r e  oper-  a t i n g p r o f i t s of f i r m s and the n u l l h y p o t h e s i s t h a t there 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 percentage o f s a l e s method as a technique f o r f o r e c a s t i n g the f u t u r e operating  p r o f i t s of f i r m s .  The t e s t 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 r e q u i r e s more time, e f f o r t and expense, the t e s t  shows t h a t a t the 0.01 l e v e l of s i g n i f i c a n c e , there  i s no  d i f f e r e n c e between the accuracy of i t s f o r e c a s t s of opera t i n g p r o f i t s and t h a t of the percentage of s a l e s method. The  hypothesis i s therefore  accepted.  The c o n c l u s i o n  r e j e c t e d and the n u l l  hypothesis  drawn from the t e s t i s t h a t the  management of a f i r m should not make use o f break-even analy-. s i s to f o r e c a s t i t s o p e r a t i n g  p r o f i t s i f i t i s n o t prepared  to make any adjustments to i t s data to recognise of changes i n the determinants ( e x c l u d i n g The  the e f f e c t s  volume) o f p r o f i t s .  percentage of s a l e s method s h o u l d be used  instead.  TABLE OF CONTENTS Chapter I.  Page INTRODUCTION  1  Statement of the Problem Hypothesis and N u l l Hypothesis . Organisation . L i m i t a t i o n s of the Study Definitions Summary II.  III.  IV.  THE  . . .  NATURE OF BREAK-EVEN ANALYSIS  2 h 8 9 11 Ih 15  Introduction Use of Break-Even A n a l y s i s The Development of Break-Even A n a l y s i s . . . The Break-Even Chart The Break-Even P o i n t Cost Breakdown Summary  15 15 16 20 25 29 39  A CRITICAL EVALUATION OF BREAK-EVEN ANALYSIS .  U-l  Introduction Static Analysis A Short-Run Concept L i n e a r and C u r v i - L i n e a r Charts S e p a r a t i o n of Costs Constant S e l l i n g P r i c e s T o t a l Cost and Constant U n i t V a r i a b l e C o s t s . P r o d u c t i o n Equals S a l e s . Sales Mix P l a n n i n g and C o n t r o l Pricing Policies C a p i t a l Expenditures Make or Buy Problems Cost C o n t r o l Summary  hi hi MrMr^8 h9 $h 60 63 67 69 70 72 73 75  TEST OF BREAK-EVEN ANALYSIS Introduction Source of Data F o r e c a s t i n g Operating The Sample Method of A n a l y s i s Summary  Profits  77 77 78 79 83 89 100  Chapter V.  SUMMARY AND CONCLUSION Summary  . . . . . .  Conclusion BIBLIOGRAPHY APPENDICES  LIST OF TABLES Table I  II  III IV  Page Number and Percentages o f Companies I n t e r viewed I n d i c a t i n g V a r i o u s Types and F r e q u e n c i e s o f Break-Even A n a l y s i s  17  Number and Percentage of Companies Answering Q u e s t i o n n a i r e s I n d i c a t i n g Types and F r e quency of P r e p a r a t i o n o f Break-Even A n a l y s i s as Reported by 3kk Companies  18  Computation of the Standard D e v i a t i o n o f the Universe  87  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 Percentage o f Sales  V  Method  90  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 Break-Even Method  93  LIST OF  ILLUSTRATIONS  Number  Page  EXHIBIT 1  C o n v e n t i o n a l Break-Even Chart  22  2  P r o f i t / V o l u m e Chart  23  3  S c a t t e r Chart  38  h  M o d i f i e d C o n v e n t i o n a l Break-Even Chart .  V3  5  C u r v i - L i n e a r Break-Even Chart  ^-6  6  The L i m i t s of Constant P r i c e s  52  7  Constant Average V a r i a b l e Cost  55  8  Economists'  Cost Curves  56  9  Economists'  Average V a r i a b l e Cost Curve.  58  CHAPTER I INTRODUCTION There has been a g r e a t d e a l o f c o n t r o v e r s y i n recent years regarding the objectives of p r i v a t e l y business organisations.  operated  Some people argue t h a t a business  o r g a n i s a t i o n ought to have l o n g - r u n p r o f i t maximisation as i t s s o l e o b j e c t i v e w h i l e o t h e r s argue t h a t t h e management o f a b u s i n e s s should n o t o n l y t h i n k o f p r o f i t s but a l s o t r y to p r o v i d e s a t i s f a c t i o n f o r the p a r t i c i p a n t s i n the o r g a n i s a t i o n , take the l e a d i n t e c h n o l o g i c a l developments and secure approval.^"  social  Whatever the arguments, i t cannot be denied t h a t ,  i n a f r e e e n t e r p r i s e system, no p r i v a t e l y operated can a f f o r d t o make l e s s than a ' h e a l t h y  1  business  p r o f i t f o r any apprec-  i a b l e p e r i o d o f time. The s u r v i v a l of a b u s i n e s s , t h e r e f o r e , depends on the a b i l i t y o f the management to earn, a t l e a s t , a 'healthy' p r o f i t f o r the b u s i n e s s .  I n order t o achieve t h i s , under ex-  i s t i n g c o m p e t i t i v e c o n d i t i o n s , the management o f a business has to p r o v i d e f o r proper f i n a n c i a l p l a n n i n g and c o n t r o l .  In  o t h e r words, management must be a b l e t o p l a n i t s p r o f i t p e r formance and r e a l i s e i t s p r o f i t p l a n s t o j u s t i f y i t s e x i s t e n c e . 1. Assuming no d i s t i n c t i o n between t h e management and the owners o f a b u s i n e s s , i t should a l s o be r e c o g n i s e d t h a t maximis a t i o n o f the v a l u e o f owners' common s t o c k s c o u l d 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  tools. One  analysis.  o f t h e more b a s i c of these t o o l s i s break-even  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 o f f i r m s as an a i d f o r t h e i r f i n a n c i a l planning  and c o n t r o l .  Graphically, o r m a t h e m a t i c a l l y , i t p e r -  mits management t o study the p r o b a b l y e f f e c t s on p r o f i t s o f changes i n s i n g l e f i n a n c i a l f a c t o r s o r combinations o f them. Statement o f the Problem Break-even a n a l y s i s does n o t p r o v i d e a completely r e l i a b l e forecast of future p r o f i t s .  The f o r e c a s t s a r e made  under a g i v e n s e t o f assumptions r e g a r d i n g production  such f a c t o r s as  and s a l e s , p r i c e s , c o s t s , and s a l e s mix.  i n any o f these assumptions w i l l a f f e c t t h e f o r e c a s t .  A change But,  g i v e n t h e assumptions, break-even a n a l y s i s may show t h e exp e c t e d p r o f i t s a t v a r i o u s volumes.  P r o f i t , then, becomes a  s i n g l e v a l u e d f u n c t i o n o f volume.  I f break-even a n a l y s i s i s  to be used to give more a c c u r a t e r e s u l t s , then changes o r expected changes n o t o n l y i n volume b u t a l s o i n t h e o t h e r v a r i a b l e s 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. T h i s , however, does not seem to go along w e l l w i t h the advantages o f break-even a n a l y s i s .  One o f the s t r o n g e s t  p o i n t s o f break-even a n a l y s i s , as a t o o l f o r f o r e c a s t i n g  - 3 f u t u r e p r o f i t s , i s t h a t i t i s simple, pare.  But,  quick and  i f a p r e r e q u i s i t e to the use  cheap to  pre-  of break-even  a n a l y s i s i s a f o r e c a s t of a l l the v a r i a b l e s t h a t 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  a n a l y s i s on the b a s i s of the r e s u l t s o f the f o r e c a s t s of these v a r i a b l e s , then the very advantages of break-even a n a l y s i s w i l l be  defeated.  I f , on the other hand, management does not the t r o u b l e to make the p r e l i m i n a r y f o r e c a s t s and but merely makes use expectations  go  to  adjustments  of break-even a n a l y s i s to show p r o f i t  under a s p e c i f i c s e t of assumptions  e x t e r n a l market c o n d i t i o n s and  regarding  i n t e r n a l management s t r a t e g y ,  then p r o f i t s w i l l be shown to vary o n l y w i t h volume.  But,  in  break-even a n a l y s i s , s a l e s revenue i s o f t e n used as a measure of volume, on the assumption t h a t volume (output) and synchronised.  sales  Under the circumstances, the q u e s t i o n a r i s e s ,  "Isn't i t simpler,  q u i c k e r and  cheaper to determine the average  o f p r o f i t s as a percentage of s a l e s f o r s e v e r a l p a s t years apply  are  and  t h i s percentage to a r r i v e a t 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 ? "  T h i s method o f f o r e c a s t i n g p r o f i t s  i s known as the percentage of s a l e s method. the problem of c o s t s e p a r a t i o n and  With t h i s method,  a host of other problems do  not a r i s e a t a l l . This study attempts to compare the accuracy of  the  r e s u l t s o f the break-even method w i t h t h a t of the percentage of s a l e s method.  On  the b a s i s of t h i s comparison, a  con-  -inc l u s i o n w i l l be drawn on the m e r i t of u s i n g break-even a n a l y s i s f o r 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 f i r m s and i t s  managerial i m p l i c a t i o n s . Hypothesis and The  N u l l Hypothesis h y p o t h e s i s i s t h a t break-even a n a l y s i s can  be  b e t t e r than the percentage o f s a l e s method as a technique 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 of f i r m s .  Since  break-even a n a l y s i s i s more s o p h i s t i c a t e d , i t i s expected t h a t , a t worst, i t w i l l be as good as the percentage of  sales  method.  be  Therefore,  the p o s s i b i l i t y t h a t the l a t t e r may  b e t t e r than the former w i l l not even be considered In order t o t e s t the h y p o t h e s i s , of f i r m s has  to be p i c k e d  the performance o f the two  f i r s t l y , a sample  s i n c e i t i s not p o s s i b l e to study methods i n a l l f i r m s .  the average d i f f e r e n c e between f o r e c a s t p r o f i t s and p r o f i t s by each of the and  two  here.  approaches has  f i n a l l y a comparison has  Secondly, actual  to be determined  to be made of the two  averages.  In e s t a b l i s h i n g the averages, the mean, the median or the mode can be used. two  I n t h i s study, the mean i s p r e f e r r e d to the other  measures s i n c e i t i s l e a s t s u b j e c t The  to sampling v a r i a t i o n . ^  a l t e r n a t i v e to the h y p o t h e s i s i s t h a t there i s  2 . In chapter IV, an e x p l a n a t i o n i s g i v e n of the manner i n which random sampling has been used to p i c k the f i f t y seven f i r m s , which form the sample. 3 . F r e d e r i c k E. Croxton and Dudley J . Cowden, A p p l i e d General S t a t i s t i c s , 2 n d Ed.; Englewood C l i f f s , N.J.: PrenticeH a l l , Inc., 1 9 5 5 , p. 1 9 7 .  no d i f f e r e n c e between break-even a n a l y s i s and  the percentage  of s a l e s method as a technique f o r f o r e c a s t i n g the operating  p r o f i t s of f i r m s .  c a l l e d the n u l l h y p o t h e s i s . represent  future  This a l t e r n a t i v e h y p o t h e s i s i s With the  symbol p^ used to  the mean d i f f e r e n c e between a c t u a l and  forecast  p r o f i t s o b t a i n e d by the percentage o f s a l e s method, and symbol p  2  used to r e p r e s e n t  t h a t o b t a i n e d through break-even  a n a l y s i s , the n u l l h y p o t h e s i s may p  l  =  P2*  the  then be f o r m u l a t e d  as  Since the p o s s i b i l i t y t h a t the l e s s s o p h i s t i c a t e d  percentage of s a l e s method may  prove to be more a c c u r a t e ,  has  been r u l e d out on the grounds t h a t 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^ >  p . 2  This a l t e r n a t i v e  i m p l i e s t h a t the average d i f f e r e n c e between a c t u a l and c a s t p r o f i t s by break-even a n a l y s i s i s s m a l l e r and,  fore-  therefore,  the h y p o t h e s i s as s t a t e d e a r l i e r , i s c o r r e c t . From the above d i s c u s s i o n , i t i s obvious t h a t acceptance of the h y p o t h e s i s depends on n u l l hypothesis.  But,  n u l l hypothesis, c a r r i e d out.  the r e j e c t i o n of  before a d e c i s i o n can be made on  a t e s t of s i g n i f i c a n c e has  f i r s t to  the the  be  The purpose of such a t e s t o f s i g n i f i c a n c e i s  to determine whether t h e r e i s any between p-^ and p . 2  s t a t i s t i c a l significance  I n order to do t h i s , i t i s necessary to  s e t a . c r i t e r i o n of s i g n i f i c a n c e and  to determine the proba-  b i l i t y o f z, where z i s the r a t i o o f p-^ - p  2  to an  of the standard e r r o r o f the d i f f e r e n c e between the sample means.  the  The  estimate two  c r i t e r i o n of s i g n i f i c a n c e e s t a b l i s h e d  - 6 depends on the type o f e r r o r t h a t i s t o be avoided. I n t e s t s o f s t a t i s t i c a l s i g n i f i c a n c e , there a r e two  types o f e r r o r s .  A type I e r r o r a r i s e s when a n u l l  h y p o t h e s i s i s a c t u a l l y c o r r e c t but the d i f f e r e n c e i s declared  t o be s i g n i f i c a n t .  involved  A type I I e r r o r a r i s e s when  a n u l l h y p o t h e s i s i s a c t u a l l y wrong but the d i f f e r e n c e i n volved i s declared i s t o reduce  t o be n o t s i g n i f i c a n t .  I f the i n t e n t i o n  type I e r r o r s t o 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 e s t a b l i s h e d s i g n i f i c a n c e i s very s m a l l .  should be such t h a t the l e v e l o f On the other hand, i f type I I  e r r o r s a r e to be reduced t o the minimum, then the l e v e l o f s i g n i f i c a n c e ought to be l a r g e r .  Whether type I o r type I I  e r r o r s ought to be minimised depends v e r y much on i n d i v i d u a l s i t u a t i o n s and c i r c u m s t a n c e s . I n t h i s study, a type I e r r o r would be committed if  the d i f f e r e n c e between the sample means i s so s m a l l  it  can almost be s a i d t h a t there i s no d i f f e r e n c e between  them but i t i s d e c l a r e d significant.  t h a t the d i f f e r e n c e between them i s  The consequence o f t h i s may be that people who  would o t h e r w i s e n o t use the break-even operating  that  method to f o r e c a s t  p r o f i t s , may now use the break-even  method.  The  r e v e r s e would be true i f a type I I e r r o r i s committed.  In  such a case, the d i f f e r e n c e between the sample means i s a c t u a l l y very l a r g e b u t a d e c l a r a t i o n i s made t h a t the d i f f e r ence i s n o t s i g n i f i c a n t . k.  Ibid.,  p. 61+0.  The r e s u l t o f such an e r r o r may be  t h a t p e o p l e , who  7  -  would otherwise make use o f break-even  a n a l y s i s to f o r e c a s t o p e r a t i n g p r o f i t s , may after a l l , time and  i t i s not worthwhile to go  expense to use The  now  consider  to a l l the e x t r a  that,  effort,  the break-even method.  above d i s c u s s i o n suggests t h a t , i n t h i s  study,  i t i s more s e r i o u s to commit a type I e r r o r s i n c e when such an e r r o r i s committed, e x t r a c o s t s are i n c u r r e d f o r which no appreciable  b e n e f i t s are r e c e i v e d .  A type I I e r r o r appears  to be l e s s s e r i o u s s i n c e i t merely r e s u l t s i n a l o s s o f b e n e f i t s , i n the form o f g r e a t e r a c c u r a c y i n the f o r e c a s t , which can otherwise be o b t a i n e d . e x t r a c o s t s are i n c u r r e d .  But,  a t the same time, no  In s h o r t , t h i s means t h a t i n  committing a type I e r r o r , e x t r a c o s t s are i n c u r r e d f o r no appreciable no new  b e n e f i t s whereas, i n committing a type I I e r r o r ,  b e n e f i t s are r e c e i v e d but no  e x t r a c o s t s are i n -  curred. I t was  s t a t e d e a r l i e r t h a t i f type I e r r o r i s to  be minimised, then the l e v e l of s i g n i f i c a n c e ought to be small.  The  l e v e l of s i g n i f i c a n c e that i s customarily  very  used  6  i s 0 . 0 5 or 0 . G 1 .  I n t h i s study, 0 . 0 1 w i l l be used.  the t - t a b l e i n Appendix I I , i t may  be noted t h a t by  From inter-  5 . I t i s , however, p o s s i b l e t h a t the l o s s i n accuracy, i f measurable i n d o l l a r terms, may be l a r g e enough to more than o f f s e t the e x t r a c o s t s and the u l t i m a t e c o s t s of committing a type I I e r r o r may i n f a c t be h i g h e r . 6 . John E. Freund and Frank J . W i l l i a m s , Modern Business Statistics. Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , Ine*, 1 9 5 8 , P. 22*f.  - 8 p o l a t i o n , f o r f i f t y - s e v e n degrees o f freedom, the value at  the 0.01 l e v e l o f s i g n i f i c a n c e , i s 2.667.  of z  I n t h i s study, a  o n e - t a i l t e s t i s used s i n c e the a l t e r n a t i v e to the n u l l hypothesis  t h a t p-|_ = p  information,  2  i s one-sided, i . e . p ^ ^> p « 2  With t h i s  i t may be s t a t e d t h a t the n u l l h y p o t h e s i s  be accepted i f z 4  2.667 and should  T h i s i s the same as saying  should  be r e j e c t e d i f z >  that the hypothesis,  2.667.  t h a t break-  even a n a l y s i s can be b e t t e r than the percentage of s a l e s method as a technique 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 of f i r m s , i s a c c e p t a b l e  if z >  2.667 and should  profits  be r e j e c t e d  i f z < 2.667. Organisation Chapter I i s the i n t r o d u c t o r y chapter t o t h i s thesis. and  Here, the statement of the problem, the h y p o t h e s i s  the n u l l h y p o t h e s i s ,  the l i m i t a t i o n s of the study, the  o r g a n i s a t i o n and the d e f i n i t i o n s of terms are g i v e n . v i d e a b a s i s f o r the c r i t i c a l  To p r o -  e v a l u a t i o n of break-even  a n a l y s i s , chapter I I i s devoted to a f a c t u a l d e s c r i p t i o n of the nature of break-even a n a l y s i s . of the extent  B r i e f l y , an i d e a i s g i v e n  to which break-even a n a l y s i s i s used, the dev-  elopment of break-even a n a l y s i s , the break-even c h a r t and the break-even p o i n t .  An i d e a i s a l s o g i v e n of how costs  of f i r m s are separated  f o r the purposes o f break-even  analysis. Against  t h i s background, a c r i t i c a l  evaluation of  - 9b r e a k - e v e n a n a l y s i s i s made i n c h a p t e r  I I I , i n terms o f the  assumptions used and t h e uses to which break-even a n a l y s i s is  put.  theory fect  The e v a l u a t i o n i s a l s o i n t e r m s o f t h e e c o n o m i c of the firm  and i m p e r f e c t  chapter  i n the s h o r t and l o n g competitive  the n u l l hypothesis,  trial  Manuals.  requires  a very  A test  of the  t o the a n a l y s i s o f cost-volume  such d e t a i l e d ,  with  using  of this  the t e s t of the hypothesis data  taken  nature,  f r o m Moody's  t o be v e r y  Unfortunately,  confidential  firms willing  o f the  to provide  information are d i f f i c u l t  The p r o b l e m i s p a r t i c u l a r l y  Indus-  accurate,  i n t i m a t e knowledge o f t h e o p e r a t i o n s  f i r m s under study.  find.  T h i s c h a p t e r and  relationships.  Chapter IV deals and  conditions.  per-  I I a r e based p r i m a r i l y on a c l o s e examination  various publications relating profit  r u n and u n d e r  to  serious since there are  7 as many a s f i f t y - s e v e n f i r m s i n t h e s a m p l e .  Under the c i r -  c u m s t a n c e s , r e s o r t h a s t o be made t o p u b l i s h e d d a t a . the purposes o f t h i s vide  study,  Moody's I n d u s t r i a l M a n u a l s  t h e most d e t a i l e d , p u b l i s h e d  the  of data  .  t h e summary a n d c o n c l u s i o n o f  study.  Limitations  o f the Study  In t h i s  size  pro-  i n f o r m a t i o n a n d have  t h e r e f o r e been chosen as t h e source Chapter V p r o v i d e s  For  study,  i n forecasting profits  by t h e b r e a k -  7. A d e t a i l e d e x p l a n a t i o n o f t h e e s t i m a t i o n o f t h e sample i s g i v e n i n chapter IV.  - 10 even method, no adjustments  were made to take i n t o  account  the e f f e c t s of p o s s i b l e changes i n the determinants profits.  T h i s i s due  f o r such adjustments  of  to the f a c t t h a t the necessary are not a v a i l a b l e .  t h a t f a i l u r e to make the adjustments  data  I t i s admitted  here  w i l l most c e r t a i n l y  reduce the accuracy of the f o r e c a s t s . Again, i n the break-even method of f o r e c a s t i n g o p e r a t i n g p r o f i t s , t o t a l c o s t s have to be separated i n t o f i x e d c o s t s and v a r i a b l e c o s t s .  To achieve t h i s , as  des-  c r i b e d i n chapter IV, the s t a t i s t i c a l approach u s i n g the method o f l e a s t squares i s used.  But, i t has been found i n  p r e l i m i n a r y s t u d i e s t h a t t h i s approach i s p o s s i b l e o n l y i f the data f o r the f i r m s show t h a t the f i r m s have experienced l o s s e s over some of the p e r i o d s i n the a n a l y s i s .  T h i s draw8  back can be avoided i f the a c c o u n t i n g or e n g i n e e r i n g approach i s used, but s i n c e 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 p r e f e r r e d to the o t h e r two  techniques.  Hence, the u n i -  verse of f i r m s , from which the sample i s chosen,  i s restricted  to o n l y those f i r m s i n Moody's I n d u s t r i a l Manuals, which have had l o s s e s a t some time i n the p e r i o d s under study.  The  data of some f i r m s do not appear i n Moody's I n d u s t r i a l Manu a l s f o r the p e r i o d p r i o r to 1951• These f i r m s have a l s o 8. This i s e x p l a i n e d 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 t o enable the use of e i t h e r the a c c o u n t i n g or e n g i n e e r i n g methods, w i t h reasonably accurate r e s u l t s .  - 11 been excluded from the  universe.  Definitions Break-even a n a l y s i s t segregation  Break-even a n a l y s i s r e f e r s t o the  o f a l l c o s t s , i n the s h o r t - r u n , between those  t h a t a r e f i x e d and those that are v a r i a b l e and t o the c o s t volume-revenue  r e l a t i o n s h i p s , which determine the amount o f  p r o f i t s a t d i f f e r e n t volume l e v e l s . Break-even p o i n t :  Break-even p o i n t r e f e r s to the volume  l e v e l a t which t o t a l revenue e x a c t l y equals t o t a l c o s t and n e i t h e r p r o f i t s nor l o s s e s are made.  I t may  a l s o r e f e r to  the : p o i n t of time i n the budgetary p e r i o d when l o s s e s  turn  into p r o f i t s . Short-run;  The s h o r t - r u n  i s a time p e r i o d so s h o r t t h a t a  f i r m cannot vary the q u a n t i t i e s of some of the resources i t uses.  that  I n a c t u a l f a c t , i t can l e g i t i m a t e l y be s a i d t h a t  the s h o r t - r u n  i s any time p e r i o d between t h a t i n which no  resources  can be v a r i e d i n q u a n t i t y and t h a t i n which a l l  resources  but one are v a r i a b l e .  definition.  Throughout  This would be a very  broad  t h i s t h e s i s , 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 s h o r t - r u n taken t o r e f e r to a time p e r i o d w i t h i n  concept w i l l  be  which a f i r m cannot  a l t e r o r add to such items as i t s c a p i t a l equipment,  build-  i n g s , l a n d and top management.  short-  run  ' f i x e d resources'.  These are the firm's  The time p e r i o d , however, w i l l  l o n g enough f o r the f i r m to vary q u a n t i t i e s o f such  be  resources  - 12 as  labour,  variable  raw  materials  and  The  uses.  Hence, i n the  whether r e s o u r c e s  Fixed  A l l resources  costs;  i n the  ity. the  Fixed  terms o f  the  are  the  costs  time t h a t i s  no  classified  and  be  defined  w i t h i n the costs  are  of  of the fixed  in  of a c t i v i t y .  ments f o r  run,  'piece  or  given  var-  as  costs  the  those  l e v e l of  activ-  e x p e c t e d range o f  activ-  short-run,  rent,  given  In  above,  fixed  resources.  be  same d i r e c t i o n as  defined  increases  as  those  increasing or  I n terms o f  materials, the  above, v a r i a b l e c o s t s a r e  fuel  d e f i n i t i o n of the  c o s t s of  or  decreases  Examples o f v a r i a b l e c o s t s  r a t e ' wages, raw  transportation.  that  to  debenture i n t e r e s t .  V a r i a b l e c o s t s may  i n the  level  resources  s u c h payments as  management and  decreasing. .  t  long  as f i x e d  c o s t s , whose amount i s a f u n c t i o n o f a c t i v i t y ,  and  firm's  p r o b l e m e x i s t s as  a t a l l i n f l u e n c e d by  definition  Variable costs:  long-run,  c o s t s may  short-run  s a l a r i e s o f top  the  the  are v a r i a b l e .  Examples of f i x e d  costs  These a r e  q u a n t i t i e s o f a l l the  o u g h t t o be  whose amount i s n o t ity  like.  long-run i s a p e r i o d of  enough f o r a f i r m t o v a r y  iable.  the  resources.  Long-run;  it  -  are  and  pay-  power  the  short-  variable  resources.  Explicit plicit the  costs:  The  explicit  payments f o r r e s o u r c e s  firm.  Examples o f  costs of a f i r m are  the  bought o u t r i g h t or h i r e d  explicit  costs  are  the f i r m ' s  exby  payroll,  - 13 payments f o r raw  and  -  s e m i - f i n i s h e d m a t e r i a l s and payments  f o r overhead c o s t s of a l l k i n d s . Implicit costs:  The  i m p l i c i t c o s t s o f a f i r m are the  of self-owned, self-employed c o s t s are the r e t u r n s ( i m p l i c i t wages) and which are p r o v i d e d  resources.  to labour p r o v i d e d  implicit  by the owner h i m s e l f  the r e t u r n s to the l a n d and  capital,  by the owner h i m s e l f r a t h e r than h i r e d  from o u t s i d e owners ( i m p l i c i t rent and Margin of s a f e t y :  Examples o f  costs  interest).  Margin of s a f e t y r e f e r s to the excess  of a c t u a l (or budgeted) s a l e s over the break-even s a l e s volume. Operating  costs:  The  operating  c o s t s of a f i r m are  c o s t s i n c u r r e d by the f i r m i n conducting activities.  the  i t s r e g u l a r major  They i n c l u d e the c o s t s of goods s o l d , commercial  c o s t s , i n t e r e s t and d e p r e c i a t i o n and a m o r t i z a t i o n . exclude a l l other c o s t s which are not  But,  s u b j e c t to the c o n t r o l s  e x e r c i s e d through everyday o p e r a t i n g procedures.  Hence,  income t a x e s , l o s s e s from s a l e s of p l a n t s and other  property  d i s p o s a l s , l o s s e s on f o r e i g n exchange and f l o o d , f i r e other  they  and  e x t r a o r d i n a r y l o s s e s are excluded.  Operating  revenue:  The  o p e r a t i n g revenue of a f i r m r e f e r s to  the gross  revenue or g r o s s  s a l e s from the f i r m ' s  regular  major a c t i v i t i e s l e s s r e t u r n s , allowances and cash d i s c o u n t s . Operating  profits:  The  o p e r a t i n g p r o f i t s of a f i r m are  the  - lk excess o f the o p e r a t i n g revenue over t h e o p e r a t i n g c o s t s . I f o p e r a t i n g c o s t s exceed operating  o p e r a t i n g revenue, the excess i s c a l l e d  losses.  Summary I n t h i s c h a p t e r , an attempt  has been made t o b r i n g  out the purpose o f t h i s study, i t s l i m i t a t i o n s and i t s organisation.  The h y p o t h e s i s and n u l l h y p o t h e s i s have a l s o been  d i s c u s s e d i n d e t a i l and the d e f i n i t i o n s of some o f the more important terms i n t h i s t h e s i s have been g i v e n . of break-even a n a l y s i s i s p r e s e n t e d i n the next  The nature chapter.  CHAPTER I I THE NATURE OF BREAK-EVEN ANALYSIS Introduction The standard  term, 'break-even' has  vocabulary  i n general.  become a p a r t of  of economists, accountants and  the  managers  Each of these three c l a s s e s o f people have  c o n t r i b u t e d i n no s m a l l way  to the i n c r e a s i n g p o p u l a r i t y of  t h i s subject i n recent years.  In f a c t , i t may  be s a i d  that,  today, the b e s t d i s c u s s i o n s on break-even a n a l y s i s are to be found i n economics, accounting journals.  But,  and management books  a l t h o u g h a g r e a t d e a l of a t t e n t i o n has  g i v e n to t h i s s u b j e c t , there i s s t i l l what the area i n v o l v e s .  and been  some vagueness as to  To many p e o p l e , when break-even  a n a l y s i s i s mentioned, the f i r s t t h i n g t h a t comes to mind i s a simple and  cross-over  c h a r t , i n d i c a t i n g t o t a l s a l e s revenue  t o t a l c o s t s , with the c r o s s - o v e r p o i n t r e p r e s e n t i n g  break-even p o i n t .  In r e a l i t y , break-even a n a l y s i s i s more  than the mere d e t e r m i n a t i o n revenue equals  the  cost.  of the volume l e v e l a t which  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 i n t e r p l a y of such f a c t o r s as p r i c e s , c o s t s , volume and product Use  mix.  of Break-Even A n a l y s i s To date, very l i t t l e has been done to determine  -  16  -  the  extent to which f i r m s are u s i n g break-even  The  study  i n 1958  analysis.  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,  by  two  p r o f e s s o r s , Burnard  Sord  Glenn Welsch of  the U n i v e r s i t y  of  study  to the extent to which break-even  relating 1  Texas, i s p r o b a b l y  and  In this  the only p u b l i s h e d  is  used.  35  l e a d i n g companies i n Canada, the D i s t r i c t  13  other  pared The  of  t h i r t y - s e v e n per  twenty-three  to 389  making use determine  that  break-even pre-  (Table I ) .  c e n t o f the companies and  same s t u d y ,  pre-  as a p a r t  q u e s t i o n n a i r e s were a l s o  o t h e r c o m p a n i e s , o u t o f w h i c h 3,hh per  the frequency  1  The  I  study  I and  also  The  As  were  tried  of p r e p a r a t i o n of break-even  the types of break-even analyses used.  mailed  responded.  c e n t o f t h e 3 t- f r e s p o n d e n t s  of break-even analyses.  given i n Tables  The  per  and  special studies.  T a b l e I I shows, f i f t y  and  found  c e n t o f t h e companies  break-even analyses only p e r i o d i c a l l y  I n the out  I t was  break-even analyses a t r e g u l a r i n t e r v a l s  remaining  pared  of Columbia  c e n t o f the companies d i d n o t p r e p a r e  analyses, while  analysis  s t u d y , 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  s t a t e s i n the U n i t e d S t a t e s .  f o r t y per  Inc.  to  analyses  details  are  II.  Development o f Break-Even A n a l y s i s  The  concept  1 . B u r n a r d H. S o r d Budgeting. New Y o r k : 1 9 f 8 7 " p p . 281-281+.  o f b r e a k - e v e n a n a l y s i s was  probably  and G l e n n A. W e l s c h , B u s i n e s s C o n t r o l l e r s h i p Foundation, Inc.,  -  17  -  TABLE I Number and Percentages of Companies Interviewed I n d i c a t i n g V a r i o u s Types and F r e q u e n c i e s o f Break-Even A n a l y s i s  P r e p a r a t i o n o f Break-Even  Analysis  Prepare break-even a n a l y s i s a t regular intervals P r e p a r e break-even a n a l y s i s p e r i o d i c a l l y as a p a r t o f s p e c i a l studies Do n o t prepare break-even a n a l y s i s  No. o f P e r Cent o f Companies V5 Companies 13  8  lit  37  ,ho 23  100  Frequency o f P r e p a r a t i o n o f Break-Even A n a l y s i s Prepare monthly Prepare semi-annually Prepare a n n u a l l y Prepare p e r i o d i c a l l y  P e r Cent o f 2 1 No. o f Companies u s i n g Companies B-E A n a l y s i s 3 1 9 _8 21  Types o f Break-Even Prepare Prepare Prepare Prepare Prepare  Analysis  f o r company as a whole f o r various divisions f o r plants f o r product l i n e s f o r branches o r t e r r i t o r i e s  Ih  J 100  P e r Cent o f 2 1 No. o f Companies u s i n g Companies B-E A n a l y s i s 13 11 5 9 3  62  ? 2h 5  ? Ih h  The number o f companies does not t o t a l 2 1 and the percentages do n o t t o t a l 1 0 0 because some companies use more than one type o f break-even a n a l y s i s . Source:  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 5 8 , p . 2 8 2 , Table 8 3 .  -  18  -  TABLE I I Number and Percentage of Companies Answering Q u e s t i o n n a i r e s I n d i c a t i n g Types and Frequency of P r e p a r a t i o n o f Break-Even A n a l y s i s as Reported by iMk Companies  Use o f Break-Even  Analysis  No. of Companies  Companies u s i n g break-even a n a l y s i s Companies not i n d i c a t i n g the use of break-even a n a l y s i s  Frequency of P r e p a r a t i o n  175  J£  \kk  100  k5  7 1 106 51  Prepare Prepare Prepare Prepare Prepare  for for for for for  Analysis  Per Cent of 1 7 5 Companies u s i n g B-E A n a l y s i s 13 2 * 31 15  ..-31 kk  Types of Break-Even  51  162  No. o f Companies  Prepare monthly Prepare quarterly Prepare semi-annually Prepare annually Prepare as needed No i n d i c a t i o n as t o frequency of p r e p a r a t i o n  P e r Cent o f ikk Companies  No. o f Companies  company as a whole various divisions plants product l i n e s s a l e s branches  182  lk-7  106 13jf  2k  100  P e r Cent of 1 7 5 Companies u s i n g B-E A n a l y s i s 3 31 39 7  Less than one per c e n t . The number of companies does not t o t a l 3 f r- and the percentages do not t o t a l 1 0 0 because some companies use more than one type of break-even a n a l y s i s . l  Source:  i  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 5 8 , p. 2 8 2 , Table 8 3 .  - 19 conceived  -  as a r e s u l t o f a t t e m p t s  businessmen to develop  by u n i v e r s i t y  teachers  tools to provide a s c i e n t i f i c  and  approach  2 to  business.  very l i t t l e  the development of t h i s  i s known a b o u t t h e e a r l y s t a g e s  tool.  Some w r i t e r s  have t r i e d  t h r o w some l i g h t o n t h i s a r e a b u t v i e w s t e n d t o The  first  attempt  to separate  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 was who,  supposedly,  holds  to  conflict.  costs into  made i n 1832  of  and  their the  man  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  attempt  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  the s e p a r a t i o n of c o s t s i s the b a s i s of break-even i t may  be  c l o s e to the formulas a n a l y s i s t o d a y , was  n o t known t i l l  "Time S a v i n g a n d  XX  16,  1897)  1897  anything  when H e n r y H e s s  I t s R e l a t i o n t o P r o f i t s " i n Volume  of the Engineering Magazine.  Henry Hess c o n t r i b u t e d a n o t h e r  C a p i t a l , Costs, P r o f i t s , Magazine  But  or charts t h a t are used i n break-even  w r o t e on  1903,  analysis,  s a i d t h a t C h a r l e s Babbage made t h e f i r s t c o n t r i b u -  t i o n to the development of break-even a n a l y s i s .  (Dec.  that  article,  and D i v i d e n d s " , t o t h e  (Volume X X V I ) a n d ,  i n t h i s a r t i c l e , he  I n December, "Manufacturing: Engineering included  c h a r t s which are q u i t e s i m i l a r to those used i n break-even 2.  S o r d and W e l s c h , op.  cit.,  p.  281.  3. Ned C h a p i n , "The D e v e l o p m e n t o f t h e B r e a k - E v e n 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 of B u s i n e s s , V o l . XXVIII, No. 2, A p r i l 1955, p p . l*t8-14-9. Raymond V i l l e r s , " C o m m u n i c a t i o n s - The O r i g i n o f t h e Break-Even Chart", J o u r n a l of Business. V o l . X X V I I I , No. h,  Oct.  1955,  K.  PP. 290-297.  Villers.  i b i d . , p.  296.  - 20 a n a l y s i s today, although he d i d not designate  his  presenta-  t i o n as break-even c h a r t s . During the p e r i o d j u s t p r i o r to World War other  i n d u s t r i a l engineers,  Walter Rautenstrauch and  Knoeppel, were prominent i n the development o f the even c h a r t .  I,  Rautenstrauch was  the f i r s t  to use  two  C.  E.  break-  the name,  6 •Break-even c h a r t s ' . s a l l y accepted.  This terminology i s , today, univer^-  I t might a l s o be mentioned t h a t i n Rauten-  s t r a u c h ' s c h a r t s , the f u n c t i o n a l r e l a t i o n s h i p between c o s t s and volume was  brought out, f o r the f i r s t time.  r e l a t i o n s h i p was used. The  Such a  never d e p i c t e d i n the c h a r t s Henry Hess  7  Break-Even Chart The  break-even c h a r t i s a p o r t r a y a l i n  form of the r e l a t i o n s h i p of production,, c o s t s and profit.  graphic s a l e s to  I t shows the amount o f f i x e d and v a r i a b l e c o s t s  the s a l e s revenue a t d i f f e r e n t l e v e l s of o p e r a t i o n . names have been g i v e n to t h i s c h a r t . as a c r o s s o v e r  and  Various  I t i s sometimes known  c h a r t , a p r o f i t r e a l i s a t i o n c h a r t or a p r o f i t -  graph. The  break-even c h a r t may  be p l o t t e d i n s e v e r a l  d i f f e r e n t forms, depending on the k i n d o f i n f o r m a t i o n 5. Chap i n ,  op.  c i t . . p.  6.  Villers, loc. c i t .  7.  I b i d . . p.  296-297.  1^9.  desired.  -  21  -  The d e t a i l s o f these c h a r t s may vary but the u n d e r l y i n g p r i n c i p l e s are a l l the same.  Some a r e q u i t e simple, con-  s i s t i n g o f a l i n e o r two, w h i l e o t h e r s a r e q u i t e complex, w i t h many l i n e s and legends.  I n essence,  they a l l i n t e r -  r e l a t e s a l e s , v a r i a b l e c o s t s , f i x e d c o s t s and volume l e v e l i n a form c o n s i d e r e d most h e l p f u l to the u s e r . S i n c e they a r e a l l b a s i c a l l y t h e same, they not be d e s c r i b e d here i n d i v i d u a l l y .  will  Only the c o n v e n t i o n a l  break-even c h a r t and the p r o f i t / v o l u m e c h a r t w i l l be examined, s i n c e r e f e r e n c e 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.  I n t h e c o n v e n t i o n a l break-even c h a r t  ( E x h i b i t I ) , the t o t a l c o s t l i n e , a t the lower  extremity,  cuts the Y a x i s a t t h e p o i n t where c o s t s a r e f i x e d and volume ( p r o d u c t i o n o r s a l e s ) i s equal to z e r o . p o i n t , i t s l o p e s upwards t o the r i g h t .  From t h i s  Revenue i s a l s o  r e p r e s e n t e d by a l i n e a r l i n e which o r i g i n a t e s a t the zero i n t e r c e p t i o n o f the Y and X axes and s l o p e s upwards to the r i g h t ; i t i s o f t e n p r e s e n t e d as a 45 degree l i n e , w i t h the h o r i z o n t a l and v e r t i c a l axes having the same s c a l e s and on the assumption t h a t p r o d u c t i o n i s equal to s a l e s 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 p o i n t  a t which t h e t o t a l revenue l i n e c r o s s e s the t o t a l c o s t l i n e i s the break-even p o i n t and, a t t h i s l e v e l o f p r o d u c t i o n and s a l e s , the f i r m a l l e g e d l y w i l l have n e i t h e r n e t p r o f i t nor net  loss. A somewhat s i m p l e r g r a p h i c p r e s e n t a t i o n o f the  * 23 *• EXHIBIT I I A PROFIT/VOLUME CHART T r - \ o u S a n d s  °f Dollars 25  Sa\e s  Volume  - 24 r e l a t i o n s h i p between p r o f i t s chart.  and volume i s the p r o f i t / v o l u m e  I t i s sometimes r e f e r r e d to as a p r o f i t g r a p h , a  m a r g i n a l income c h a r t , o r a p r o f i t - v o l u m e a n a l y s i s graph.  8 I t i s s a i d to have been developed  by C. E. Knoeppel.  Although p r o f i t / v o l u m e c h a r t s are g e n e r a l l y s i m p l e r  than  break-even c h a r t s , they are not always p r e f e r r e d to breakeven c h a r t s because they do not show the r e l a t i o n s h i p s between c o s t s , revenue and volume.  N i c k e r s o n , however,  argues t h a t s i n c e p r o f i t i s the r e s i d u e of c o s t 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 p r o f i t / v o l u m e c h a r t i n d i c a t e s the path of p r o f i t and c o n s i s t s of two  a r e a s , the p r o f i t area and  the  l o s s a r e a , both of which are c r e a t e d by the h o r i z o n t a l a x i s which r e p r e s e n t s the t o t a l s a l e s volume.  The l o s s area i s  composed o f the f i x e d c o s t s which i s marked o f f on vertical axis.  the  The p r o f i t area i n d i c a t e s the amount o f  p r o f i t earned as the p r o f i t l i n e passes over the h o r i z o n t a l axis.  The p o i n t s o f the p r o f i t l i n e are computed by  8. Knoeppel e x p l a i n e d 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 f i n a n c i a l t o o l r a t h e r than a management t o o l . It is a historical document and not i n the l e a s t p r o p h e t i c . I t i s s t a t i c r a t h e r than dynamic. I t performs o n l y a p a r t of the f u n c t i o n of which i t i s capable. Few accountants have c r o s s e d the l i n e between accounting and e n g i n e e r i n g , w h i l e many engineers have jumped the f e n c e between the two" - C. E. Knoeppel and Edgard C. Seybold, Managing f o r P r o f i t . New Y o r k : McGrawH i l l Book Company, Inc., 1957, PP. 53-54* 9. C l a r e n c e B. N i c k e r s o n , Co s t Ac c o u n t i n g . McGraw-Hill Book Company, Inc., 1954, p. 272.  Toronto:  - 25 s u b t r a c t i n g from s a l e s income the t o t a l c o s t s i n d i c a t e d f o r each s a l e s volume.^°  The break-even p o i n t i s the p o i n t a t  which the p r o f i t l i n e i n t e r s e c t s the h o r i z o n t a l a x i s . The Break-Even P o i n t Various break-even p o i n t .  d e f i n i t i o n s have been advanced f o r the G e n e r a l l y , i t may be s a i d t h a t the "break-  even p o i n t i s the volume l e v e l a t which t o t a l revenue exa c t l y equals made.  t o t a l c o s t and n e i t h e r p r o f i t s nor l o s s e s are  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 p o i n t can be determined by u s i n g the following  equation:  Break-even p o i n t  _  F i x e d Costs -j_ V a r i a b l e Costs Sales  To i l l u s t r a t e , the f o l l o w i n g budget data o f a f i c t i t i o u s company, the ABC Company, may be used.  10. The s l o p e o f the p r o f i t l i n e i s a l s o equal to the p r o f i t - v o l u m e (P/V) r a t i o , which i s the r a t e a t which p r o f i t i n c r e a s e s with i n c r e a s e s i n volume and i s g i v e n by the f o r m u l a : p V or  _P V  or  J?. V  "  =  =  V a r i a b l e Costs Sales Sales - V a r i a b l e Costs Sales F i x e d Costs + P r o f i t s Sales  The p r o f i t - v o l u m e r a t i o i s sometimes c a l l e d the m a r g i n a l income r a t i o o r v a r i a b l e p r o f i t r a t i o .  -  -  26  Annual P r o f i t P l a n - ABC  Company  Fixed Costs Budgeted S a l e s (200,000 u n i t s @  Variable Costs $3,000,000.  $15.)  Budgeted C o s t s : Direct Material D i r e c t Labour F a c t o r y Overhead A d m i n i s t r a t i o n Expenses D i s t r i b u t i o n Expenses  $^50,000. ^25)000. ^25.000.  $500,000. 550,000. 200,000. ' 100,000. 150.000.  $1,200,000.  $1,500,000.  Total  2.700.000.  Budgeted P r o f i t  $  300.000.  I f the above d a t a i s a p p l i e d to the break-even p o i n t e q u a t i o n g i v e n e a r l i e r , the r e s u l t w i l l be as f o l l o w s : $1.200.000. Break-even p o i n t _ ± _ $ 1 , 5 0 0 v000.  ft  .  m  n  o  n  ^..^i^o^ovo.  $3,000,000. = $2,^-000,000. S i n c e the c o s t of each u n i t i s equal to $ 1 5 ,  there-  fore, r> , ^ Break-even p o i n t  _  $2,i+OO,000. ——,— $15.  =  160,000  '  units  I t i s claimed t h a t the break-even p o i n t i s u s e f u l p a r t l y because i t i s a p r e r e q u i s i t e to the d e t e r m i n a t i o n of the margin of s a f e t y , which i s the excess of a c t u a l or budgeted s a l e s over the break-even s a l e s volume.  Expressed  as a p e r c e n t a g e , i t i s e q u a l to s a l e s above the break-even  - 27 p o i n t d i v i d e d by s a l e s ( a c t u a l or budgeted) m u l t i p l i e d by The  amount or the percentage i n d i c a t e s to what extent  revenue may higher  drop before  l o s s e s begin.  100.  sales  I t i s obvious t h a t  the  the margin of s a f e t y , the b e t t e r i s the p o s i t i o n of  the f i r m .  I t o f t e n pays management to determine the margin  of s a f e t y a t the average volume over a business c y c l e . low margin o f t e n s p e l l s danger.  The  low margin may  A  be  to the f a c t t h a t the break-even p o i n t i s too h i g h and  due since  h i g h f i x e d c o s t s i s an important cause of high-break-even p o i n t s , the remedy may the long run.  But,  be a r e d u c t i o n of the f i x e d c o s t s over  Bruce W i l l i s warns t h a t the blame  should  not be put on f i x e d c o s t s without a c a r e f u l s t u d y . ^ suggests t h a t i n e f f i c i e n t p r o d u c t i o n , i n e f f e c t i v e s e l l i n g techniques may  He  inadequate p r i c i n g  and  be the cause of the poor  performance. Another u s e f u l n e s s from i t s very d e f i n i t i o n . break-even p o i n t may  of the break-even p o i n t  As was  follows  s t a t e d i n Chapter I ,  the  a l s o be d e f i n e d as the p o i n t of time  i n the budgetary p e r i o d when l o s s e s t u r n i n t o p r o f i t s . Hence, the break-even p o i n t may  be used to i n d i c a t e the  p o i n t of time i n the budgetary p e r i o d when c o n t r i b u t i o n s p r o f i t s begin.  I t may  a l s o be used to i n d i c a t e the  to  portion  of the budgetary p e r i o d t h a t remains f o r the accumulation of the c o n t r i b u t i o n s to p r o f i t s .  11. Bruce C. W i l l i s , "The Use of Break-Even A n a l y s i s i n Management," Canadian Chartered Accountant. V o l . 73, Dec. 1958, p. 526.  - 28 Although fulness,  i t s  It  should  at  a l l  time  Howard the  always  time  break-even  determination  times,  to  the  be  for as  factors  a  professor  of  Kansas  not  that  particular  the  Stettler,  University  should  remembered  any  point be  i t  have  does  i t  not  use-  remain  but  fixed  varies  undergo  Business  states  some  over-emphasised.  enterprise,  affecting of  may  from  change.  Administration i n  that:  Although s t a t i s t i c a l confirmation is not available, t h e r e a p p e a r s t o be c o n siderable j u s t i f i c a t i o n for concluding that m o s t p e o p l e who a r e f a m i l i a r w i t h break-even charts and the analysis of break-even informat i o n assume t h a t the r e a s o n f o r s e e k i n g such information i s to determine the break-even p o i n t f o r a l l o r some s e g m e n t o f a p r o f i t making e n t e r p r i s e . True, break-even analys i s i s c a p a b l e o f l i v i n g up t o i t s name a n d showing the volume l e v e l a t which expenses and revenues are e q u a l , but i f , as contended, t h i s i s the only use g e n e r a l l y made of such i n f o r m a t i o n , the use i s not o n l y d e f i c i e n t , b u t may 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 as w e l l . ^  i s ,  at  It  must  also  best,  only  an  s t r i c t i v e  assumptions  be  stressed  that  the  approximation because that  have  to  be  made  break-even of  the  i n  i t s  point  many  re-  computa-  13 tion. of  the  Under term,  •point', better  and  the  circumstances,  'break-even  carries  term might  point'  even  is  the  appropriateness  questionable.  the  connotation  of  great  be  'break-even  area'  to  The  exactness. indicate  word, A  that  the  12. Howard F . S t e t t l e r , "Break-Even Analysis: Its Uses 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.  This  i s  discussed  i n Chapter  3.  - 29 precise can  be  Cost  location estimated  evident  that  fixed This  or can  there  lines, two  into  volume  is  not  known  and  roughly.  because  iable  behaviour  analysis.  If  and  be  any  the  lines  t o t a l  w i l l  losses  costs  the  into  the  would have  costs  never  turn At  this  break-even  to  an  be  the  can  a l l  costs so  already central  be  chart  point  are  may  be  long  as by  of  intersect  provide  profits time,  or  costs  unrealistic  separated  the  whereby  a l l  the  total  straight  X and a  Y  axes.  situation  profits  cannot  their  as  variable,  be  situation.  into  problem  constructed.  are  represented  to  be  c l a s s i f i e d  intersection  same  be  i t  cannot  If  break-even  from  far,  costs  explained.  be  so  constitutes  easily  turn fixed  Therefore,  fixed  and  var-  components.  Fixed amount  discussion  no  losses.  total  the  starting  whereby  On  break-even  variable,  cannot  revenue  the  only  cost  break-even  The  the  Breakdown  From  i n  of  i s  not  short-run  costs  at  a l l  and  other  hand,  costs,  whose  amount  decreasing  i n  the  t o t a l  to  the  change  i n  is  the  the  defined  the  variable  variable i n  be  influenced  within  the  or  may  a  by  costs  of  may of  or  those level  range  may  direction  costs l e v e l  the  expected  function  same  as  be  costs of  of  may  a c t i v i t y .  a c t i v i t y  defined  as  be  those  increasing  activity. not  i n  activity.  a c t i v i t y , as  whose  The  change  proportional  However,  i t  is  - 30 usually  assumed  straight not  line  uncommon  costs  which  i n  conventional  relationships to  find  break-even  exist  variable  and,  costs  increase  or  decrease  decreases  i n  volume.  analysis  that  consequently,  being  defined  proportionately  i t  is  as  those  with  i n -  lit creases  or  The  assumption  change  i n  output  change  i n  technology  absent. may by  If  not  be  linear  for  i n  the  iency  the  may  variable at  or  factors  production  which  and  of  change per  resources.  The  be  explained  In made  to  time  within which  as  i t s  that  the  our 1  unit.  are  the  greater  run' a  firm  equipment  classification  which  of  may  work,  detail  i n  fixed may  be  alter  into  the  the  level  differ  or  add  the  a  change  of  effic-  when  quantities  chapter  defined  caused  factors  i n  variable  costs,  are  i n  diminishing  buildings.'  costs  of  costs.  a  on  to  fixed  and  This  I I I .  as  now  of  returns  reference  It  no  costs  be  change  given  or  is  returns.  result  may  with  there  could  prices  the  variable  large  average  cannot and  a  Further,  increasing  change  This  this  used  d e f i n i t i o n of  short  capital  the  i n  and  the  i f  promotion  diminishing  the  resources  the  w i l l  that,  production,  them  also  u n i t ) .  with  variable  may  per  that  sales  large,  fact  of  result  too  j u s t i f i e d  and  or  amounts  that  are  is  assuming  increasing  also  costs  -  advertising  different fixed  great  (constant  from  of  l i n e a r i t y  too  changes  prices  follows  demand  not  output  changing  This  is  of  was  period items  becomes  of such clear  variable  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 of Analysis", N.A.A. B u l l e t i n . V o l . kO, Sec. 1, Jan.  Break-Even 1959, p. 2h.  - 31 c a t e g o r i e s i s p o s s i b l e o n l y when the time p e r i o d i s s p e c i f i e d . I f a s u f f i c i e n t l y l o n g time p e r i o d i s p r o v i d e d ,  almost a l l  c o s t s become v a r i a b l e through changes i n the s c a l e of the firm's operations.  The f i x e d - v a r i a b l e d i s t i n c t i o n i s gen-  e r a l l y a l s o based on the assumption that volume w i l l move  15 w i t h i n a c e r t a i n expected range o f a c t i v i t y ,  because move-  ments o u t s i d e t h i s range would be accompanied by changes i n the s o - c a l l e d f i x e d  costs.  Some w r i t e r s , however, a r e not too happy about the c l a s s i f i c a t i o n o f c o s t s as f i x e d o r v a r i a b l e . cases,  I n most  the v a r i o u s w r i t e r s are prepared t o accept  the i d e a  t h a t v a r i a b l e c o s t s v a r y i n d i r e c t p r o p o r t i o n to the r a t e of a c t i v i t y .  I t i s the n o n - v a r i a b l e  disagreement among the w r i t e r s . disagreement i s nothing  c o s t s that have caused  I n a t l e a s t one case, the  more than a q u e s t i o n o f semantics.  Gardner i s a g a i n s t the use o f the word, ' f i x e d ' .  He argues  t h a t t h i s word i s p s y c h o l o g i c a l l y u n f i t to d e s c r i b e  costs 16  which do n o t vary w i t h volume but, which vary  with'time.  He suggests t h a t a b e t t e r word f o r such c o s t s would be  'stand-  by'  costs. 15. This i s the range of a c t i v i t y which management exp e c t s to handle w i t h the equipment and o r g a n i s a t i o n p r o v i d e d f o r i n the budget. York:  1 6 . F r e d V. Gardner, P r o f i t Management and C o n t r o l , New McGraw-Hill Book Company, Inc., 1955> P« 2 8 . "  1 7 . The same c o s t s are a l s o known as p e r i o d c o s t s or time c o s t s s i n c e they are a f u n c t i o n of time or c a p a c i t y c o s t s s i n c e they r e p r e s e n t the c o s t s o f p r o v i d i n g the c a p a c i t y t o do b u s i n e s s .  - 32 W r i t i n g i n the Harvard Business Review i n 195 *, he 1  states: To me, the term f i x e d c o s t i s very u n s a t i s f a c t o r y , because no c o s t i s r e a l l y f i x e d ; I p r e f e r to l a b e l expenditures t h a t continue regardlesSpOf p r o d u c t i o n 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 g i v e n by Wally George about t h i r t e e n years 19^1»  George had g i v e n the f o l l o w i n g  earlier.  In  advice:  Regard no c o s t s as f i x e d or s a c r e d . From t h i r t y t o f i f t y p e r c e n t o f ' f i x e d c o s t ' i s . , g e n e r a l l y s u b j e c t t o management control. 7  Apparently, choice o f words.  Gardner i s o n l y q u a r r e l l i n g w i t h the  What he p r e f e r s to c a l l stand-by costs  are e s s e n t i a l l y the same c o s t s as those commonly r e f e r r e d to as f i x e d c o s t s .  There a r e , however, more s e r i o u s  ments over the problem o f n o n - v a r i a b l e  costs.  disagree-  I n one approach,  i t has been suggested t h a t the term, ' f i x e d c o s t s ' be r e p l a c e d by the term, 'constant regulated costs.  c o s t s ' to be made up o f f i x e d c o s t s and  I n t h i s case, f i x e d c o s t s would r e f e r to  c o s t s which are f i x e d and beyond the c o n t r o l o f management at  a moment i n time  ( f o r example, the s a l a r y  of s a l e s -  18. F r e d V. Gardner, "Break-Even P o i n t C o n t r o l f o r Higher P r o f i t s " , Harvard Business Review, V o l . XXXII, Sept.-Oct. 195S P. l^+T "~" 19. Wally E. George, "How t o C o n t r o l Your Break-Even P o i n t " , F a c t o r y Management and Maintenance. O c t . 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 c o s t s w h i c h , though fixed,  are n e v e r t h e l e s s  subject  t o 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 t o s a l e s m e n ) .  This k i n d  of a p p r o a c h seems t o 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 t e x t b o o k s 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 y e a r s t o come, t h e r e 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 .  Admittedly,  i t i s n o t the i d e a l term to d e s c r i b e the k i n d o f c o s t s  to  which i t r e f e r s .  it,  But, i t s c r i t i c s should r e a l i s e that  nonetheless,  i s perhaps a b e t t e r term t h a n any t h a t  they  can s u g g e s t ,  to the e x t e n t t h a t i t has the advantage of  widely e s t a b l i s h e d usage. I n the p a s t , many p e o p l e 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 p e o p l e a r e 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 ification.  class-  I n the y e a r s t o come, more p e o p l e may j o i n the  ranks of t h i s d i s s a t i s f i e d g r o u p .  I t i s true that  the  c l a s s i f i c a t i o n of c o s t b e h a v i o u r i n t h i s way i s f a r f r o m being p e r f e c t ;  but, i t i s also true that f o r years,  costs  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 b u d g e t i n g p u r poses and a l t h o u g h t h e t e c h n i q u e s u s e d i n the s e p a r a t i o n were s i m p l e o n e s , the u l t i m a t e r e s u l t s have been q u i t e satisfactory. ^2  There i s no doubt t h a t the a l a r m r a i s e d  2 1 . W i l l i a m J . V a t t e r , " A c c o u n t i n g Measurements of I n c r e m e n t a 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 , N o . 1 , J a n . 1945, p p . 1 4 7 - 1 4 8 .  - 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 g r e a t e r than i s warranted by the nature  of  the  problem. In break-even a n a l y s i s , i t i s assumed t h a t i t i s reasonable  to c l a s s i f y c o s t s as f i x e d o r v a r i a b l e .  b r i n g s us to the problem of s e m i - v a r i a b l e c o s t s .  This  Such c o s t s  vary w i t h volume though not i n d i r e c t p r o p o r t i o n 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 v a r i a b l e c o s t s and are sometimes c a l l e d f i x e d - v a r i a b l e c o s t s o r semifixed costs.  Examples i n c l u d e items such as s u p e r v i s i o n ,  power and maintenance c o s t s .  In break-even a n a l y s i s , one  i s f a c e d w i t h the problem of s e p a r a t i n g these 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.  One  way  out of  this  problem i s to measure the v a r i a b i l i t y of these c o s t s . G e n e r a l l y , t h e r e are three approaches to measurement of c o s t v a r i a b i l i t y . (a) The Accounting (b) The  the  They a r e :  Approach - I n s p e c t i o n of  accounts.  S t a t i s t i c a l Approach- S t a t i s t i c a l a n a l y s i s o f h i s t o r i c a l costs.  (c) The E n g i n e e r i n g Approach- I n d u s t r i a l studies. The of the t h r e e .  accounting  engineering  approach i s , by f a r , the  I t also requires  the l e a s t time.  simplest By  this  22. J o e l Dean,"Methods and P o t e n t i a l i t i e s of BreakEven A n a l y s i s " i n David Solomons (ed*>, S t u d i e s i n C o s t i n g . London: Sweet & Maxwell, L t d . , 1952, pp. 232-233.  -  35  -  method, a c a r e f u l study has f i r s t to be made of the c h a r t of  accounts.  On the b a s i s of t h i s study, c o s t s which are  e i t h e r f i x e d or wholly v a r i a b l e , are then p i c k e d out, l e a v ing  behind  tical  the s o - c a l l e d s e m i - v a r i a b l e c o s t s .  technique  and/or the e n g i n e e r i n g  The  technique may  be a p p l i e d to the s e m i - v a r i a b l e c o s t s to separate f i x e d and v a r i a b l e components. accounting behaviour  statis-  I t i s obvious  then  their  t h a t the  approach r e q u i r e s a thorough knowledge of of the c o s t s i n each of the accounts.  the  Unless  a f a i r l y complete knowledge of the o p e r a t i o n s and  activi-  t i e s of the e n t e r p r i s e i s obtained beforehand, the r e s u l t s a r r i v e d a t , by u s i n g t h i s method, may  be m i s l e a d i n g .  In  any case, the very f a c t , t h a t t h i s approach r e q u i r e s the e x e r c i s e of judgement, means that i t i s f a r from being infallible  an  one. The  s t a t i s t i c a l approach, i n v o l v i n g the  statis-  t i c a l a n a l y s i s of h i s t o r i c a l c o s t s i s probably more t h o r ough and  s c i e n t i f i c than the accounting method.  But,  u n l e s s computers are used, i t can a l s o be more time consuming  and expensive.  I t can be c a r r i e d out by u s i n g  t i c a l c o r r e l a t i o n techniques to  some measure of a c t i v i t y .  statis-  which r e l a t e each c o s t component The best example of  approach i s the s c a t t e r c h a r t technique  this  under which the  h i s t o r i c a l c o s t and volume ( p r o d u c t i o n or s a l e s d o l l a r s  as  a measure of a c t i v i t y ) d u r i n g each of s e v e r a l p a s t months o r years are p l o t t e d on a c h a r t w i t h volume as the h o r i z o n -  - 36 t a l a x i s and  costs  as the v e r t i c a l a x i s .  p a t t e r n formed by the grouping may  Depending on  the  of the p o i n t s p l o t t e d , a l i n e  then be f i t t e d through the p o i n t s , e i t h e r by the  simple  and p r a c t i c a l method of i n s p e c t i o n 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 u s u a l behaviour 23  of the c o s t s at v a r i o u s volumes ( E x h i b i t I I I ) .  The  point  (above the i n t e r s e c t i o n of the h o r i z o n t a l and v e r t i c a l at which t h i s l i n e cuts the v e r t i c a l a x i s , r e p r e s e n t s f i x e d c o s t s i . e . those volume.  c o s t s not a f f e c t e d by any  A h o r i z o n t a l l i n e may  axes), the  changes i n  then be drawn through t h i s  p o i n t to r e f l e c t the f i x e d c o s t s . Another s t a t i s t i c a l technique p o i n t s method. and  i s the high-low  In t h i s method, the p e r i o d s with the h i g h e s t  lowest volumes are f i r s t  selected.  ences i n the volumes of the two  differ-  p e r i o d s are r e l a t e d to the  d i f f e r e n c e s i n the c o s t s of the two cost v a r i a b i l i t y pattern.  Then, the  p e r i o d s , to give  This method i s almost as  the simple  as the method of i n s p e c t i o n , but i t i s very seldom used because i t i s extremely v u l n e r a b l e i n costs.  Unusually  h i g h or low  to random v a r i a t i o n s  c o s t f i g u r e s may  the whole p i c t u r e s i n c e only the extremes are  distort  considered  i n t h i s method. 2 3 . This i s 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 chapter IV, which d e s c r i b e s a study of 57 f i r m s i n Worth America to determine the extent to which break-even a n a l y s i s i s u s e f u l as a t o o l f o r f o r e c a s t i n g o p e r a t i n g 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 c o s t s and the l e a s t squares method i s used to f i t the l i n e through the p o i n t s i n the s c a t t e r c h a r t s .  - 37 *  EXHIBIT I I I  A SCATTER CHART  Thousands of Dollars loot-  So -  0  4.0 -  Fixed Cost Lir->e  F(*edl  !  t  io V o l u m e  1  4-0 ( ^QWS —  Costs  >  €>o  \r-\ l l n o u " s a » n c l s  1  1  SO  loo t>o\\c»rs)  - 38 The main d i f f i c u l t y w i t h the s t a t i s t i c a l i s that h i s t o r i c a l c o s t data o f t e n show poor w i t h volume.  T h i s i s so mainly because  approach  correlation  costs often vary  not s o l e l y because of volume but a l s o because of many o t h e r factors.  These f a c t o r s i n c l u d e changes i n p l a n t , equipment,  m a t e r i a l s used, methods of manufacturing, p e r s o n n e l , working  hours, f a c t o r p r i c e s and managerial p o l i c y .  I n study-  ing  c o s t behaviour f o r purposes of break-even a n a l y s i s , i t  i s n e c e s s a r y to assume t h a t these non-volume f a c t o r s , which a f f e c t c o s t s , w i l l remain c o n s t a n t . The e n g i n e e r i n g approach i s the o n l y f e a s i b l e method, when h i s t o r i c a l data are u n a v a i l a b l e or too unr e l i a b l e but I t can a l s o be used f o r supplementing  statis-  t i c a l or a c c o u n t i n g a n a l y s i s when i t i s d e s i r e d to p r o j e c t c o s t behaviour beyond the range of p a s t output experience or  when i t i s n e c e s s a r y to estimate the e f f e c t of major  changes i n technology o r p l a n t s i z e upon c o s t behaviour over a f a m i l i a r or u n f a m i l i a r output range. t h i s method attempts  to determine  In essence,  the p h y s i c a l i n p u t s nec-  essary to achieve c e r t a i n l e v e l s of output and then conv e r t these to d o l l a r s a t c u r r e n t or a n t i c i p a t e d 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 t h a t i t attempts to work w i t h r e l a t i o n s h i p s between v a r i o u s p h y s i c a l i n p u t s and the volume of a c t i v i t y r a t h e r than w i t h observed h i s t o r i c a l p a t t e r n s , which may factors.  be d i s t o r t e d by c e r t a i n non-volume  However, l i k e the s t a t i s t i c a l approach, i t a l s o  - 39 can i n v o l v e very h i g h expenses.  In addition, i t suffers  from the drawback t h a t t h e p r a c t i c a l f e a s i b i l i t y o f i t s estimates cannot be p r e t e s t e d . These three approaches to the measurement of c o s t v a r i a b i l i t y are n o t n e c e s s a r i l y m u t u a l l y e x c l u s i v e .  In  f a c t , i t i s o f t e n a good p r a c t i c e t o use them to supplement each  other.  Summary Break-even a n a l y s i s does n o t merely i n v o l v e the determination  o f the break-even p o i n t .  I t a l s o 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 i n t e r p l a y o f such f a c t o r s as p r i c e s , c o s t s and volume. little  Although there i s very  agreement among w r i t e r s r e g a r d i n g  the development o f  break-even a n a l y s i s , i t may g e n e r a l l y be s a i d t h a t  Charles  Babbage, Henry Hess, Walter Rautenstrauch and C. E. Knoeppel were the p i o n e e r s .  Henry Hess was r e s p o n s i b l e f o r the b a s i c  i d e a o f the break-even c h a r t but i t s u n i v e r s a l l y accepted terminology has been c r e d i t e d to P r o f e s s o r The graphic  Rautenstrauch.  break-even c h a r t I s b a s i c a l l y a p o r t r a y a l i n  form of the r e l a t i o n s h i p of p r o d u c t i o n ,  c o s t and  s a l e s to p r o f i t , though i t may be p l o t t e d i n s e v e r a l ent ways.  I n t h i s chapter,  o n l y the c o n v e n t i o n a l  even c h a r t and the p r o f i t / v o l u m e 2^. Dean, op. c i t . . p. 231.  differ-  break-  c h a r t have been p r e s e n t e d .  - ho In the d i s c u s s i o n s on break-even c h a r t s , i n l a t e r reference  chapters,  w i l l be made mainly t o these two c h a r t s . In any break-even c h a r t , there must be a break-  even p o i n t , which may be d e f i n e d as the volume l e v e l o r p o i n t o f time i n the budgetary p e r i o d when l o s s e s t u r n i n t o profits.  The break-even p o i n t I s u s e f u l because i t i s a  p r e r e q u i s i t e t o the d e t e r m i n a t i o n which i s a u s e f u l r e f e r e n c e  o f the margin o f s a f e t y ,  device f o r a c t i o n .  I t i s also  u s e f u l because i t i n d i c a t e s the p o i n t of time i n the budg e t a r y p e r i o d when c o n t r i b u t i o n s to p r o f i t s begin.  However,  i t must be r e a l i s e d t h a t the break-even p o i n t i s n o t as exact  as i t s name i m p l i e s and that i t does n o t remain f i x e d  at a l l times.  Therefore,  i t s usefulness  should n o t be over-  emphasised. One  o f the most important steps  i n break-even  a n a l y s i s i s the c l a s s i f i c a t i o n o f c o s t s as f i x e d o r v a r i a b l e . Three approaches may g e n e r a l l y be used. ing,  s t a t i s t i c a l and engineering  They a r e the account-  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 o f the data a v a i l a b l e and w i l l be used i n the t e s t , which w i l l be d e s c r i b e d  i n chapter IV.  From the f a c t s t h a t are p r e s e n t e d on break-even a n a l y s i s i n t h i s chapter,  a c r i t i c a l e v a l u a t i o n of break-even  a n a l y s i s i s made i n the next  chapter.  CHAPTER I I I A CRITICAL EVALUATION OF BREAK-EVEN ANALYSIS Introduction In was  chapter I I , the nature of break-even a n a l y s i s  g i v e n and some of the methods of s e p a r a t i n g the t o t a l  c o s t s of f i r m s were p r e s e n t e d .  I n t h i s chapter, a c r i t i c a l  e v a l u a t i o n of break-even a n a l y s i s i s attempted i n terms of the  economic  theory of the f i r m i n the s h o r t and l o n g run  and under p e r f e c t and i m p e r f e c t c o m p e t i t i v e  conditions.  The assumptions which are used i n break-even a n a l y s i s and the  uses to which break-even a n a l y s i s may  be put are a l s o  dis-  cussed. Static Analysis The r e l i a b i l i t y of break-even a n a l y s i s i s dependent upon r e a s o n a b l y a c c u r a t e p o r t r a y a l s of c o s t behaviour, which are  a f f e c t e d by the i n t e r p l a y of a number of f a c t o r s .  f a c t o r s , as was ing  d i s c u s s e d i n chapter I I , are c o n s t a n t l y  as management seeks to improve p r o f i t s .  These chang-  Break-even  a n a l y s i s attempts to a r r e s t the motion of these dynamic  forces  by assuming t h a t a l l of them, except volume, w i l l remain cons t a n t d u r i n g the p e r i o d i n which the a n a l y s i s w i l l  be used.  Hence, break-even a n a l y s i s assumes a s t a t i c a n a l y s i s , being a p i c t u r e of r e l a t i o n s h i p s which p r e v a i l only under one s e t o f assumptions.  - 42  Since  -  s t a t i c assumptions u n d e r l i e the c o n s t r u c t i o n  of break-even c h a r t s , c e r t a i n c a u t i o n s the use of these c h a r t s .  have to be observed i n  To begin with,  the p o s i t i o n s o f the  l i n e s on the c h a r t s are r e l i a b l e o n l y w i t h i n the range o f normal volume f l u c t u a t i o n s i . e . , the r e l e v a n t range which 1 the b a s i s f o r drawing the c h a r t s .  was  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 c h a r t s were not extended back to the o r i g i n but i n s t e a d were drawn as i l l u s t r a t e d i n E x h i b i t IV. The revenue-cost r e l a t i o n s h i p s may  be v a l i d  within  the r e l e v a n t range of volume but the same r e l a t i o n s h i p s 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 o u t s i d e the l i m i t s of the r e l e v a n t range.  An extreme r e d u c t i o n of volume may  management to reduce many f i x e d c o s t s . s a l a r i e s may  cause  F o r example,  executive  be reduced o r excess p l a n t and equipment may  s o l d to reduce d e p r e c i a t i o n , insurance  and p r o p e r t y  taxes.  By such a c t i o n s , the break-even p o i n t i s lowered.  A large  increase  costs  i n volume has the opposite  e f f e c t because  be  which are f i x e d w i t h i n the normal range o f volume w i l l be increased.  As examples, a d d i t i o n a l s u p e r v i s o r s  and c l e r k s  are o f t e n added and more machinery and equipment might be bought.  1. I t i s true t h a t even w i t h i n t h i s range, the e f f e c t s of the dynamic f o r c e s may be f e l t , but as w i l l be p o i n t e d out l a t e r i n the chapter, r e s e a r c h s t u d i e s have shown t h a t , w i t h i n t h i s range, t o t a l v a r i a b l e c o s t s i n c r e a s e a t a constant r a t e and p r i c e s are u n l i k e l y to change s i n c e f i r m s tend to f e e l t h a t t h e i r customers p r e f e r s t a b l e p r i c e s .  - h3 -  EXHIBIT I V MODIFIED CONVENTIONAL  BREAK-EVEN CHART  loor-  80  y> « 0  Rev/enUe  Total  Costs  0  u 0  C  Total S O r  0  0  U  n  IT  2 "4  >  J  fl; 0  2oh  Relevfcint"  20  4 0  Volumne  Range SO  ( " T h o u s a n d s  80  of  D o l o r s )  loo  - ¥* A Short-Run Concept The  s t a t i c s i t u a t i o n that break-even a n a l y s i s  assumes cannot e x i s t f o r long p e r i o d s of time because the l o n g e r the p e r i o d covered  i n the p r o j e c t i o n , the l e s s  i s the f o r e c a s t of revenue and c o s t s . may  reliable  In the s h o r t - r u n , i t  be t r u e t h a t there e x i s t s a unique f u n c t i o n a l r e l a t i o n s h i p  between the p r o f i t s of a f i r m and i t s volume and t h a t , g i v e n the volume, the corresponding mined.  But,  l e v e l of p r o f i t c o u l d be  t h i s Is p r o g r e s s i v e l y l e s s t r u e as the  deter-  time  p e r i o d i n c r e a s e s 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 g r e a t many other f a c t o r s , a p a r t from volume and, long-run,  i n the  dynamic f o r c e s c o n t i n u a l l y work to s h i f t and  these o t h e r f a c t o r s as w e l l as volume.  modify  I t , t h e r e f o r e , becomes  c l e a r t h a t break-even a n a l y s i s i s e s s e n t i a l l y a s h o r t - r u n concept and i s more u s e f u l i n s h o r t - r u n , as opposed to f i n a n c i a l planning.  In f a c t , i f a l o n g - r u n  to break-even a n a l y s i s , i t s u s e f u l n e s s dubious.  long-run,  concept i s attached  immediately becomes  P r o f e s s o r Neuner s t a t e s t h a t : Break-even a n a l y s i s and c h a r t s must be kept c u r r e n t and not attempt to r e f l e c t probable o p e r a t i n g circumstances over a p e r i o d longer than a year because not o n l y the mixture of v a r i a b l e c o s t and income elements may change but a l s o f i x e d c o s t s g r a d u a l l y s h i f t over extended p e r i o d s of time. d  L i n e a r and C u r v i - L i n e a r  Charts  There i s an i n t e r e s t i n g and perhaps deceptive 2. John J . ¥. Neuner, Cost A c c o u n t i n g . R i c h a r d D. I r w i n Company, 1957, p. 790.  resem-  Homewood, I l l i n o i s :  - K5 blance between the l i n e a r and c u r v i - l i n e a r The  break-even c h a r t s .  b a s i s f o r the c o n s t r u c t i o n o f the l a t t e r stems from t h e  cost-volume and revenue-volume f u n c t i o n s o f the economic theory  o f the f i r m , as i l l u s t r a t e d i n E x h i b i t "V. P r e s e n t e d i n  t h i s form, the c u r v i - l i n e a r c h a r t , as d e s c r i b e d  chart closely  i n chapter I I , except f o r the nature of i t s  t o t a l c o s t and t o t a l revenue f u n c t i o n s . in detail later. as the l i n e a r linear  resembles the l i n e a r  This w i l l be d i s c u s s e d  Meanwhile, i t must be p o i n t e d o u t t h a t where-  c h a r t has o n l y one break-even p o i n t , the c u r v i -  c h a r t r e v e a l s two break-even p o i n t s , i . e . , two l e v e l s  o f output a t which the f i r m ' s r e v e n u e j u s t covers i t s c o s t s so t h a t n e t p r o f i t i s z e r o . (Exhibit  ¥).  i n the l i n e a r curvi-linear  These a r e the p o i n t s B-^ and B  2  P o i n t B-^ i s analogous t o the break-even p o i n t c h a r t and p o i n t B^ i s the l o g i c a l r e s u l t o f the nature o f the t o t a l c o s t and t o t a l revenue  func-  tions. Another b a s i c d i f f e r e n c e between the two analyses i s i n the p o i n t o f maximum p r o f i t s .  P r o f i t s may be d e f i n e d as  the excess o f t o t a l revenue over t o t a l c o s t s . t h e r e f o r e , t h a t the l a r g e s t  I t i s clear,  p r o f i t s , which a f i r m c o u l d make,  w i l l be earned when the v e r t i c a l d i s t a n c e between the t o t a l c o s t and the t o t a l revenue curves i s a t i t s g r e a t e s t . i s i n d i c a t e d by MP a t volume K, i n E x h i b i t 7.  This  The l i n e a r  break-even c h a r t , on the other hand, shows p r o f i t maximised at f u l l capacity. the c u r v i - l i n e a r  This tends t o give the impression  that  a n a l y s i s has a s l i g h t advantage over the  EXHIBIT V CURVI-LINEAR BREAK-EVEN CHART  l i n e a r a n a l y s i s , s i n c e 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 s p e c i f y the p o s i t i o n w i t h i n the p r o f i t area a t which the f i r m should endeavour to operate.  L i n e a r break-even a n a l y s i s ,  merely suggests t h a t the business should operate above the break-even p o i n t and  i t i m p l i e s , what i s l o g i c a l l y untenable,  that the p r o f i t area w i t h i n the range of normal volume f l u c t u a t i o n s w i l l keep on widening as p r o d u c t i o n  volume expands.  D i f f e r e n t concepts of p r o f i t s u n d e r l i e 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.  revenue over both types of c o s t s .  construc-  In the l a t t e r  d i s t i n c t i o n i s made between i m p l i c i t c o s t s and and p r o f i t s are d e f i n e d as the surplus  the  explicit  or excess of  costs  total  E x p l i c i t costs take  the  form of e x 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 h i r e d by the f i r m . semi-finished  The  m a t e r i a l s , payments of overhead c o s t s of  are examples of e x p l i c i t c o s t s . accountants l i s t as expenses.  depreciation  I m p l i c i t c o s t s , on the  s a l a r y of a s i n g l e p r o p r i e t o r , who  f o r himself  but who  and various  charges  They are the c o s t s which  hand, are those c o s t s of self-owned, self-employed The  or  f i r m ' s p a y r o l l , payments f o r raw  k i n d s and payments i n t o s i n k i n g funds and  a  s e t s a s i d e no  other  resources. salary  takes the f i r m ' s p r o f i t s as payment f o r  h i s s e r v i c e s i s an e x c e l l e n t example.  In accordance w i t h  opportunity  the s i n g l e p r o p r i e t o r ' s  c o s t d o c t r i n e , the c o s t of  the  s e r v i c e s i n producing h i s product i s the foregone a l t e r n a t i v e p r o d u c t , which would have been produced, had  he worked f o r  -  43 -  someone e l s e i n .a s i m i l a r c a p a c i t y .  To the economist, a  s a l a r y f o r the p r o p r i e t o r equal to t h e value o f h i s s e r v i c e s i n h i s next best a l t e r n a t i v e employment may be c o n s i d e r e d as a p a r t o f the f i r m ' s c o s t s .  I t i s an i m p l i c i t  cost.  In l i n e a r c h a r t s , however, i m p l i c i t cost i s i g nored and a f i r m ' s t o t a l c o s t s are c o n s i d e r e d only the e x p l i c i t o b l i g a t i o n s t o resource circumstances, gross  to i n c l u d e  owners.  Under the  a f i r m ' s n e t income becomes the remainder o f  revenue a f t e r o p e r a t i n g and f i n a n c i a l expenses have  been deducted.  No c o n s i d e r a t i o n I s g i v e n to i m p l i c i t  costs  such as i n t e r e s t and d i v i d e n d payments equal t o what i n v e s t o r s c o u l d earn had they i n v e s t e d elsewhere i n the economy. Separation  of Costs I n chapter  I I , i t was s t a t e d t h a t i n break-even  a n a l y s i s , i t i s necessary t o separate c o s t s and v a r i a b l e c o s t s . made, i t i s i m p o s s i b l e  t o t a l costs i n t o f i x e d  U n l e s s such a c l a s s i f i c a t i o n i s  t o c o n s t r u c t a break-even c h a r t .  i f as d e f i n e d e a r l i e r , f i x e d c o s t s equal  But,  those c o s t s which  remain f i x e d , i r r e s p e c t i v e o f volume and v a r i a b l e c o s t s  equal  those c o s t s which vary i n d i r e c t p r o p o r t i o n t o volume, and if  c o s t s can o n l y 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 , then  t h e r e a r e bound to be some c o s t s which are beyond cation.  classifi-  Sidney Robbins s t a t e s t h a t , "many c o s t s and the  components o f these c o s t s do n o t f a l l i n t o neat b l a c k o r white, f i x e d or v a r i a b l e c a t e g o r i e s , but are r a t h e r grey-  .  1,9 -  hued, p a r t a k i n g of the c h a r a c t e r i s t i c s o f both t y p e s . . . . "  J  Some o f these c o s t s , p o p u l a r l y known as s e m i - v a r i a b l e c o s t s , i n c l u d e c o s t s f o r such items as s u p e r v i s i o n l a b o u r , power, maintenance, and accounting  services.  I n break-even a n a l y s i s , as i n d i c a t e d i n chapter I I , these c o s t s a r e u s u a l l y broken down i n t o t h e i r f i x e d and v a r i a b l e components by e i t h e r the a c c o u n t i n g , s t a t i s t i c a l o r e n g i n e e r i n g methods.  None o f these methods can produce com-  p l e t e l y a c c u r a t e r e s u l t s but t h e r e i s a l s o 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 .  the circumstances, the assumption  Under  made i n break-even a n a l y s i s  that a l l c o s t s can be reasonably separated i n t o t h e i r  fixed  and v a r i a b l e components should not p r o v i d e any cause f o r alarm.  What i s important i s r e c o g n i t i o n of the f a c t t h a t  i r r e s p e c t i v e o f the method used i n the d i v i s i o n of the c o s t s , the r e s u l t w i l l n o t be completely a c c u r a t e and the more i n a c c u r a t e the d i v i s i o n o f the c o s t s , the more i n a c c u r a t e w i l l the r e s u l t s o f the break-even a n a l y s i s be. Constant S e l l i n g  Prices  The p r e s e n t a t i o n of t o t a l c o s t and t o t a l revenue  3. Sidney M. Robbins, "Emphasizing the M a r g i n a l F a c t o r i n Break-Even A n a l y s i s " , N.A.A. B u l l e t i n , V o l . V3, O c t . I96I, P. 59. W i l l i a m J . V a t t e r , "Accounting Measurements o f I n c r e mental Cost", J o u r n a l o f B u s i n e s s . V o l . XVIII, No. 1, J a n .  19^5, PP. 1H7-IWI  - 50 f u n c t i o n s as s t r a i g h t l i n e s has o f t e n been questioned.  The  l i n e a r i t y o f the t o t a l revenue curve i m p l i e s a c o n s t a n t s e l l i n g p r i c e over the e n t i r e range of output.  T h i s i s not  unusual i f c o n d i t i o n s of pure c o m p e t i t i o n 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 p r o p o r t i o n of the t o t a l output of a homogenous product and no s i n g l e s e l l e r can, by h i s own e f f o r t s , i n f l u e n c e 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 o f supply and demand i n the market.  I n a d d i t i o n , every s e l l e r can s e l l a l l h i s out-  put a t t h e market p r i c e .  U n f o r t u n a t e l y , such c o n d i t i o n s o f  pure c o m p e t i t i o n are r a r e o r i m p o s s i b l e to achieve i n the r e a l world.  T h i s , t h e r e f o r e , tends to suggest t h a t the  p r e s e n t a t i o n o f the t o t a l revenue f u n c t i o n as a s t r a i g h t l i n e i s not v a l i d . Under any o t h e r market c o n d i t i o n , o t h e r than pure c o m p e t i t i o n , a f i r m can i n c r e a s e i t s s a l e s volume o n l y by l o w e r i n g i t s s e l l i n g p r i c e , when a l l other determinants o f demand - consumer incomes, consumer t a s t e s and p r e f e r e n c e s , number of consumers and range o f goods a v a i l a b l e to consumers - remain unchanged and i f a d v e r t i s i n g and s a l e s p r o motion are assumed to be absent.  I n o t h e r words, the demand  curve s l o p e s downward t o the r i g h t when the s e l l e r has any degree o f m o n o p o l i s t i c c o n t r o l over p r i c e , i m p l y i n g t h a t f o r each p o s s i b l e s e l l i n g p r i c e , there i s a corresponding s a l e s volume.  Under such circumstances, the t o t a l revenue f u n c t i o n  - 51 t a k e s a c u r v i - l i n e a r f o r m , a s shown i n E x h i b i t V. almost a l l cases, monopolistic acceptable as  producers face  competition,  one t h e r e f o r e  the p r e s e n t a t i o n  c u r v i - l i n e a r rather  conditions  than  of the t o t a l  Since i n  of imperfect  tends to f i n d revenue  or  more  function  linear.  However, i t must n o t be f o r g o t t e n  that over the  r a n g e o f s a l e s volume w i t h w h i c h most p r o d u c e r s a r e f a m i l i a r , a n u n c h a n g e d p r i c e c a n be c h a r g e d and h e n c e 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 price', the  i t i s not implied  market w i l l  held  Assuming  revenue f u n c t i o n .  here that  bear o r that  indefinitely  this  this  that non-price  i s the p r i c e  increases.  the producer  to clear a l l h i s  m a r k e t demand, a n y f u r t h e r i n c r e a s e i n  b e l o w t h e demand c u r v e f a c e d  I t i s only  t h e n o r m a l s a l e s volume by t h e p r o d u c e r t h a t  t o have a n u n c h a n g e d p r i c e .  demand c u r v e i s bound t o make i t s i n f l u e n c e f e l t .  can  be i l l u s t r a t e d .  the  vertical  firm  range,  i t is  But, sooner o r l a t e r ,  the  axis.  sales  beyond t h e l e v e l a t which the s e l l i n g  when t h e p r i c e c h a r g e d , w i t h i n  axis  which  i s t h e p r i c e w h i c h c a n be  o u t p u t must n e c e s s a r i l y be s o l d a t a l o w e r p r i c e .  possible  'unchanged  i n d u c e m e n t s a r e a b s e n t , once  i s j u s t r i g h t to enable  output w i t h the given  is  By  i n a s s o c i a t i o n w i t h s a l e s volume  volume h a s i n c r e a s e d price  total  I n E x h i b i t V I , p r i c e I s measured  and s a l e s volume a l o n g  This along  the h o r i z o n t a l  I f OP i s t h e p r i c e and DD t h e demand c u r v e a n d i f t h e i s only  c o n c e r n e d w i t h t h e r a n g e o f s a l e s volume  MN,  t h e n t h e p r i c e OP c a n be c h a r g e d t h r o u g h o u t t h a t r a n g e .  So  - 52 -  EXHIBIT V I THE L I M I T S OF CONSTANT PRICES  O  H  5<a|es  Nl  Voluw-\e  Q  - 53l o n g as the demand does not change, the f i 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  Obviously,  OQ.  f o r q u a n t i t i e s l e s s than OQ, the f i r m c o u l d 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 output.  F o r example, f o r q u a n t i t y OM, the f i r m c o u l d 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 a t OP even though i t i s w i l l i n g to s e l l o n l y OM q u a n t i t i e s , with the g i v e n demand curve DD.  T h i s i s so  because f i r m s tend to f e e l t h a t t h e i r customers p r e f e r s t a b l e p r i c e s and hence once p r i c e i s s e t and shown to be p r o f i t a b l e , i t i s l i k e l y to be r e t a i n e d u n t i l some major change  5 i n c o n d i t i o n s causes an i n r o a d i n t o the d e s i r e d p r o f i t  goal.  Since PP and DD, i n E x h i b i t VI, have to I n t e r s e c t somewhere, it  t h e r e f o r e f o l l o w s t h a t the t o t a l revenue curve cannot con-  t i n u e i n d e f i n i t e l y as a s t r a i g h t l i n e but, sooner o r l a t e r , must f a l l  quite steeply.  Beyond the s a l e s volume OQ, the  p r i c e l i n e PP i s above the demand l i n e DD and any d e s i r e d i n c r e a s e i n s a l e s must t h e r e f o r e n e c e s s a r i l y 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 t h a t , i n the v a s t m a j o r i t y o f n o n - a g r i c u l t u r a l , i n d u s t r i a l e n t e r p r i s e s i t u a t i o n s , which are c h a r a c t e r i s e d by conditions of imperfect  or monopolistic  c o m p e t i t i o n , the  l i n e a r break-even c h a r t i s i n c o r r e c t on the revenue s i d e , except f o r s m a l l range of s a l e s volume over which i t i s 5. Robert F. L a n z i l l o t t i , " P r i c i n g O b j e c t i v e s i n Large Companies", American Economic Review, VOL. XLVIII, No. 5» Dec. 1958, p. 937.  - 5k p o s s i b l e t o have an unchanged p r i c e . T o t a l Cost and Constant U n i t V a r i a b l e The  Costs  l i n e a r break-even c h a r t a l s o c a r r i e s the  assumption t h a t cost-volume r e l a t i o n s h i p s a r e u s u a l l y chara c t e r i s e d by s t r a i g h t l i n e s and s i n c e the f i x e d c o s t component i s always taken as given, i t t h e r e f o r e f o l l o w s it  that  i s the shape of the v a r i a b l e c o s t f u n c t i o n that determines  the shape o f the t o t a l c o s t f u n c t i o n .  I f t h i s i s the case,  then to draw a l i n e a r t o t a l c o s t f u n c t i o n from zero percent  of productive  to 100  c a p a c i t y i s to suggest t h a t v a r i a b l e  c o s t per u n i t i s constant  f o r a l l volumes o f a c t i v i t y up to  f u l l c a p a c i t y and t h a t marginal c o s t i s a l s o constant and equal to v a r i a b l e c o s t p e r u n i t , as i l l u s t r a t e d i n E x h i b i t VII.  A l i n e a r t o t a l c o s t f u n c t i o n a l s o suggests, as the  same E x h i b i t shows, t h a t t o t a l c o s t p e r u n i t d e c l i n e s cont i n u o u s l y over the e n t i r e volume range up to f u l l and  i s always higher  costs.  capacity  than v a r i a b l e c o s t s per u n i t or m a r g i n a l  Diseconomies of s c a l e a r e supposedly  non-existent.  T h i s d i s t u r b s economists because i t c o n f l i c t s w i t h the economic theory  o f the f i r m .  Economists have g e n e r a l l y  drawn the t o t a l c o s t f u n c t i o n as a curve which r i s e s f i r s t a t a d e c l i n i n g r a t e and then a t an a c c e l e r a t i n g r a t e , as i l l u s trated i n Exhibit VIII.  They b e l i e v e t h a t , as the volume o f  output o f a f i r m i n c r e a s e s from zero l e v e l to 'optimum  1  - 55 EXHIBIT V I I CONSTANT AVERAGE  VARIABLE  COST  7o  5oh x->  0 4o|  u  3oh  2oh  or  loh  M^r-<^\v-\o\ C o s V  AsVer-cacje  Var\ot>\e Cost  2 0  Vol  30  AO  (Output )  SO  GO  EXHIBIT  Sol-  7°h  ECONOMISTS'  VIII COST  CURVES  - 57 volume l e v e l , slightly  u n i t v a r i a b l e c o s t s w i l l most l i k e l y  fall  (assuming t h a t f a c t o r p r i c e s remain c o n s t a n t ) ,  since  the v a r i a b l e f a c t o r s w i l l produce somewhat more e f f i c i e n t l y near the f i r m ' s levels.  The  'optimum' volume l e v e l than a t very low  i n c r e a s e d e f f i c i e n c y may  specialisation.  But,  be due  to  volume  increased  as the f i r m approaches i t s 'optimum'  volume l e v e l , economists argue that a f u r t h e r i n c r e a s e  in  the volume of output w i l l most c e r t a i n l y i n c r e a s e u n i t v a r iable costs quite sharply.  Economists p o i n t out t h a t  i n c r e a s e d volume of output can o n l y come from the use of the v a r i a b l e f a c t o r s of p r o d u c t i o n  an of more  or from o b t a i n i n g  work or g r e a t e r output from the e x i s t i n g ones.  The  harder  fact  that  more of the v a r i a b l e 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 l e a d to overcrowding bad o r g a n i s a t i o n .  and  Moreover, the f a c t t h a t e x i s t i n g f a c t o r s  have to be used more i n t e n s i v e l y w i l l mean t h a t workers tend to s u f f e r from o v e r s t r a i n and more f r e q u e n t l y .  t h a t machines tend to break down  Hence, economists envisage u n i t v a r i a b l e  c o s t curves as f a l l i n g l e v e l j u s t short of the  s l i g h t l y from zero volume to a volume 'optimum' volume l e v e l and  rising  s h a r p l y from there onwards, as i l l u s t r a t e d i n E x h i b i t U n i t v a r i a b l e c o s t curves,  according  IX.  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 a t which a l l the f a c t o r s of p r o d u c t i o n used by the f i r m are being employed i n the ' r i g h t ' or 'optimum' p r o p o r t i o n s w i t h each other. At t h i s volume l e v e l , the average c o s t of the f i r m i s t h e r e f o r e a t a minimum. 7. I t may be added t h a t s a l e s promotion e f f o r t s may work t o d e s t r o y the l i n e a r i t y of c o s t curves.  also  - 59 M e t i c u l o u s 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. L e s t e r , R.  H. Whitman and  o t h e r s , however, do not seem  8 to support the arguments of the economists.  In an  article  i n an N.A.C.A. b u l l e t i n , John Kempster mentioned t h a t : In the economic r e s e a r c h which has been done on c o s t , one of the important p o i n t s which has been a t stake i s the q u e s t i o n of whether u n i t v a r i a b l e c o s t s f a l l and then r i s e w i t h expanding output or are constant i n t h e i r v a r i a b i l i t y . P u t t i n g i t another way, t h i s i s the same q u e s t i o n as whether t o t a l v a r i a b l e c o s t s would be expressed as a curve or a s t r a i g h t l i n e i n diagrammatic p r e s e n t a t i o n s . Somewhat c o n t r a r y to theory, the r e s e a r c h i n v e s t i g a t i o n s o f economists have concluded, i n g e n e r a l , t h a t u n i t v a r i a b l e s are cons t a n t throughout the r e l e v a n t ranges of volume, t h a t i s , t o t a l v a r i a b l e c o s t s i n crease a t a constant r a t e . " Summarising from the above d i s c u s s i o n , i t may  be  s a i d t h a t s i n c e f i x e d c o s t s remain f i x e d a t a l l volumes, i t i s the v a r i a b l e c o s t f u n c t i o n t h a t determines the shape of the t o t a l c o s t f u n c t i o n .  In the l i n e a r break-even a n a l y s i s ,  the t o t a l c o s t f u n c t i o n i s drawn as a s t r a i g h t l i n e , g i v i n g the i m p r e s s i o n  t h a t u n i t v a r i a b l e c o s t s remain constant  a l l volumes.  This i s c o n t r a d i c t o r y to the economic  of the f i r m .  In economic a n a l y s i s , u n i t v a r i a b l e c o s t s  described  as having a ' T J ' shape.  The  at  theory are  research i n v e s t i g a t i o n s  of some economists, however, support the impression  of  constant  8 . J . Johnston, S t a t i s t i c a l Cost A n a l y s i s , New Y o r k : McGraw-Hill Book Company, Inc., I 9 6 0 , pp. I 3 6 - I 6 8 . 9. John H. Kempster, "Break-Even A n a l y s i s - 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 v a r i a b l e costs g i v e n i n l i n e a r break-even a n a l y s i s , f o r r e l e v a n t ranges of volume. Production  Equals  Sales  So f a r , v a r i o u s  assumptions i n break-even a n a l y s i s ,  r e l a t i n g to the t o t a l c o s t and made.  To t h i s l i s t , may  that s a l e s and p r o d u c t i o n  revenue f u n c t i o n s , have been  be added the f u r t h e r assumption are synchronised  n i f i c a n t amount of p r o d u c t i o n  and  f o r inventory  amount of s a l e s from i n v e n t o r y .  there i s no  or no  substantial  A l l f i x e d costs incurred  the f i r m a r e , t h e r e f o r e , considered  sig-  as p e r i o d c o s t s  by  and  charged a g a i n s t the revenue r e a l i s e d i n the same p e r i o d . T h i s assumption i s o b v i o u s l y  not e n t i r e l y t r u e .  times, f i r m s produce more than what they can s e l l , of which i n v e n t o r i e s are b u i l t up may  as a r e s u l t  a t other times, they  produce l e s s than what they can s e l l  i n v e n t o r i e s are d e p l e t e d . dom  and,  and  consequently,  In f a c t , i n p r a c t i c e , f i r m s  f i n d t h a t t h e i r s a l e s e x a c t l y equal t h e i r  In many p e r i o d s , however, f i r m s may between s a l e s and p r o d u c t i o n  sel-  production.  f i n d t h a t the d i f f e r e n c e  i s not v e r y  significant  and  t h i s i s the p o s i t i o n t h a t i s g e n e r a l l y taken i n d i s c u s s i o n s on break-even a n a l y s i s .  One  At  writer stated  that:  I n v e n t o r i e s , though, are u s u a l l y very s m a l l i n comparison to t o t a l p r o d u c t i o n and, f o r p r a c t i c a l purposes, are i g n o r e d i n comparing s a l e s a t v a r i o u s l e v e l s of production....The l e a s t probable e r r o r , then, i s obtained by d i s r e g a r d i n g the i n v e n t o r y problem i n determining s a l e s  -  61  -  a t any volume and to c o n s i d e r t i o n immediately s a l e a b l e .  a l l produc-  1 U  Glenn A. Welsch i s of the o p i n i o n tivity  and  inventory  sequence w i t h i n any  that  "produc-  change are f r e q u e n t l y of l i t t l e one  l a c k of s y n c h r o n i z a t i o n  p e r i o d " but added t h a t  " i n case of  between p r o d u c t i o n  sales, i t i s  and  important t h a t adjustment be made f o r the i n c r e a s e decrease i n i n v e n t o r y " . the u s e f u l n e s s  of  con-  1 1  or  However, t h i s tends to weaken  break-even a n a l y s i s .  As G.  R.  Crowning-  s h i e l d puts i t : The adjustments t h a t are r e q u i r e d i n the break-even a n a l y s i s , when s a l e s and product i o n volumes do not c o i n c i d e , take away one of the p r i n c i p a l m e r i t s of the break-even analysis, i t s simplicity. I f synchroniza t i o n w i t h i n reasonable l i m i t s cannot be presumed, the u s e f u l n e s s of the a n a l y s i s may be d e s t r o y e d and some o t h e r device w i l l have to be s u b s t i t u t e d f o r i t . 1  Since that production  conventional  2  break-even a n a l y s i s assumes  equals s a l e s , t h e r e f o r e , 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 c o s t s i n i n v e n t o r i e s . i s c o n s i s t e n t w i t h the procedure known i n accounting  This as  d i r e c t c o s t i n g , v a r i a b l e c o s t i n g or m a r g i n a l c o s t i n g , where1 0 . W. L. F i l l , "The Break-Even C h a r t " j Review. V o l . 2 7 , A p r i l 1 9 5 2 , p. 2 0 3 .  The  Accounting  1 1 . Glenn A. Welsch, "The C o n s t r u c t i o n and Uses of BreakEven A n a l y s i s " , C o n t r o l l e r . Y o l . 2 1 , Oct. 1 9 5 3 , p . k65. 1 2 . G e r a l d R. Crowningshield, Cost Accounting,: P r i n c i p l e s and M a r g i n a l A p p l i c a t i o n s " . . Boston: Houghton M i f f l i n Company, 1 9 6 2 , p. ^ 0 3 .  - 62 by o n l y v a r i a b l e c o s t s are i n c l u d e d i n i n v e n t o r i e s . t h i s i s not c o n s i s t e n t w i t h normal c o s t accounting  But, proced-  1^ ures.  J  In accounting  current production,  theory,  i f an i n v e n t o r y a r i s e s from  t h a t p o r t i o n of f i x e d c o s t s , which i s  u t i l i s e d to produce the goods going i n t o i n v e n t o r i e s , i s d e f e r r e d i n the i n v e n t o r i e s . inventory who  To use  direct costing i n  v a l u a t i o n i s to assume t h a t the wage of a worker  operates a machine i n producing goods i s a product c o s t  while a p r o p o r t i o n a t e a product  p a r t of the cost of the machine i s not  cost. From the c o n v e n t i o n a l  break-even a n a l y s i s , i t  be i m p l i e d t h a t even i f p r o d u c t i o n  i s not e q u a l to s a l e s ,  a l l f i x e d c o s t s w i l l s t i l l be charged a g a i n s t the same p e r i o d .  may  the revenue of  Under such circumstances, expenses  are  not p r o p e r l y matched a g a i n s t revenue because the concept of break-even a n a l y s i s i m p l i e s t h a t revenue equals expenses i n c u r r e d i n r e a l i s i n g revenue, a t the break-even l e v e l of activity.  If production  i s greater  than s a l e s and  a l l fixed  c o s t s are f u n n e l l e d through the p r o f i t and l o s s statement 13. The Committee on Accounting Concepts and Standards of the American Accounting A s s o c i a t i o n e x p l i c i t l y s t a t e s t h a t : "...the c o s t of a manufactured product i s the sum of the a c q u i s i t i o n c o s t s reasonably t r a c e a b l e to that product and should i n c l u d e 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 R e v i s i o n " , The Accounting Review. V o l . XXXII, Oct. 1957? P» 539. Two members of the Committee d i s s e n t e d from t h i s p o r t i o n of the statement. Gordon S h i l l i n g l a w s t a t e s t h a t " . . . t h e r e are two d i v e r g e n t p o i n t s of view as to which c o s t elements should be a s s i g n e d to products. The most w i d e l y h e l d view i s t h a t product c o s t should i n c l u d e a share of a l l manufacturing c o s t s " . However he adds t h a t d i r e c t c o s t i n g has been winning i n c r e a s i n g support i n recent years. S h i l l i n g l a w , Gordon, Cost A c c o u n t i n g : A n a l y s i s and C o n t r o l , Homewood, I l l i n o i s : R i c h a r d D. I r w i n , Inc., 1961, p. 291.  - 63 f o r the p e r i o d , then i t means t h a t , at the break-even l e v e l of a c t i v i t y , revenue f o r the p e r i o d equals  the expenses  i n c u r r e d i n r e a l i s i n g t h i s revenue p l u s the expenses i n c u r r e d i n r e a l i s i n g the revenue of l a t e r p e r i o d s , when the i n v e n t o r i e s from c u r r e n t p r o d u c t i o n  are s o l d .  This tends  to d i s t o r t the p i c t u r e of the p r o f i t a b i l i t y of the  business  f o r the c u r r e n t p e r i o d as w e l l as f o r those p e r i o d s i n the f u t u r e , whose s a l e s i n c l u d e i n v e n t o r i e s from p r i o r production. Although c o n v e n t i o n a l  break-even a n a l y s i s e l i m i n -  ates t h i s problem by assuming t h a t p r o d u c t i o n i t i s wise to be aware o f the e x i s t e n c e  and s a l e s , the  I n f a c t , i n f i r m s i n which  e x i s t s a s i g n i f i c a n t d i f f e r e n c e between p r o d u c t i o n i t may  sales,  of t h i s problem.  The g r e a t e r the d i f f e r e n c e between p r o d u c t i o n more s e r i o u s i s the problem.  equals  there  and s a l e s ,  be a d v i s a b l e not to c o n s i d e r the use o f break-even  analysis. Sales  Mix The s y n c h r o n i z a t i o n o f p r o d u c t i o n  and s a l e s i s ,  however, n o t the l a s t o f the b a s i c assumptions of break-even analysis.  An e x e c u t i v e , who  intends  to make use of break-  even a n a l y s i s , i s a l s o f a c e d w i t h the problem of p r o d u c t mix o r s a l e s mix.  T h i s problem a r i s e s so long as the f i r m  i s a multi-product  f i r m and i f ,  i n a d d i t i o n , the v a r i o u s  p r o d u c t s have d i f f e r e n t margins o f r e t u r n over v a r i a b l e  - 6h costs.  T h i s becomes c l e a r when we c o n s i d e r the f a c t  that,  i n a f i r m , i f the t o t a l s a l e s revenue i s made up of the revenue o f p r o d u c t s w i t h h i g h margins over v a r i a b l e the break-even p o i n t w i l l be lower than i f t o t a l  costs,  sales  revenue i s composed of the revenue of low margin i t e m s .  This  being the case, each time the s a l e s mix changes, the breakeven p o i n t and the p r o f i t p a t t e r n w i l l a l s o change.  Hence,  other t h i n g s being e q u a l , management i s g e n e r a l l y c o n s i d e r e d to be making a good move, p r o f i t w i s e , i f i t t r i e s to i n crease the s a l e s of a h i g h - p r o f i t margin product a t the expense o f a l e s s p r o f i t a b l e i t e m . The s a l e s mix i s , i n break-even a n a l y s i s .  t h e r e f o r e , an important f a c t o r  With a g i v e n t o t a l c o s t f u n c t i o n  and a g i v e n t o t a l revenue f u n c t i o n , an i n c r e a s e i n t o t a l s a l e s , f r o m a s a l e s volume above the break-even volume,  may  not produce the expected i n c r e a s e i n p r o f i t s , i f there i s a change i n the s a l e s mix.  The i n c r e a s e i n p r o f i t s may  be  g r e a t e r or l e s s than what i s expected, depending on whether the change i n s a l e s mix i s from the h i g h e r margin p r o d u c t s to the lower margin p r o d u c t s o r the r e v e r s e .  To overcome  t h i s problem, the u s e r s of break-even a n a l y s i s assume a g i v e n mix o r t h a t the s a l e s mix w i l l remain constant as s a l e s volume changes.  T h i s assumption, however, p r e s e n t s  a s e r i o u s l i m i t a t i o n when the composition of demand f o r the p r o d u c t s of the f i r m  changes.  To a v o i d t h i s assumption and to make break-even  -  65  -  a n a l y s i s more u s e f u l , v a r i o u s w r i t e r s have advanced many p o s s i b l e s o l u t i o n s to t h i s problem. which has  Perhaps, the approach  r e c e i v e d the g r e a t e s t a t t e n t i o n , i s the one  r e q u i r e s a separate  which  c a l c u l a t i o n or graph f o r each p r o d u c t .  F i x e d c o s t s , t h e r e f o r e , have to be a p p r o p r i a t e l y a l l o c a t e d to the v a r i o u s products and l i e s w i t h t h i s method.  t h i s i s where the  I t has  difficulty  a l r e a d y been mentioned  earlier  t h a t the s e p a r a t i o n of c o s t s as f i x e d costs or v a r i a b l e c o s t s i s f r a u g h t 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  c o s t s among the v a r i o u s products i s even more t r y i n g . c o s t s may  fixed Some  be common c o s t s , the a l l o c a t i o n of which i s j u s t  not p r a c t i c a b l e .  T h i s means t h a t the sum  of the i n d i v i d u a l  break-even p o i n t s w i l l not equal the break-even p o i n t f o r the f i r m as a whole. The conventional  assumption of a constant  s a l e s mix,  made i n  break-even a n a l y s i s , i s thus necessary o n l y i n  a multi-product  f i r m ; but then the s i n g l e - p r o d u c t 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 b u s i n e s s . None l^f. P a u l May recommends the use of a p r o f i t polygraph P. A. May " P r o f i t P o l y g r a p h f o r P r o d u c t Mix E v a l u a t i o n " , N.A.C.A. B u l l e t i n . V o l . 37, Sec. 1, Nov. 1955, pp. 307-318. R i c h a r d Conway suggests the method of s e q u e n t i a l cons i d e r a t i o n on a s i n g l e c h a r t or the use of m u l t i - d i m e n s i o n a l a n a l y s i s - R. W. Conway, "Breaking out of the L i m i t a t i o n s of Break-Even A n a l y s i s " , N.A.C.A. B u l l e t i n . V o l . 38, Sec. 1, June 1957, pp. 1265-1272. J o e l Dean suggests the use of a f a m i l y 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, u s u a l l y t h i s i s achieved a t the expense of the advantages of break-even a n a l y s i s , such as, ease of understanding, inexpens i v e n e s s and quickness i n p r e p a r a t i o n .  - 66 of the methods, which have been advanced to overcome l i m i t a t i o n s of t h i s assumption, seems to be satisfactory.  Each has  i t s weaknesses and  the  completely consequently,  the  problem of a d j u s t i n g break-even a n a l y s i s to the dynamic s i t u a t i o n of changing product mix was  when break-even a n a l y s i s was  y e a r s ago.  i s as s e r i o u s now first  as i t  used more than  Today, as f a r as the problem of s a l e s mix  fifty goes,  u s e r s of break-even a n a l y s i s can do l i t t l e more than r e c o g n i s e the f a c t t h a t g e n e r a l l y , the u s e f u l n e s s  of break-even  a n a l y s i s , f o r the f i r m as a whole, decreases as the number o f p r o d u c t s s o l d by T h i s , however, may  the f i r m i n c r e a s e s , not n e c e s s a r i l y be  o f the m u l t i - p r o d u c t  ceteris paribus.  true i f the s a l e s  mix  f i r m changes so s l o w l y over time t h a t  when break-even a n a l y s i s i s used f o r s h o r t - t e r m f o r e c a s t i n g , 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 c o n s t a n t s a l e s mix, multi-product provide  may  be only n e g l i g i b l e .  Further,  f i r m s p r i c e t h e i r products i n such a way  some as  on a l l p r o d u c t s s o l d , a constant r e t u r n over v a r i a b l e  c o s t s , i n which case, the problem of changes i n s a l e s  mix  does not  even a r i s e , because i n such a s i t u a t i o n , assuming  t h a t the  s a l e s volume and  change i n the s a l e s mix even p o i n t .  f i x e d c o s t s remain the same, a  w i l l not cause a s h i f t i n the  T h i s , however, presupposes the use  of  Such a p r e s u p p o s i t i o n  may  be v a l i d .  c l a i m t h a t c o s t - p l u s p r i c i n g i s the  15.  I b i d . , p. 'ifitf-if57.  break-  cost-plus  p r i c i n g as opposed to the marginal c o s t p r i c i n g of the mists.  to  econo-  Some w r i t e r s  common method of p r i c i n g .  - 67 This has been confirmed i n some s t u d i e s . a study undertaken before  H a l l and H i t c h , i n  the outbreak of World War I I ,  i n d i c a t e d t h a t about s i x t y - f i v e p e r cent o f f i r m s i n mono p o l i s t i c competition  and s e v e n t y - f i v e p e r cent o f monopo-  16 listic  and o l i g o p o l i s t i c f i r m s adopt c o s t - p l u s p r i c i n g .  Planning  and C o n t r o l I t has been mentioned before  s i s i s u s e f u l f o r f i n a n c i a l planning  t h a t break-even  and c o n t r o l .  analy-  This  a r i s e s mainly from the f a c t t h a t break-even a n a l y s i s i s capable o f d e p i c t i n g g r a p h i c a l l y the r e l a t i o n s h i p s between c o s t , volume, revenue and p r o f i t .  Hence, i f management i s  f a c e d w i t h s e v e r a l a l t e r n a t i v e courses o f a c t i o n , break-even a n a l y s i s i s capable of b r i n g i n g out f o r the b e n e f i t o f management, the probable e f f e c t s on c o s t , volume and revenue and u l t i m a t e l y on p r o f i t o f each o f the d i f f e r e n t courses o f action. and  This w i l l h e l p management i n i t s decision-making  planning. In p l a n n i n g ,  f o r instance,  break-even a n a l y s i s  may a l s o show whether e f f o r t s would be b e t t e r d i r e c t e d toward 16. R. L. H a l l and C. J . H i t c h , " P r i c e Theory and Business Behaviour", Oxford Economic Papers, No. 2, Hay 1939, Table 6, p. 26. In another study o f 20 companies i n the U n i t e d S t a t e s , over a p e r i o d of years i n the 1950's, P r o f e s s o r L a n z i l l o t t i found t h a t t a r g e t r e t u r n on investment p r i c i n g was the most f r e q u e n t l y used method o f p r i c i n g . He a l s o found t h a t the most f r e q u e n t use o f t h i s method was i n the p r i c i n g of new products, and t h a t some companies, which used t h i s method f o r t h e i r new products, employed c o s t - p l u s p r i c i n g f o r 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 r e d u c t i o n o f f i x e d c o s t s o r o f v a r i a b l e c o s t s o r whether the e f f o r t s should be exerted  t o i n c r e a s e volume.  I f the  f i x e d c o s t s of a f i r m c o n s t i t u t e a very h i g h p r o p o r t i o n of t o t a l c o s t s , then i t must operate a t a s u b s t a n t i a l percentage of c a p a c i t y to cover such c o s t s but, once the break-even volume i s reached, p r o f i t s i n c r e a s e a t a very r a p i d r a t e , with i n c r e a s e s i n volume.  On the other hand, i f the t o t a l  costs o f a f i r m are made up mainly of v a r i a b l e c o s t s , 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 t o cover f i x e d c o s t s 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 r a t e .  On the f i n a n c i a l s i d e , i f  a f i r m has a h i g h percentage of f i x e d c o s t s , an i n c r e a s e i n volume may n o t cause a s e r i o u s demand f o r cash but, i f the f i r m has a h i g h percentage of v a r i a b l e c o s t s , an i n c r e a s e i n volume i s l i k e l y  to cause an i n c r e a s e i n v a r i a b l e c o s t s and  e v e n t u a l l y a d r a i n on cash. I n c o n t r o l , break-even a n a l y s i s i s u s e f u l f o r d e t e c t i n g any i n s i d i o u s upward creep o f c o s t s , which might otherwise go u n n o t i c e d .  I t can a l s o be used t o compare a c t u a l  and planned performances and to show the l o g i c a l p o i n t s of a t t a c k to e f f e c t improvement.  A common e r r o r made by manage-  ment i s to overemphasize the importance o f volume as a d e t e r minant o f p r o f i t s .  Some management people may assume t h a t  an i n c r e a s e i n volume w i l l a u t o m a t i c a l l y i n c r e a s e  profits.  A c t u a l l y , t h i s happens above the break-even p o i n t only i f p r i c e s remain unchanged and o n l y i f v a r i a b l e costs are kept  - 69 under c o n t r o l .  Unfortunately,  an i n c r e a s e  o f t e n i s accompanied by an i n c r e a s e  i n volume very  i n c o s t s , which i s f r e -  quently  l a r g e anough to more than o f f s e t the b e n e f i c i a l volume  effect.  Break-even a n a l y s i s comes i n handy here s i n c e i t i s  capable o f b r i n g i n g  to the a t t e n t i o n o f management the p r o f i t  determinant t h a t has been r e s p o n s i b l e  f o r 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 i n t r o d u c t i o n to the uses o f breakeven a n a l y s i s , we can now go on to examine more s p e c i f i c areas of management p l a n n i n g  and c o n t r o l , i n which break-  even a n a l y s i s I s capable o f p l a y i n g a s i g n i f i c a n t r o l e . Pricing Policies P r i c i n g a product i s one o f the most d e l i c a t e problems o f management. i n t o bankruptcy.  A poor p r i c i n g p o l i c y may l e a d a business  Many f a c t o r s i n f l u e n c e the p r i c i n g d e c i s i o n s  of management but the most important f a c t o r i s probably Some f i r m s adopt the p o l i c y o f s e l l i n g  some o f t h e i r minor  products below c o s t , i n order t o a t t r a c t customers. i s , however, h a r d l y any p r o f i t - m a k i n g to s e l l c o n s i s t e n t l y below c o s t . f i r m s have to recover n o t only  cost.  There  f i r m which can a f f o r d  I n order to be s u c c e s s f u l ,  t h e i r c o s t s but a l s o a p r o f i t  t h a t i s adequate to m a i n t a i n the i n c e n t i v e f o r t h e i r continued operation. Break-even a n a l y s i s can p r o v i d e some help agement i n the e s t a b l i s h m e n t of p r i c e s .  Break-even  to mancharts  - 70 can be drawn t o show the e f f e c t on p r o f i t s o f d i f f e r e n t p r i c e levels.  These c h a r t s may then be compared w i t h one drawn  under e x i s t i n g c o n d i t i o n s  to show the volume o f s a l e s  that  would be necessary to achieve the same l e v e l o f p r o f i t s . higher p r i c e , c e t e r i s paribus, profit/volume costs.  A  has the e f f e c t o f r a i s i n g the  r a t i o and a c c e l e r a t i n g the recovery o f f i x e d  Hence, a lower volume of s a l e s 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 o b j e c t i v e . would lower the p r o f i t / v o l u m e recovery of f i x e d c o s t s .  Conversely, a lower p r i c e  r a t i o and reduce the r a t e of  Attainment of the p r o f i t  objective,  i n t h i s case, would r e q u i r e a h i g h e r volume o f s a l e s . The  usefulness  o f break-even a n a l y s i s , i n p r i c i n g  d e c i s i o n s , a r i s e s mainly from the f a c t t h a t i t can a b l y show the cost-volume-revenue s t r u c t u r e of a b u s i n e s s . should never overestimate the u s e f u l n e s s  But, one  of break-even  a n a l y s i s i n p r i c i n g d e c i s i o n s because the e f f e c t on p r o f i t s of a change i n p r i c e depends not o n l y on the cost-volumerevenue s t r u c t u r e o f t h e business but a l s o on the e f f e c t on volume of the change i n p r i c e , t h a t i s , on the p r i c e e l a s t i c i t y of demand.  I n a c t u a l f a c t , i n any p r i c i n g d e c i s i o n ,  the l a t t e r would appear to be, as important a s , i f not more important than the former.  Unfortunately,  break-even a n a l y -  s i s does n o t , i n any way, t e l l us what the p r i c e  elasticity  of demand f o r a product i s l i k e .  C a p i t a l Expenditures C a p i t a l expenditures u s u a l l y i n v o l v e l a r g e sums  - 71 of money.  F i r m s , very o f t e n , have t o r e s o r t to o u t s i d e  sources of funds to f i n a n c e  t h e i r c a p i t a l expenditures.  An  unwise investment d e c i s i o n by management may put an end to the o p e r a t i o n be  of a business.  T h e r e f o r e , management has to  extremely c a r e f u l i n every investment d e c i s i o n that i t  makes.  T h i s r e q u i r e s management t o have a good i d e a o f ,  among o t h e r t h i n g s ,  the changing r e l a t i o n s h i p s of c o s t ,  volume, revenue and p r o f i t s . i n decisions  Break-even a n a l y s i s i s u s e f u l  i n v o l v i n g c a p i t a l expenditures s i n c e i t i s  extremely capable o f b r i n g i n g  out these r e l a t i o n s h i p s .  I f a f i r m i s t h i n k i n g o f making an investment, i t can make use of break-even a n a l y s i s t o compare i t s p o s i t i o n under the two a l t e r n a t i v e s i t u a t i o n s ; (a) i f the investment i s undertaken and (b) i f the investment i s not undertaken. The  d i f f e r e n c e i n the p r o f i t s under the two s i t u a t i o n s ,  a f t e r adjustments f o r p r e s e n t v a l u e s , w i t h the c o s t o f c a p i t a l . relevant  may then be compared  On the b a s i s o f t h i s and o t h e r  evidence, a d e c i s i o n may be made as t o whether the  investment ought to be undertaken.  In looking  at i t s position  under the two s i t u a t i o n s , the f i r m s h o u l d r e c o g n i s e the changi n g cost-volume-revenue r e l a t i o n s h i p s and the r e s u l t a n t e f f e c t upon p r o f i t , caused by v a r i a t i o n s i n the volume o f b u s i n e s s . Occasionally,  f i r m s have made the e r r o r of computing c o s t and  revenue estimates on the b a s i s  of maximum u t i l i s a t i o n of p r o -  posed p r o d u c t i v e f a c i l i t i e s o r on the b a s i s o f a c e r t a i n 17 ' r e p r e s e n t a t i v e ' , 'normal' o r 'average' volume of b u s i n e s s . 17. John 1. t>. Tse, P r o f i t P l a n n i n g through Volume-Cost A n a l y s i s . New Y o r k : The M a c m i l l a n Company, I960, p. 21.  - 72 An i m p l i c i t assumption i s then made t h a t the u n i t c o s t and p r o f i t w i l l remain the same a t a l l o t h e r l e v e l s o f o p e r a t i o n , as they would a t the maximum or r e p r e s e n t a t i v e volume o f business.  This tends t o d i s t o r t the p i c t u r e and l e a d t o un-  sound d e c i s i o n s because the changing cost-volume-revenue r e l a t i o n s h i p s are i g n o r e d . Break-even a n a l y s i s , by making management aware o f 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 t h i n k i n g .  With t h i s method,  management can o b t a i n a c l e a r p e r c e p t i o n  of c o s t s , revenue and  p r o f i t s o r l o s s e s to be expected under a c t u a l o p e r a t i n g  con-  d i t i o n s and not under some imaginary o r deceptive s i t u a t i o n . The use of break-even a n a l y s i s does n o t mean t h a t management's judgement can now be completely e l i m i n a t e d and d e c i s i o n s can be made s o l e l y on an o b j e c t i v e b a s i s .  But, break-even a n a l y s i s  can help management to make b e t t e r and more i n t e l l i g e n t ions about c a p i t a l  decis-  expenditures.  Make o r Buy Problems Many f i r m s have f a c e d the problem o f having to decide whether i t i s more p r o f i t a b l e to make o r to buy component p a r t s t h a t are used i n the f i r m ' s assembled p r o d u c t s .  A  d e c i s i o n of t h i s nature r e q u i r e s c o n s i d e r a t i o n of a number o f factors.  For instance,  f o r an assured supply, of product q u a l i t y .  the f i r m may have t o c o n s i d e r  the need  c o n t i n u i t y o f d e l i v e r y and maintenance  I f i t i s assumed t h a t the f i r m 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 r e v o l v e  q u e s t i o n of c o s t s .  This means t h a t proper c o s t  around  the  information  would be r e q u i r e d so t h a t the c o s t of making can be  compared  with the c o s t of buying. I f a f i r m has short-run,  unused p r o d u c t i v e  the c o s t of making may  c a p a c i t i e s i n the  be based on the a d d i t i o n a l  c o s t s t h a t i t w i l l have to i n c u r i f the orders were kept i n the company.  In the long-run,  however, the f i r m ' s c o s t of  making should  include d i r e c t materials, d i r e c t labour,  v a r i a b l e c o s t s i n v o l v e d , a share of f i x e d c o s t s and  the  a profit  figure. Break-even a n a l y s i s i s u s e f u l i n the comparison of the c o s t of making and  the c o s t of buying s i n c e i t can show  the e f f e c t s on p r o f i t s , a t d i f f e r e n t volume l e v e l s , of two  a l t e r n a t i v e s and  the  thereby help management to make i t s  decision. Cost  Control Cost c o n t r o l i s one  of the most important aspects  of the management of a b u s i n e s s .  Operating p r o f i t s , as  f i n e d i n chapter I, are equal to o p e r a t i n g operating  costs.  But,  c o n t r o l over o p e r a t i n g  revenue minus  management does not have too much revenue s i n c e there i s a l i m i t  the amount t h a t a b u s i n e s s can s e l l and to a l a r g e extent,  de-  selling prices  e s t a b l i s h e d by competition.  Hence,  to are, the  - 7h profit-making  c a p a c i t y o f a business depends l a r g e l y on the  e f f i c i e n c y w i t h which c o s t s are c o n t r o l l e d . One of the ways i n which c o s t c o n t r o l can be achieved  i s through the use o f f l e x i b l e budgets, which  " r e f l e c t the amount Of- c o s t t h a t i s reasonably necessary to 18 achieve each of s e v e r a l s p e c i f i e d volumes of a c t i v i t y . " F o r purposes o f c o s t c o n t r o l , the predetermined c o s t s a r e based on standards s e t f o r m a t e r i a l s , l a b o u r and expenses. These predetermined c o s t s may then be compared w i t h a c t u a l c o s t s and the d i f f e r e n c e s , c a l l e d v a r i a n c e s , may be From the a n a l y s i s of the v a r i a n c e s , management may measures t o check the unfavourable trends from the predetermined c o s t s .  analysed. introduce  and departures  I n t h i s way, f l e x i b l e  budgets  a i d i n the c o n t r o l of c o s t s . There i s a g r e a l d e a l of s i m i l a r i t y between f l e x i b l e budgets and break-even c h a r t s .  I n f a c t , i t may be s a i d  t h a t whereas f l e x i b l e budgets are t a b u l a r v a r i a b l e income statements, break-even c h a r t s are graphic  v a r i a b l e income  19 statements. '  The c o n s t r u c t i o n of break-even c h a r t s i s very  o f t e n based on the data o f f l e x i b l e budgets; and j u s t as f l e x i b l e budgets are u s e f u l f o r c o s t c o n t r o l , so a r e break-even charts. and  F o r purposes o f c o s t c o n t r o l , the predetermined  costs  the a c t u a l c o s t may be p l o t t e d on a break-even c h a r t t o 18. S h i l l i n g l a w , op. c i t . , p. 217.  19. A d o l f Matz, O t h e l J . Curry and George W. Frank, Cost A c c o u n t i n g , C i n c i n n a t i : South-Western P u b l i s h i n g Company, 1952, p. 678.  - 75 b r i n g out the v a r i a n c e s these v a r i a n c e s ,  and on the b a s i s of the a n a l y s i s o f  c o r r e c t i v e a c t i o n s may be taken by management.  Summary In t h i s chapter,  i t has been shown t h a t break-even  a n a l y s i s can be used i n decision-making i n v o l v i n g make o r buy problems and i n problems r e l a t e d to c a p i t a l expenditures, c o n t r o l and p r i c i n g d e c i s i o n s .  cost  These a r e , by no means, the  o n l y uses to which break-even a n a l y s i s can be p u t .  In f a c t ,  break-even a n a l y s i s has been used i n the s o l v i n g o f many other problems concerning  a l t e r n a t i v e s , which i n v o l v e c o s t , volume  and p r o f i t r e l a t i o n s h i p s . I t was a l s o p o i n t e d o u t , i n t h i s chapter,  that i n  u s i n g break-even a n a l y s i s , many r e s t r i c t i v e assumptions have to be made.  The assumptions i n c l u d e the f o l l o w i n g :  (a) A l l c o s t s can be r e a s o n a b l y separated i n t o t h e i r f i x e d and v a r i a b l e components and whereas f i x e d c o s t s remain f i x e d a t a l l volumes, v a r i a b l e c o s t s vary i n d i r e c t p r o p o r t i o n to volume. (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 equals o r c l o s e l y f o l l o w s s a l e s and a l l f i x e d c o s t s i n c u r r e d i n a p e r i o d are, t h e r e f o r e , deducted from t h a t p e r i o d ' s revenue. (d) There i s o n l y one product o r i f s e v e r a l p r o d u c t s are being produced and s o l d , the s a l e s mix w i l l remain cons t a n t . These assumptions are more v a l i d f o r some f i r m s for others.  than  I n those f i r m s i n which these assumptions are very  u n r e a l i s t i c , break-even a n a l y s i s i s v i r t u a l l y u s e l e s s ,  unless  - 76 the f i r m s are w i l l i n g to make adjustments to overcome the limitations  that are i n h e r e n t i n these assumptions.  CHAPTER IV TEST OF BREAK-EVEII ANALYSIS Introduction There a r e many ways o f 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 firms.  Some of these techniques a r e r a t h e r  An example i s the environmental a n a l y s i s method. t i a l i d e a here i s t o d i s c o v e r  naive.  The essen-  a functional relationship  between a f i r m s p r o f i t s and one or more i n d i c a t o r s o f 1  n a t i o n a l a c t i v i t y - such a s , d i s p o s a b l e  income or any r e -  l i a b l e i n d e x o f i n d u s t r i a l p r o d u c t i o n - on the assumption t h a t the w e l l - b e i n g  o f a f i r m , 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 c o n d i t i o n s economy.  A modification  i n the t o t a l  o f t h i s technique i s the c o r r e l a t i o n  a n a l y s i s method, whereby a f u n c t i o n a l r e l a t i o n s h i p i s f i r s t determined between a f i r m ' s p r o f i t s and some i n t e r n a l v a r i a b l e f a c t o r , f o r example, the s a l e s o f the f i r m .  On the  b a s i s o f t h i s r e l a t i o n s h i p , f o r e c a s t s o f the f i r m ' s p r o f i t s may then be made.  I n t h i s study, t h i s technique w i l l be  c a l l e d the percentage o f s a l e s method.  I t i s obvious  that  the a c c u r a c y o f the p r o f i t f o r e c a s t , by t h i s method, depends d i r e c t l y on:  (a) the e x t e n t to which the f i r m ' s p r o f i t s are  t r u l y r e l a t e d t o the independent v a r i a b l e , s a l e s and (b) the accuracy of the f o r e c a s t made f o r the independent v a r iable .  - 78 -  A more s o p h i s t i c a t e d way  of f o r e c a s t i n g  i n v o l v e s the use of the break-even technique.  profits  Break-even  a n a l y s i s - i t s nature and i t s pros and cons - needs no f u r t h e r comment here.  The purpose i n t h i s chapter I s to  t e s t the hypothesis and the n u l l h y p o t h e s i s , as d e t a i l e d i n chapter I . Source o f 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 i n d i c a t e d i n chapter I , the  statis-  t i c a l approach ( l e a s t squares method) i s used to separate the t o t a l c o s t s of the f i r m i n t o f i x e d c o s t s and  variable  c o s t s , s i n c e 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 t o g i v e more r e l i a b l e r e s u l t s than the accounting or engine e r i n g methods.  I n c l u d e d i n the u n i v e r s e of f i r m s are o n l y  those f i r m s i n Moody's I n d u s t r i a l Manuals, which have had l o s s e s a t some time or o t h e r over the p e r i o d covered i n the study.  T h i s i s so because p r e l i m i n a r y s t u d i e s to t h i s  showed t h a t , i n the case of those f i r m s , which had s u f f e r e d any l o s s e s , i t was  test  never  not p o s s i b l e to separate  their  t o t a l 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, by the s t a t i s t i c a l  approach.  In t h i s t e s t , the year chosen f o r the f o r e c a s t i s 1956.  Any o t h e r year c o u l d have been chosen so l o n g as  i t i s a p a s t y e a r ; o t h e r w i s e , i t would not be p o s s i b l e t o 1. D e t a i l e d i n chapter I .  - 79 compare t h e mine t h e  forecast profits  accuracy of  the  with the  forecasts.  to measure c o s t v a r i a b i l i t y , firm  i n the  years,  the  sample i s s t u d i e d  f r o m 1946  t o 1955.  For  the  test,  b e h a v i o u r of  in  costs  to  deter-  order  of  f o r a maximum p e r i o d o f  As  I n d u s t r i a l M a n u a l s f r o m 1946  actual profits,  each ten  i n d i c a t e d i n c h a p t e r I , Moody's t o 1958  are  used to o b t a i n  the  2 data.  A  c l o s e examination of  showed t h a t  589  Forecasting  Operating  A.  firms  could  by  the  universe.  made :  the  operating  b r e a k - e v e n method, the  can  reasonably  be  (c) P r o d u c t i o n  and  s a l e s mix The  level  following  classified  S e l l i n g p r i c e s remain constant  The  profits  of  the  sample  assumptions  3  (a) A l l c o s t s variable.  (d)  included  i n the  period  B r e a k - E v e n Method  firms  (b)  this  Profits  In f o r e c a s t i n g  are  be  the Manuals f o r  s a l e s are remains  operating  i s equal to  the  as f i x e d  or  at a l l volumes.  synchronised  and  constant.  profits  operating  of  firms  a t any  given  r e v e n u e minus the  volume  operating  2. T h e r e i s a t i m e l a g i n Moody,'.s I n d u s t r i a l M a n u a l s . The d a t a o f some c o m p a n i e s a p p e a r i n the manuals one o r two y e a r s a f t e r t h e end o f t h e i r f i s c a l y e a r . 3. The n e e d f o r t h e s e a s s u m p t i o n s have b e e n 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 t h e sample f i r m s . F o r most o f t h e sample f i r m s , t h e f i r s t t h r e e a s s u m p t i o n s a r e quite v a l i d . The f o u r t h a s s u m p t i o n , however, i s n o t v a l i d f o r a l m o s t a l l t h e f i r m s b u t has t o be made i n o r d e r t o c a r r y o u t the t e s t .  - 80 c o s t s a t t h a t volume l e v e l .  I n t h i s study, the f o r e c a s t  volume l e v e l i s g i v e n and i s equal t o t h a t a t which the actual operating p r o f i t s are r e a l i s e d .  The o p e r a t i n g revenue  i s a l s o g i v e n and i s e q u a l t o the volume l e v e l , on the assumpt i o n t h a t p r o d u c t i o n and s a l e s a r e s y n c h r o n i s e d .  Therefore,  i n o r d e r t o f o r e c a s t the o p e r a t i n g p r o f i t s , i t i s o n l y necessary t o determine the o p e r a t i n g c o s t s . The d e t e r m i n a t i o n o f the o p e r a t i n g c o s t s , a t a g i v e n volume l e v e l , can be attempted i n many ways.  The  a c c o u n t i n g , e n g i n e e r i n g and s t a t i s t i c a l approaches have a l r e a d y been e x p l a i n e d i n chapter I I .  The s t a t i s t i c a l  approach, with the s c a t t e r c h a r t technique of l e a s t squares,  i s used here.  d i s c u s s e d i n chapter I .  and the method  The reason f o r t h i s has been  By t h i s method, the o p e r a t i n g c o s t '  f i g u r e s o f a l l the sample f i r m s a r e c o l l e c t e d f o r as many as p o s s i b l e o f the years between 19*+6 and 1955  (inclusive).  These f i g u r e s a r e then p l o t t e d on s c a t t e r c h a r t s w i t h s a l e s volume as the h o r i z o n t a l a x i s and o p e r a t i n g c o s t s as the vertical axis.  The i d e a here i s to achieve an estimate of  the c o r r e l a t i o n between c o s t s and s a l e s volume.  Shilling-  law a d v i s e s t h a t the s t a t i s t i c a l approach "must be regarded as f i r s t approximations. reasons  f o r doubting  i s reasonable,  I f there a r e strong common-sense  t h a t the r e s u l t i n g cost-volume p a t t e r n  then the c o n c l u s i o n o f 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 o f judgement." h. Gordon' S h i i l i n g l a w , Cost A c c o u n t i n g : A n a l y s i s and C o n t r o l . Homewood, I l l i n o i s : R i c h a r d D. I r w i n , I n c . , 196l, P. 235.  - 81 I n t h i s study, those c o s t f i g u r e s which show.an 'abnormal'  5 r e l a t i o n s h i p to s a l e s volume are e l i m i n a t e d . Once t h i s stage has been reached, a l i n e o f best f i t may  be e s t a b l i s h e d through the remaining p l o t t e d p o i n t s  6  by the method of l e a s t squares. l i n e t r e n d i s y = a + bx. two  The formula f o r a s t r a i g h t  The l e a s t squares method p r o v i d e s  simultaneous equations which when s o l v e d determine  the  v a l u e s of the c o n s t a n t s , a and b i n the e q u a t i o n o f the straight line trend.  7  These two  simultaneous equations are  as f o l l o w s : •£y = Na + £ x y - a-^x  b^x + bi:x  2  where: - sigma, sum o f , summation. N = No. of items, y e a r s o r p l o t t e d p o i n t s of the data under c o n s i d e r a t i o n . x = Value of the independent v a r i a b l e , f o r example, the s a l e s volume i n t h i s study. y = Value of the dependent v a r i a b l e , f o r example, the operating, c o s t s i n t h i s study. 5. A c o s t f i g u r e i s c o n s i d e r e d t o have an abnormal r e l a t i o n s h i p to s a l e s volume i f i t l i e s some d i s t a n c e away from the t r e n d t h a t o t h e r c o s t f i g u r e s seem to be e s t a b l i s h i n g . Judgement i s , of course, i n v o l v e d here. 6. F o r a t e c h n i c a l e x p l a n a t i o n of t h i s s t a t i s t i c a l p r o c e s s , r e f e r e n c e may be made to F r e d e r i c k E . Croxton and Dudley J . Cowden, A p p l i e d 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. F o r t r a n Programming i s used t o a s s i s t i n a r r i v i n g a t the v a l u e s of the c o n s t a n t s , a and b. See Appendix V I .  -  82 -  S i n c e , i n t h i s study, x r e p r e s e n t s the s a l e s volume and y, the o p e r a t i n g c o s t s , once the v a l u e s of a and b have been d e r i v e d , the o p e r a t i n g c o s t s o f any f i r m , f o r any s a l e s volume, may be estimated merely by s u b s t i t u t i n g x, i n the formula y = a + bx, w i t h the v a l u e o f the g i v e n s a l e s volume. When the o p e r a t i n g c o s t s , a t the g i v e n s a l e s volume, have been determined, a f o r e c a s t of the o p e r a t i n g p r o f i t s , a t t h a t s a l e s volume, can be made by s u b t r a c t i n g the operat i n g c o s t s from the g i v e n o p e r a t i n g revenue. B. Percentage o f S a l e s Method The percentage o f s a l e s method o f f o r e c a s t i n g o p e r a t i n g p r o f i t s i s v e r y much s i m p l e r than the break-even method.  By the percentage o f s a l e s method, f o r each sample  f i r m , the o p e r a t i n g p r o f i t s as a percentage o f the s a l e s volume i s determined f o r as many as p o s s i b l e of the years between 19^6  and 1955  (inclusive). The mean average o f these 8 percentages i s then determined. The u l t i m a t e purpose here, 8. The mode i s n o t used here because, f o r most o f the sample f i r m s , the same percentage d i d n o t appear more than once. There i s no s p e c i a l reason to p r e f e r the median. Simpson and Kafka s t a t e t h a t "the a r i t h m e t i c mean i s the most commonly used and b e s t known o f the averages, and i s p r e f e r r e d u n l e s s p r e c l u d i n g circumstances a r e p r e s e n t , such as extreme v a l u e s a t e i t h e r end of the s e r i e s , o r open-end c l a s s e s o r v a r y i n g c l a s s i n t e r v a l s o r u n l e s s we d e f i n i t e l y wish t o e s t a b l i s h the most f r e q u e n t v a l u e o r some o t h e r p o s i t i o n a l average." George Simpson and F r i t z Kafka, B a s i c S t a t i s t i c s . Hew York: W. W. Norton and Company, I n c . , 1957» p . 171. I n t h i s study, the p r e c l u d i n g circumstances a r e e i t h e r absent o r a r e v e r y i n s i g n i f i c a n t .  - 83  -  as i n the case of break-even a n a l y s i s , i s to compare f o r e c a s t o p e r a t i n g p r o f i t s with the a c t u a l  the  operating  p r o f i t s , t h e r e f o r e , i t i s assumed t h a t the s a l e s volume i n the f o r e c a s t year, 1956,  i s given and  Is equal to the  volume a t which the a c t u a l o p e r a t i n g p r o f i t s are i n 1956.  sales  realised  Once the s a l e s volume i s known, a f o r e c a s t of  the  o p e r a t i n g p r o f i t s can be made by a p p l y i n g to the g i v e n s a l e s volume, the average percentage o f p r o f i t s as a percentage of s a l e s f o r the years 1946 The  to  1955.  Sample Before making a d e c i s i o n on the f i r m s to be  cluded i n the sample, a d e c i s i o n has  to be made on  number of f i r m s to be i n c l u d e d i n the sample.  In-  the  For  this  purpose, i t i s necessary to s t a t e the d e s i r e d degree o f accuracy. of 0.95  In t h i s study, i t i s a s s e r t e d w i t h a p r o b a b i l i t y  t h a t the estimated  t r u e mean.  The  confidence  mean w i l l be w i t h i n $0.10  of  interval i s arbitrarily  fixed,  depending on what i s f e l t to be reasonable, cumstances.  I n t h i s case, c o n s i d e r a t i o n was  under the  f a c t t h a t the sample mean of the e x p l o r a t o r y i s o n l y $0.26m.  (Table I I I ) .  shows t h a t f o r a 95  percent  The  study,  the  _ X^,  t - t a b l e (Appendix I I )  degree of c o n f i d e n c e ,  degrees of freedom ( n - 1 ) , the standard 9.  cir-  given to  9  the  with  9  e r r o r of the mean  This i s e x p l a i n e d i n the next page.  -  i s equal t o 2 . 2 6 2 .  8 if 1°  From t h i s , the f o l l o w i n g formula,  may  be used t o determine t h e s i z e of the sample: 2.262  (-Jc)  =  $0.10m  where  6  =  standard d e v i a t i o n of the u n i v e r s e (population)  and  n  =  s i z e o f the sample.  I n order t o determine the standard d e v i a t i o n o f the u n i v e r s e , a s t a r t has to be made w i t h an e x p l o r a t o r y study o f some f i r m s , p i c k e d a t random from the u n i v e r s e . t h i s case, 1 0 f i r m s are used f o r the e x p l o r a t o r y study. b a s i c p r i n c i p l e behind random sampling  The  i s t h a t every f i r m i n  the u n i v e r s e must have an equal chance o f being chosen. achieve t h i s , use can be made of prepared numbers.  In  To  t a b l e s o f random  F i r s t l y , a l l the 5 8 9 f i r m s i n the u n i v e r s e a r e  l i s t e d i n a l p h a b e t i c a l order and numbered from 1 t o 5 8 9 . A d e c i s i o n i s then made t o use K e n d a l l and Smith's "Tables o f Random Sampling Numbers, T r a c t s f o r Computers No. X X I V " (Appendix I ) .  11  To a v o i d any p o s s i b i l i t y t h a t the c h o i c e o f  a s t a r t i n g p o i n t might be nonrandom, i t i s a r b i t r a r i l y  decided,  before examining the Random Number T a b l e s , t o s t a r t p i c k i n g 1 0 f i r m s from Row 1 2 j and columns 6 , 7 and 8 o f the random numbers shown on page 1 5 o f the t a b l e s .  T h i s would g i v e the  numbers: 1 0 . John S. Freund and Frank J . W i l l i a m s , Modern Business S t a t i s t i c s . Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , I n c . , 1 9 5 8 , p. 1 9 3 . 1 1 . M. G. K e n d a l l and B. B. Smith, Tables o f Random Sampling Numbers. T r a c t s f o r Computers No. XXIV. Cambridge: Cambridge University Press, 1 9 5 1 .  -  85  -  377  339  218  043  157  144  451  498  070  525  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 , 589 i s i g n o r e d .  number e x c e e d i n g  I n t h e same way,  any  number w h i c h a p p e a r e d more t h a n o n c e i s a l s o i g n o r e d i t had appeared f o r t h e f i r s t o f t h e number,  time.  any  after  T h i s happened i n the case  043.  Once t h e f i r m s f o r t h e e x p l o r a t o r y s t u d y h a v e b e e n 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 o f t h e u n i v e r s e X ( 6 ) c a n be determined  by u s i n g t h e f o r m u l a :  -J  6  where:  =  6  —  x  standard d e v i a t i o n of the universe  =  s i g m a , sum o f , s u m m a t i o n  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 profits  X^  =  mean o f 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 study _  T a b l e I I I shows t h a t  £(X&  2  - X ) d  = $0.9127m.  Therefore, the standard d e v i a t i o n of the u n i v e r s e , 6 i  s  equal t o : ^(X  d  - X ) n - 1 d  '$0.1014m.  _  =  J  / $o  > 9 1 2  7m  9  $0.3184m.  E a r l i e r , the f o r m u l a f o r the s i z e o f the sample  - 86 had been g i v e n a s :  2.262 ( T = T ) where: and  = standard  6  n  = $0.10m. d e v i a t i o n o f the u n i v e r s e  = s i z e o f the sample  This i s the same a s : n  = ( - jO.lOm"  27262  v  S i n c e , i t has a l r e a d y been found t h a t 6 = $0.318^111. Therefore,  n  =  ($0.3l8Um ^  =  ftQ.^18^  2  1°/^ )  2  = 7.2036  2  = 51.88 T h i s means t h a t a random sample o f s i z e , 52 w i l l s u f f i c e t o g i v e the d e s i r e d degree o f accuracy. and Kafka a d v i s e s t h a t "the use of a formula estimate  But Simpson  t o o b t a i n an  o f sample s i z e does not g i v e us more than a rough  approximation.  I n p r a c t i c e , i t i s a d v i s a b l e t o take the  sample estimate  as a bare minimum t o be i n c r e a s e d f o r  12 safety."  T h e r e f o r e , f o l l o w i n g the advice o f Simpson and  Kafka, f i v e more f i r m s a r e added t o the 52 f i r m s t o g i v e a sample s i z e o f 57 f i r m s . Once the number o f f i r m s t o be i n c l u d e d i n t h e 12.  Simpson, op. c i t . , p. Wf.  TABLE I I I Computation o f t h e Standard D e v i a t i o n o f the U n i v e r s e ($ Amounts i n M i l l i o n s )  Name o f Company  Volume or Sales Revenue (x)  Auto S o l e r Company ( g a . ) $2.02 Bolsa Chica O i l 1.20 Corp. (Del.) Diamond T . M o t o r Car C o . ( 1 1 1 . ) 45.43 Dauega S t o r e s Corp.(N.J.) 24.64 Globe American Corp. (Ind.) k.39 Mohawk L i q u e r Corp. (Mich.) 5.07 New E n g l a n d Box Co. (Mass.) k.Ok Ronson C o r p . ( N . J . ) 3 1 . 9 5 S t a n d a r d Commerc i a l Tobacco Co.Inc.(Del.) if. 8 7 12th Street S t o r e (111.) 3.85  Fixed Costs (a)  Slope of Trend Line  Variable Costs  (b)  (bx)  Total Costs (a+bx)  Forecast Profits Pf = x-(a+bx)  Difference Between A c t u a l and Actual Forecast Profits Profits P -Pf Pa  = *d  N2  -  a  x  •  d"^d  (Xd-Xd) •  $0.09  0.81  $1.64  $1.73  $0.29  $0.37  $0.08  -$0.18  $0.0324  • 00  0.08  0.0064  0.80  o.64oo  0.06  0.93  1.12  1.18  0.02  0.20  0.18  0.02  0.97  44-. 07  1+4.09  1.3k  2.  kO  1.06  2.24  0.90  22.19  24.42  0.22  0.1k  0.06  -0.20  0.0400  1.42  0.76  3-3k  if. 76  (0.37)  (0.28)  0.09  -0.17  0.0289  0.79  0.70  3.55  4.34  0.73  0.28  0.55  0.29  0.0841  -  o.6o  0.84  7.91  0.65  3.39 20.77  3.99 28.68  0.05 3.27  (0.01) 3.07  0.06 0.20  -0.20 -0.06  0.0400 0.0036  0.06  0.9^  4.58  k.6k  O.23  0.04  0.19  -0.07  0.0049  0.91  0.80  3.08  3.99  (0.1*0  (0.06)  0.08  -0.18  0.0324  Zi51 The sum o f t h e d i f f e r e n c e s between a c t u a l a n d f o r e c a s t p r o f i t s mean o f t h e d i f f e r e n c e s (Id) = $ 2 . 5 5 " 1 0 = $ 0 . 2 6 m.  ( ^ X ^ ) = $ 2 . 5 5 m.  0.9127 Therefore, the  ^ 1  In determining 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 ( p - p ), s i g n s are ignored because we are o n l y i n t e r e s t e d 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 d i f f e r e n c e s . f  CO CO  sample i s known, the f i r m s can be drawn a t random from universe use  o f 589 a l p h a b e t i c a l l y l i s t e d f i r m s .  can be made o f K e n d a l l and  Here,  the  again,  Smith's "Tables o f Random  Sampling Numbers, T r a c t s f o r Computers No. XXT?"" " 1  3  (Appen-  d i x I ) , f o l l o w i n g the same procedure as t h a t used t o o b t a i n the f i r m s f o r the e x p l o r a t o r y  study.  Method o f A n a l y s i s I n o r d e r t o determine whether break-even a n a l y s i s or  the percentage o f s a l e s method can p r o v i d e a b e t t e r f o r e -  cast o f operating of  p r o f i t s , a comparison must f i r s t be made  the f o r e c a s t s o f the two methods w i t h the a c t u a l  profits.  operating  A comparison o f the f o r e c a s t o f the percentage o f  s a l e s method w i t h the a c t u a l o p e r a t i n g  p r o f i t s i s given  in  Table I V and a comparison o f the f o r e c a s t o f break-even a n a l y s i s w i t h the a c t u a l o p e r a t i n g  p r o f i t s i s g i v e n i n Table  V.  The method which gives a s m a l l e r d i f f e r e n c e between f o r e c a s t o p e r a t i n g  p r o f i t s and a c t u a l o p e r a t i n g  s h o u l d be the more a c c u r a t e method. the  profits  Table V shows t h a t , f o r  57 f i r m s shown i n the sample, the d i f f e r e n c e between the  forecast operating  p r o f i t s and a c t u a l o p e r a t i n g  the percentage o f s a l e s method, t o t a l s $24.27m.  p r o f i t s , by This  gives  a mean d i f f e r e n c e o f $0.4257m, t h a t i s $24.27m d i v i d e d by  14  57.  Table V shows t h a t the d i f f e r e n c e between the 13. K e n d a l l ,  forecast  i o c .c i t .  1 4 . The mean i s used i n s t e a d o f the mode o r the median because i t i s l e a s t s u b j e c t e d t o sampling v a r i a t i o n . This was d i s c u s s e d i n chapter I .  TABLE IV DIFFERENCE BETWEEN ACTUAL AND FORECAST PROFITS - PERCENTAGE OF SALES METHOD ($ Amounts i n M i l l i o n s )  Name o f Company  Av.Percentage of P r o f i t s as a Percentage o f Sales (a)  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  Baush Machine Tool Co. B e l l Company Bishop and Babcock Manufacturing Co. Brown-McLaren Manufacturing Co. C a r p e n t e r (L.E.) & Co. C h i e f C o n s o l i d a t e d M i n i n g Co. Cleveland-Sandusky Brewing Corp. Consolidated R e t a i l Stores, Inc. Cooper T i r e and Rubber Co. C u r t i s L i g h t i n g , Inc. Dixon (Joseph) C r u c i b l e Co. E . & B. Brewing Co. I n c . F l a g g - U t i c a Corp. F l o t i l l Products, Inc. F l o u r M i l l s o f America, I n c . Gerotor May Corp. Gum P r o d u c t , I n c . Hathaway B a k e r i e s , I n c . H i l l e r Helicopters Jacob Ruppert J e a n n e t t e Glass Co. Jessop S t e e l Co. Lanston Industries, Inc. Longchamps, I n c . M a c m i l l a n Petroleum Corp.  9.84 - 0.55 3.69 3.44 - 2.52 0.74 5.76 2.59 3.13 2.01 3.20 1.35 - 1.17 1.73 0.44 - 5«55 - 4U-3 §.8l 4.39 0.03 5.69 3.06 10.21 2.16 2.63  Sales Volume in 1956 (b) h.03  6.64  5.72 1.62 3^5 0.56 1.38  21.04  3.73 12.65 0.92  17.18 21.41 48.55  1.3^ 2.10 18.89 9.83 47.57  5.18 24.85 2.91 7.73 14.16  Forecast Profits P = 6 a x 100 f  .39 (0.04) 0.21 0.05 (0.09) 0.00 0.08 0.55 0.74 0.08  0.41  0.01 (0.20) 0.37 0.21 (0.07) (0.09) 0.53 0.43 0.01 0.30 0.76 0.30 0.17 0.37  Actual Profits  Difference Between A c t u a l and Forecast Profits  Pa  ( P -P  .44  (o!28)  10.05 0.24  0.64)  0.84  a  (0.15) (0.10) (0.43) (0.07) 0.02 (1.77) 1.07 0.15 O.98 0.05  0.36 0.15 0.34 0.07 0.06 2.32 0.33 0.07 0.57 0.04  1.92 6.97 (0.25) 0.13 (1.00) 0.32 (0.19) 0.44 3.^7 (0.02) (0.02) 0.53  1.55 O.76 0.18 0.22 1.53 0.11 0.20  0.14 2.71 0.32 0.19 0.16  f  )  Name o f Company  Av. Percentage of P r o f i t s as a Percentage of Sales (a)  26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4l h2 43 hh U-5 ho 47 48 49 50 51 52  Maguire I n d u s t r i e s , I n c . Mandel B r o t h e r s , I n c . Merrimac Hat Corp. Michigan Bakeries, Inc. Morgan's, I n c . N a t i o n a l Research C o r p o r a t i o n Nelson (N.O.) Co. Oceanic O i l Co. 0 ' S u l l i v a n Rubber Corp. Peck, Stow & Wilcox Co. P l a s t i c Wire & Cable Corp. Plume and Atwood Manufacturing Co. P o w d r e l l & Alexander, I n c . Queen Anne Candy Co. Reis (Robert) & Co. Reymer & B r o t h e r s , I n c . Richmond Cedar Works Rochester & P i t t s b u r g h C o a l Co. Rock-Ola Manufacturing Co. Rudy Manufacturing Co. Sandura Co. S c r a n t o n Lace Co. Seneca F a l l s Machine Co. Shasta Water Co. Sherman P r o d u c t s , I n c . Sidney Blumenthal & Co. S t y l o n Corp.  - 3.82 0.05 2.26 1.72 - 2.24 - 1.49 1.5^ 17.35 ^•35 6.03 5.29 0.67 3.67 4.17 0.86 1.82 2.16 2.35 0.41  0.75 - 0.75 5.3^ - 5.H 2.26 3.71 2.14  6.02  Sales Volume i n 1956 (b)  $2.50 31.55 3.04 8.38 4.76 7.14  15.62 1.85 6.35 2.51  11.43 10.16 4.75 2.73 4.83 1.73 1.51 45.76 5.97 9.03 8.67 6.05 2.44 2.32 5.84  20.23 6.45  Forecast Profits Pf a  x  = TOO 6  1(0.10) 0.02 0.07 0.14  (0.11) (0.11) 0.24 0.32 0.28 0.15 0.61 0.07 0.17 6.11 0.04  0.03 0.03  1.08  0.02 0.07 (0.07) 6.32 (0.37) 0.05 0.22 0.43 0.39  Actual Profits  Difference Between A c t u a l and Forecast Profits  Pa  ( p -P  $0.08  $0.18 O.38 0.08 0.13  (O.36)  0.15 0.27 0.05 0.49 (0.09) 0.58 0.08 0.29 1.1+8 0.00 0.73 0.08 0.06 (0.01) (0.19) 1.87 0.73 1.05 1.00 (6.09) (0.06) 0.04 0.5s 0.27  0.90  a  0.16  0.60 0.33 0.26 0.20 0.14  0.87 0.07 0.56 0.03 0.02 0.04  0.22 0.79 0.71 0.98 1.07 o.4i 0.31 0.01 0.36 0.16 0.51  f  )  Name o f Company  Av.Percentage of P r o f i t s as a P e r centage of Sales (a)  5 3 U n e x c e l l e d Chemical Corp. 5H- V i c t o r P r o d u c t s Corp. 55Wayne Screw Products Co. 56 Wilson Brothers 5 7 Yolande Corp.  -  3.29  6.37 7.16 1.63  2.64  Sales Volume in 1956 (b) 11.04  5.42  1.18  19.55  2.19  Forecast Profits Pf =  Actual Profits  Difference Between A c t u a l and Forecast Profits  Pa  ( Pa-Pf )  6  a  x  V5b~  $(o.03) 0.35 0.08 0.32 0.06  $(0.17) (0.22) (0.06)  0.14 (0.09)  $0.14 0.57  0.14 0.18  o.i? 24.27  i  ro  TABLE V DIFFERENCE BETWEEN ACTUAL AND FORECAST PROFITS - BREAK-EVEN METHOD ($ Amounts i n M i l l i o n s )  1 Baush Machine Tool Co.  1  2  3  (x)  (a)  (b)  $4.03  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  2 B e l l Co. ' 6.64 3 BishoD and Babcock Manufacturi n g Co. 5'72 4 Brown-McLaren Manufacturing Co. 1.62 5 Carpenter (L.E.) & Co. 3.45 6 C h i e f C o n s o l i d a t e d Mining Co. 0.56 7 C l e v e l a n d Sandusky Brewing Corp. I.38 8 Consolidated R e t a i l Stores, Inc. 21.04 9 Cooper T i r e and Rubber Co. 23.74 10 C u r t i s L i g h t i n g , Inc. 3.73 11 Dixon (Joseph) C r u c i b l e Co, 12.65 12 E & B Brewing Co. I n c . 0.92 13 F l a g g - U t i c a Corp. 17.18 14 F l o t i l l P r o d u c t s , Inc. 21.41 15 F l o u r M i l l s o f America, Inc. 48.55 16 Ge r o t o r May Corp. 1.34 17 Gum P r o d u c t s , Inc. 2.10 18 Hathaway B a k e r i e s , I n c . 18.89 19 H i l l e r H e l i c o p t e r s 9.83 20 Jacob Ruppert 47.57 21 Jeannette Glass Co. 5.18  22Jessop S t e e l Co.  23 24 25 26 27 28  Lanston Industries, Inc. Long champs, I n c . M a c M i l l a n Petroleum Corp. Maguire I n d u s t r i e s , I n c . Mandel B r o t h e r s , I n c . Merrimac Hat Corp.  24.85  2.91 7.73 14.16 2.50 31.55 3.04  4  5  (bx)  (a+bx)  0.7MO.67  $2.98 4.45  $3.33 7.85  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  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  1.46 3.57 0.77 1.29 23.46 22.56 3A5 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  *-  8  6  x-(a+bx)  Pa  ( p -P a  f  $0.70 (1.21)  $0.44 (0.28)  10.26 0.93  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)  (0.15) (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  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  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 5^ 55 56 57  Michigan Bakeries, Inc. Morgan's I n c . N a t i o n a l Research C o r p o r a t i o n N e l s o n (N.O.) Company O c e a n i c O i l Company 0 ' S u l l i v a n Rubber C o r p . P e c k , Stow & W i l c o x Co. P l a s t i c W i r e and C a b l e C o r p . Plume & Atwood M a n u f a c t u r i n g Co. P o w d r e l l & Alexander, I n c . Queen Anne Candy Co. R e i s ( R o b e r t ) & Co. R@ymer & B r o t h e r s I n c . RiehiDnd C e d a r Works R o c h e s t e r & P i t t s b u r g C o a l Co. R o c k - O l a M a n u f a c t u r i n g Co. Rudy M a n u f a c t u r i n g Co. S a n d u r a Company S c r a n t o n L a c e Co. S e n e c a F a l l s M a c h i n e Co. S h a s t a W a t e r Co. Sherman P r o d u c t s , I n c . S i d n e y B l u m e n t h a l & Co. S t y l o n Corp. U n e x c e l l e d Chemical Corp. V i c t o r P r o d u c t s Corp. Wayne S c r e w P r o d u c t s Co. Wilson Brothers Yolande Corp.  -  2  3  (x)  (a)  (b)  $8.38 4.76 7.14 15.62 1.85 6.35 2.51 11.43 10.16 4.75 2.73 4.83 1.73 1.51 45.76 5.97 9.03 8.67 6.05 2.44 2.32 5.84 20.23 6.45 1.04 5.42 1.18 19*55 2.19  10.52 0.65 0.02 1.26 0.34 0.12 0.29 0.43 1.3"i 1.22 0.69 1.52 0.34 0.27 7.48 1.79 0.19 0.75 1.25 0.31 0.21 0.3*+  0.90  3.60  0.49 0.11 1.15 0.18 0.19 0.91  0.79  1.00  0.92  0.51  0.93 0.87 O.83  0.83 0.68 0.72 0.70  0.84 0.99 0.79 0.61 0.91  0.84 0.75 0.71 0.90 O.78  0.81 0.73 0.99 0.79 0.78  I.03  0.64  ^  5 (bx)  $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 36.15  3.64 8.22 7.28  4.54 1.73  2.09  4.56 16.39 4.71 1.03  4.28 0.92  20.14 1.40  6 (a+bx) $8.06  4.41  7.16 15.63 1.28 6.03 2.47 9.92 9.77 4.45 2.66 4.90 1.79 1.76 ^3.63 5 A3  8.41  8.03 5.79  2.04  2.30 4.90 19.99 5.20  1.14  5.43 1.10 20.33 2.31  P = x-(a+bx)  7  8  f  $0.32 o.35 (0.02) (0.01) 0.57 0.32 o.o4 1.51 0.39 0.30 0.07 (0.07) (0.06) (0.25) 2.13 0.54 0.62  0.64  0.26 o.4o 0.02 0.94 0.24 1.25 (0.10) (0.01) 0.08 (0.78) (0.12)  Pj  |o. 27  0.05 0.49 (0.09) 0.58 0.08 0.29  1.48  0.00 0.73 0.08 0.06 (0.07) (0.19) I.87 0.73 1.05 1.00 (0.09) (0.06) 0.04 0.58 0.27 0.90 (0.17) (0.22) (0.06)  0.14  (0.09)  ( P -Pf > a  $0.05 0.30 0.51 0.08 0.01 0.24 0.25 0.03 0.39 0.43 0.01 0.13 0.01 0.06 0.26 0.19 0.43 0.36 0.35  0.46  0.02 0.36 0.03 0.35 0.07 0.21  0.14  0.92 0.03 16.51  See  Note n e x t  page.  1 vO  1  NOTE:  Column 1  =  Volume or S a l e s Revenue  2  =  Fixed  3  =  Slope o f the Trend Line  h  =  V a r i a b l e Costs  5  =  Total  6  =  Forecast  7  =  Actual P r o f i t s  8  =  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 .  Costs  Costs Profits  -  operating  p r o f i t s and  96  -  the a c t u a l o p e r a t i n g  break-even method, f o r the 57  p r o f i t s , by  the  sample f i r m s , t o t a l s $ 1 6 . 5 1 m .  The mean d i f f e r e n c e , i n t h i s case, i s $ 0 . 2 8 9 6 m , t h a t i s , $ 1 6 . 5 1 m d i v i d e d by On V, one  57.  the b a s i s of the r e s u l t s shown i n Tables IV  would be tempted to conclude t h a t the  and  break-even  method produces more a c c u r a t e f o r e c a s t s than the percentage o f s a l e s method.  T h i s , however, would be a r a t h e r  conclusion unless  one  subjects  hasty  the r e s u l t s to a t e s t o f  s i g n i f i c a n c e to determine whether the d i f f e r e n c e i n the r e s u l t s of the two factors.  For  methods was  example, i t may  p l e of 57 f i r m s had  brought about by  chance  be p o s s i b l e t h a t , i f the sam-  been p i c k e d from a d i f f e r e n t page i n the  Tables of Random Numbers, the d i f f e r e n c e i n the r e s u l t s might have been i n f a v o u r of the percentage of s a l e s method o r t h e r e might not have been any Therefore, the two  d i f f e r e n c e i n the r e s u l t s .  a conclusion  been c a r r i e d out.  symbol, p^ r e p r e s e n t  2  t a i n e d by the break-even method. i s e q u a l to $ 0 . 4 2 5 7 m and p  discussed  two  2  the  the mean d i f f e r e n c e I t i s already  to go about  ob-  known t h a t  i s equal to $ 0 . 2 8 9 6 m .  i n chapter I, the best way  mining whether there the  F o r t h i s t e s t , l e t the  the mean d i f f e r e n c e o b t a i n e d by  percentage of s a l e s method and p ,  x  the a c c u r a c y of  methods should be a r r i v e d a t , only a f t e r a t e s t of  s i g n i f i c a n c e has  P  regarding  As  deter-  i s a s i g n i f i c a n t d i f f e r e n c e between  means i s to s e t up  the n u l l h y p o t h e s i s t h a t p-^ i s  - 97 -  equal t o p (' "Tr ) .  2  and i s a l s o equal to the mean o f the u n i v e r s e  The r e j e c t i o n o f the n u l l h y p o t h e s i s w i l l mean t h a t  there i s a s i g n i f i c a n t d i f f e r e n c e between the two means, w h i l e acceptance o f the n u l l h y p o t h e s i s w i l l mean t h a t there' i s no s i g n i f i c a n t d i f f e r e n c e between the two means. order to do t h i s , i t i s necessary z, where z i s the r a t i o o f P i ~ P  2  In  t o determine t h e v a l u e o f  to an estimate o f the  standard e r r o r o f the d i f f e r e n c e between the two sample means.  The standard e r r o r o f the d i f f e r e n c e between the  sample means i s : 2 Pl-P  2  '6  +6  Pi  2  n  where:  6  =  ?2  +  l  n  2  The standard e r r o r of the d i f f e r ence between p^ and p  P1-P2  2  6  =  the standard e r r o r o f  6  =  the standard e r r o r o f p  f  =  mean o f t h e u n i v e r s e  r  =  1 - TT  =  s i z e o f the sample  n I n t h i s study,  ^  i s not known.  i t would be b e t t e r t o t e s t p^ a g a i n s t ^  2  I f i t i s known,  and p  2  r a t h e r than t o examine the s i g n i f i c a n c e o f P i - P g .  against Since,  ft ,  - 98 i s n o t known, a n e s t i m a t e , p , h a s t o be made f o r i t , b a s e d o n t h e i n f o r m a t i o n i n t h e two s a m p l e s . n  =  l  P  Thus:  P2  +  ). 4257m + 1 0 . 2 8 9 6 m 2  2 * $0.35765m. Under t h e c i r c u m s t a n c e s , o.  Pl~P2  J  n  n  x  the e a r l i e r  2  now b e c o m e s :  Pl-P  V  2  n  n  x  T h i s i s t h e same a s : 6  pi-p  2  J -  FC1 F)  =  since:  and  =  $0.4257m  .=  $0.2896m  P"  =  $0.35765m  n^  =  p  x  P  2  n  2  = 5 7  +  2  formula;  - 99 Therefore: 6 p  l" 2 P  *  ( 1  ~  P )  ^  =ii0O5765m  +  |0.64235m  X  =J$o.00806m P -P 1  2  Since:  =  =  P  l  "  P  |  '  0  3  5  7  5  m  ( -^°-35765m) (57- + 1  = /|oT2297 +m  ^7  x  6  l  x  $0.03508m  $o.08978m  = $0.4257m - $0.2896m z -  i  = $0.1361m  2  A. 6  Therefore: z  p  l  * p2  = lo^^lm  =  1  '  5  1  5  6  The d e t e r m i n a t i o n o f the z v a l u e , however,  alone  w i l l not i n d i c a t e whether the d i f f e r e n c e between the sample means i s s i g n i f i c a n t o r n o t , u n l e s s and u n t i l the c r i t e r i o n of s i g n i f i c a n c e has been e s t a b l i s h e d .  I n chapter I , i t was  e x p l a i n e d t h a t a l e v e l o f s i g n i f i c a n c e o f 0.01 should be used and i t was a l s o p o i n t e d out t h a t s i n c e , a t t h i s l e v e l o f s i g n i f i c a n c e the value o f z i s 2.667, the n u l l hypothesis should t h e r e f o r e be accepted i f z ^ rejected i f z >  2.667.  2.667 and should be  I t has a l r e a d y been shown t h a t , i n  t h i s study the value o f z i s equal t o 1.5156.  Under the  circumstances, the n u l l hypothesis should be accepted and the hypothesis should be r e j e c t e d .  On t h i s b a s i s , a con-  c l u s i o n may be drawn t h a t there i s no d i f f e r e n c e break-even a n a l y s i s and the percentage  between  o f s a l e s method as a  technique 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  - 1Q0firms. But,  i t m u s t be p o i n t e d  out that this  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 .  conclusion  From t h e  t - t a b l e i n A p p e n d i x I I , i t may be f o u n d t h a t , f o r 57 d e g r e e s o f f r e e d o m , a t t h e 0.10 l e v e l o f s i g n i f i c a n c e , t h e z i s equal  value  t o 1.673 a n d 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 equal  becomes t h e v a l u e  t o 1.297*  B y i n t e r p o l a t i o n , 1.516  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 b e t w e e n the  two s a m p l e means w i l l  be s i g n i f i c a n t a n d t h e n u l l  hypoth-  e s i s t h a t P i = P 2 w i l l h a v e t o be r e j e c t e d a n d t h e h y p o t h e s i s t h a t pi_> p if  2  w i l l h a v e t o be a c c e p t e d .  On t h e o t h e r  hand,  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 used, the reverse  will  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 that the hypothesis i s  t h a t b r e a k - e v e n a n a l y s i s c a n 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 t h e f u t u r e operating there  p r o f i t s o f f i r m s and t h e n u l l h y p o t h e s i s  i s that  i s no d i f f e r e n c e b e t w e e n b r e a k - e v e n a n a l y s i s a n d 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 If  p r o f i t s of firms.  the r e s u l t s o f the 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 a r e n o t s u b -  - 101 j e c t e d t o a t e s t o f s i g n i f i c a n c e , the c o n c l u s i o n may be drawn t h a t the former produces more accurate f o r e c a s t s of o p e r a t i n g p r o f i t s than the l a t t e r s i n c e the mean o f the d i f f e r e n c e between f o r e c a s t o p e r a t i n g p r o f i t s and a c t u a l o p e r a t i n g p r o f i t s a r r i v e d a t by the former i s s m a l l e r than t h a t a r r i v e d a t by the l a t t e r .  The n u l l hypothesis  t h e r e f o r e , be r e j e c t e d and the h y p o t h e s i s But,  would be  would, accepted.  a c o n c l u s i o n o f t h i s nature would be somewhat dubious  s i n c e chance f a c t o r s c o u l d have caused the d i f f e r e n c e i n the means obtained by the two methods. A t e s t o f s i g n i f i c a n c e would c e r t a i n l y l e n d g r e a t e r v a l i d i t y to the c o n c l u s i o n .  But, u n f o r t u n a t e l y ,  the r e s u l t s o f t e s t s o f s i g n i f i c a n c e , depend t o a l a r g e extent on the c r i t e r i o n o f s i g n i f i c a n c e chosen.  I t was  Shown t h a t i f a l e v e l o f s i g n i f i c a n c e o f g r e a t e r than 0.14 i s chosen, then the d i f f e r e n c e i n the means o b t a i n e d by the two  methods would t u r n out t o be s i g n i f i c a n t .  mean a r e j e c t i o n o f the n u l l hypothesis the h y p o t h e s i s .  T h i s would  and acceptance o f  On the other hand, i f a l e v e l o f s i g n i f i -  cance of l e s s than 0.14 I s chosen, the d i f f e r e n c e i n the means o b t a i n e d significant. hypothesis  by the two methods would t u r n out to be not This would permit  the acceptance o f the n u l l  and the r e j e c t i o n o f the h y p o t h e s i s ,  as they  have been s t a t e d . The choice o f the l e v e l o f s i g n i f i c a n c e depends on the type o f e r r o r t h a t i s to be avoided.  In chapter I ,  - 102 i t was  -  argued t h a t type e r r o r I s h o u l d be minimised and  a l e v e l of s i g n i f i c a n c e o f 0.01  should be used.  With t h i s  argument, the n u l l h y p o t h e s i s should be accepted and conclusion  i s t h a t there  even a n a l y s i s and  the  i s no d i f f e r e n c e between break-  the percentage of s a l e s method, as  technique 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 firms.  that  a  profits  of  CHAPTER V SUMMARY AND CONCLUSION i Summary Break-even a n a l y s i s i s a management a i d , which shows the e f f e c t of changes i n the l e v e l o f a c t i v i t y on c o s t s , revenue and p r o f i t s , assuming that other  t h i n g s are  equal and break-even c h a r t s are g r a p h i c p r e s e n t a t i o n s cost-volume-profit there  relationships.  of  I n every break-even c h a r t ,  i s a break-even p o i n t which shows the volume l e v e l a t  which t o t a l revenue e x a c t l y equals t o t a l c o s t s . c h a r t s , however, can a l s o be c o n s t r u c t e d  Break-even  such t h a t the break-  even p o i n t shows the p o i n t of time i n the budgetary p e r i o d when l o s s e s t u r n i n t o p r o f i t s .  These break-even p o i n t s are  u s e f u l i n the sense t h a t they a r e p r e r e q u i s i t e s to the d e t e r m i n a t i o n o f the margin o f s a f e t y and a l s o because they i n d i c a t e t h e p o r t i o n o f the budgetary p e r i o d t h a t remains f o r the accumulation o f the c o n t r i b u t i o n s to p r o f i t s . t h e i r usefulness  But,  should not be overemphasised, s i n c e they do  not remain f i x e d f o r long but keep on changing as the f a c t o r s a f f e c t i n g them undergo change. as exact  Besides,  they are not  as t h e i r name seems to suggest. I t i s claimed  t h a t break-even a n a l y s i s can be  used by management f o r v a r i o u s purposes.  They i n c l u d e  p r o f i t p r o j e c t i o n s , cost c o n t r o l , p r i c e determination  and  - 104 decision-making i n v o l v i n g make or buy problems and c a p i t a l expenditure problems.  But i n p u t t i n g break-even a n a l y s i s  to these uses, v a r i o u s  assumptions have to be made.  These  assumptions a r e as f o l l o w s : (a) A l l c o s t s can be reasonably separated i n t o t h e i r f i x e d and v a r i a b l e components and whereas f i x e d c o s t s remain f i x e d a t a l l volumes, v a r i a b l e c o s t s v a r y i n d i r e c t p r o p o r t i o n to volume. (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 equals or c l o s e l y f o l l o w s s a l e s and a l l f i x e d c o s t s i n c u r r e d i n a p e r i o d are, t h e r e f o r e , deducted from t h a t p e r i o d ' s revenue. (d) There i s only one product o r i f s e v e r a l p r o d u c t s a r e being produced and s o l d , the s a l e s mix w i l l remain constant. A t e s t was c a r r i e d out to determine the u s e f u l ness o f break-even a n a l y s i s as a technique f o r f o r e c a s t i n g profits.  I n t h i s t e s t , break-even a n a l y s i s was compared  w i t h the percentage o f s a l e s method.  F o r t h i s t e s t , no  adjustments were made to the data, which were taken from Moody's I n d u s t r i a l Manuals.  I t was found t h a t , a t the 0.01  l e v e l o f s i g n i f i c a n c e , there was no d i f f e r e n c e i n the a c c u r acy  of the f o r e c a s t s o f the tv/o t e c h n i q u e s .  The h y p o t h e s i s  t h a t break-even a n a l y s i s can be b e t t e r than the percentage of s a l e s method as a technique f o r f o r e c a s t i n g the f u t u r e operating  p r o f i t s o f f i r m s was, t h e r e f o r e ,  rejected.  Conclusion Break-even a n a l y s i s may be r e l e v a n t f o r  various  -  managerial economic problems.  105  -  But, i n u s i n g  break-even  a n a l y s i s many r e s t r i c t i v e assumptions have to be made. v a l i d i t y o f these assumptions v a r i e s with f i r m s .  The  I n some  firms, (a) The t o t a l c o s t s may be predominated by the c o s t o f items whose p r i c e s f l u c t u a t e w i d e l y . (b) There may be a great d i f f e r e n c e between p r o d u c t i o n volume and s a l e s volume i n any g i v e n budgetary p e r i o d of time. (c) A d v e r t i s i n g and s a l e s promotion may be very and h i g h l y s h i f t a b l e .  important  (d) Many products may be produced and s o l d . These products may have d i f f e r e n t margins of r e t u r n over v a r i a b l e c o s t s and the s a l e s mix may vary g r e a t l y . (e) The product d e s i g n o r technology may change over s h o r t p e r i o d s . For obviously  continuously  such f i r m s , the r e s t r i c t i v e assumptions a r e  very u n r e a l i s t i c .  the r e s u l t s obtained v i r t u a l l y useless.  I f break-even a n a l y s i s i s used,  w i l l be so i n a c c u r a t e  that they w i l l be  Under the circumstances, management  must e i t h e r t o t a l l y abandon the break-even device  o r make  adjustments t o overcome the l i m i t a t i o n s of the assumptions. Fortunately, natives.  n o t a l l f i r m s a r e f a c e d w i t h these two a l t e r -  I n some f i r m s , even without adjustments, the  assumptions are q u i t e r e a l i s t i c and more accurate  fore-  c a s t s can be made. In the t e s t i n t h i s t h e s i s , i t was found t h a t t h e percentage o f s a l e s method i s as r e l i a b l e as break-even a n a l y s i s , as a technique f o r f o r e c a s t i n g p r o f i t s .  But, i t  - 106 must be emphasised  t h a t i n the t e s t , i n f o r e c a s t i n g p r o f i t s  by the break-even method, no adjustments were made to the data.  Hence, any c o n c l u s i o n drawn, based on the t e s t ,  has  to be r e s t r i c t e d to s i t u a t i o n s i n which no adjustments are made. On the b a s i s of t h i s study, i t may  be concluded  t h a t management should use the percentage o f s a l e s method i n s t e a d of break-even a n a l y s i s to f o r e c a s t p r o f i t s , i f i t i s not prepared to a d j u s t i t s data to r e c o g n i s e the  effects  of changes i n the determinants of p r o f i t s , other than volume.  On the o t h e r hand, i f management i s p r e p a r e d to  make the adjustments, i t i s o n l y p o s s i b l e to s t a t e , as f a r as t h i s study i s concerned, that the f o r e c a s t s by the breakeven technique w i l l now  be more a c c u r a t e than i f a d j u s t -  ments were not made; but i t i s not p o s s i b l e to s t a t e whether they w i l l be b e t t e r than those by the percentage o f s a l e s method.  F u r t h e r , i f adjustments are to be made, management  must a l s o r e a l i s e t h a t some of the advantages analysis, particularly  of  break-even  s i m p l i c i t y and quickness of p r e p a r -  a t i o n , 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 p r e s s e d f o r time or i f the funds of the f i r m are limited,  i t may  altogether. the  be a d v i s a b l e not to use break-even  analysis  The i n c r e a s e i n the a c c u r a c y , as a r e s u l t o f  adjustments, may  not j u s t i f y the i n c r e a s e i n expense,  time and e f f o r t t h a t would be r e q u i r e d , though i t i s r e c o g n i s e d t h a t o t h e r managerial f u n c t i o n s such as p l a n n i n g ,  - 107 p r i c e - s e t t i n g and p r e p a r a t i o n of budgets a l s o r e q u i r e the a n a l y s i s o f c o s t behaviour and adjustments so t h a t the a d d i t i o n a l expense, time and e f f o r t i n making the a d j u s t ments, may not be v e r y g r e a t . On the whole, i t may be s a i d t h a t t h i s study has a n e g a t i v e approach i n the sense t h a t i t merely shows the circumstances under which break-even a n a l y s i s s h o u l d n o t 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 c o - o p e r a t i o n o f some f i r m s ,  further  r e s e a r c h may be c a r r i e d out to determine the u s e f u l n e s s of break-even a n a l y s i s , i f adjustments are made.  -  108  -  BIBLIOGRAPHY  A.  BOOKS  A n d e r s o n , D a v i d R. Practical Controllership, Illinois: R i c h a r d D. I r w i n , I n c . , 1 9 5 4 .  Homewood,  A n t h o n y , R. N. Management A c c o u n t i n g : T e x t and C a s e s . Homewood, I l l i n o i s : R i c h a r d D. I r w i n , I n c . , 1 9 5 6 . Bierman, Harold. Managerial Accounting, M a c M i l l a n Company, 1 9 5 9 .  New Y o r k :  The  C r o w h i n g s h i e l d , G e r a l d R. Cost Accounting: Principles and M a r g i n a l A p p l i c a t i o n s , B o s t o n : Houghton M i f f l i n Company, 1 9 6 2 . C r o x t o n , F r e d e r i c k E . a n d D u d l e y J . Cowden. 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'.'Break-Even A n a l y s i s f o r Cash F o r e c a s t i n g " , C o n t r o l l e r , V o l . 2 3 (December 1955), pp. 5 7 8 - 5 8 0 . Bac, Alexander. "Advantages o f Break-Even Income Statement Compared w i t h C o n v e n t i o n a l Statement", J o u r n a l o f Accountancy. V o l . 9 1 (January 1 9 5 D , pp. 1 0 6 - 1 1 1 . Burchard, Joseph R. " C r i t i c a l Look a t the M a r g i n a l Graph Technique", N.A.A. B u l l e t i n . V o l . 4 2 , S e c t i o n I (May 1961),  pp.  2^-32.  Campbell, Alexander. "Use o f Break-Even P o i n t s i n P o l i c y D e c i s i o n s " , Cost and Management, (December 1 9 5 4 ) , pp. 433-H41. Chapin, Ned. "The Development of 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 of B u s i n e s s , V o l . 2 8 ' ( A p r i l 1 9 5 5 ) , PP.- 1U8-149. Conway, R i c h a r d W. "Breaking Out of the L i m i t a t i o n s of Break-Even A n a l y s i s " , N.A.C.A. 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J a e d i c k e , Robert K. "Improving Break-Even A n a l y s i s by L i n e a r Programming Technique", N.A.A. B u l l e t i n , V o l . 42, S e c t i o n I (March 1 9 6 1 ) , pp. 5 - 1 2 . Kempster, John H. "Break-Even A n a l y s i s - Common Ground f o r the Economist and the Cost Accountant", N.A.C.A. B u l l e t i n . (Feb. 1 5 , 1949), pp. 711-721. L a n z i l o t t i , Robert F. " P r i c i n g O b j e c t i v e s i n Large Companies", American Economic Review. V o l . XLVTII, No. 5 , (December 1958), pp. 921-940. Lawson, G e r a l d H. "Marginal C o s t i n g And Break-Even A n a l y s i s " , Cost Accountant, V o l . 3 8 (September i 9 6 0 ) , pp. 3 1 7 - 3 2 5 . May,  P a u l A. " P r o f i t P o l y g r a p h f o r Product Mix E v a l u a t i o n " , N.A.C.A. B u l l e t i n , V o l . 3 7 , S e c t i o n I (November 1 9 5 5 ) , PP. 307-318.  P a t r i c k . A. W. "Some O b s e r v a t i o n s on the Break-Even Chart", A c c o u n t i n g Review, V o l . 3 3 (October 1 9 5 8 ) , pp. 5 7 3 - 5 8 0 . Pye, Malcolm L. "How t o Determine Break-Even P o i n t s w i t h Simple A l g e b r a i c Formulas", J o u r n a l o f Accountancy. V o l . 8 6 (August 1948), pp. 1 3 3 - 1 3 7 . Robbins, Sidney M. "Emphasising the M a r g i n a l F a c t o r i n the Break-Even A n a l y s i s " , N.A.A. B u l l e t i n , V o l . 4 3 , S e c t i o n I (October 1 9 6 1 ) , pp. 53-60. Robbins, Sidney M. and E. F o s t e r J r . , " P r o f i t P l a n n i n g and the F i n a n c e F u n c t i o n " , J o u r n a l o f F i n a n c e , V o l . 1 2 (December 1957), pp. 451-467. Rucker, A l l e n W. "Clocks f o r Management C o n t r o l " , Harvard B u s i n e s s Review, V o l . 3 3 No. 5 (Sept.-Oct. 1 9 5 5 ) , pp. oTTcJo.  - 112 S c o t t , J . A. and J . A r k l e y . "Break-Even A n a l y s i s " , Cost Accountant, V o l . 37 (September 1959), pp. 547-548. Smitten, L o u i s J . " P r o f i t C o n t r o l f o r Management, An E x p l a n a t i o n o f t h e C o n s t r u c t i o n and Use o f a BreakEven Chart", Cost and Management,(September 1959), pp. 291-306; (October 1959), pp. 324-346. S o l d o f s k y , R. M. "Accountants vs Economists Concepts o f Break-Even A n a l y s i s " , N.A.A. B u l l e t i n 4l, V o l / 41 (December 1959), PP. 5-18. Spencer, Leland G. " P r o f i t g r a p h Technique and A p p l i c a t i o n s " , N.A.C.A. B u l l e t i n , V o l . 38, S e c t i o n I (December 1956),  PP. 493-507.  S t e e l e , A l l a n T. "Break-Even Computations - Use w i t h C a u t i o n " . N.A.A. B u l l e t i n , V o l . 39, S e c t i o n I ( J u l y  1958) , pp. 91-92.  S t e t t l e r , Howard F. "Break-Even A n a l y s i s : I t s Uses and Misuses", A c c o u n t i n g Review, V o l . 37 ( J u l y 1962), pp.  460-463.  T u t t l e , Roy E. " E f f e c t o f Inventory Change on Break-Even A n a l y s i s " , N.A.A. B u l l e t i n , V o l . 40, S e c t i o n I (January  1959) , PP. 77-87.  V a t t e r , W i l l i a m J . "Accounting Measurements o f Incremental Cost", J o u r n a l o f Business, V o l . 18, No. 1 (January 1945), pp. 145-162. . "Toward a G e n e r a l i z e d Break-Even Formula", N.A.A. B u l l e t i n . V o l . 43, S e c t i o n I (December 1961), pp. 5-10. V i c k e r s , Douglas. "On the Economics o f Break-Even", Accounting Review, V o l . 35 ( J u l y i960), pp. 405-412. V i l l e r s , Raymond, "Communications - The O r i g i n o f the BreakEven Chart", J o u r n a l of B u s i n e s s , V o l . XXVIII, No. 4 (October 1955) PP. 296-297. Wehn, W i l b e r t C. "Break-Even P o i n t s t h a t Mean More i n P r o f i t C o n t r o l " , C o n t r o l l e r , V o l . 27 ( J u l y 1959), pp.  311-31^5 3^6.  Welsch, Glenn A. " C o n s t r u c t i o n and Uses of Break-Even A n a l y s i s " , C o n t r o l l e r , V o l . 21 (October 1953), PP. 466.  *+62-  W i l l i s , Bruce C. "Use of Break-Even A n a l y s i s i n Management", Canadian Chartered Accountant, V o l . 73 (December 1958),  pp. 52^528.  - 113 Yacobian, Paul, " P r a c t i c a l E v a l u a t i o n of Break-Even A n a l y s i s " , N.A.A. B u l l e t i n . V o l . 40, S e c t i o n I (January  1959), PP. 23-29.  APPENDIX I TABLE OF RANDOM SAMPLING NUMBERS Twenty-Third Thousand 1- - 4 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  28  46 8 0 04 9 0 1 0 63 18 39 91 70 16 82 10 95 20  36 03  K5  01 03 . 75 25 96 18 52 71 14 3 7 7 0 57 16 x 8 8 48 23 31 90 44 0 9 18 67 90  3  84 42 89 36  5-8 07 66 17 61 26 87 76 80 47 11 81 53 83 52 19 95 10 31  41  08 90  24 64  30 08  30 58 03 17 07  32  86  V-  26 61 77 39  18 87 90 ^3 57 44 29 ^3 51 98 70 56  9- •12 0 2 k3 1 3 64 32 01 17 79  9h 49  59 10 23 85 71 05  36 30  85 78 00 68  72 40 54  V>  2 61 ? 3^ 89  K5 64  57 16 85 19 42 17 80 69 17  68 44 52 86  48 14 91 23 77  13-16  17--20  2 1 - -24  06 16 20 62 22 92 07 94 81  68 79 11 65  75 05 66 73 93 36 63 31  64  76 98 19 43 01 04 02  7h 45  64  15 99 43 51  9h  47 96 58  14  30 76 38  84  70 10 42 69 35 02 88 03 32 33 11 57 88 61 61 73 13  19  78 44 11 37 62 21  13  88  14 75  5h  07  41  18 09 23 05 22 33 23 72 90 26 25 06 68 86  04 27  26 49 76 75 08 5 * 0 2 29 7 4 52 59 7 5 62 12 1 6 43  84 16 26  24  24 66 99 ^3 13 97 90 92 23  84  61 81 3^  25-28  98 51  5h  04  06 90 56 31 33 38 *3 36 01 30 17 15 79 01 67 70 29 35 19 92 82  81 93 66  74 39  64  33 13  14 66  24  89 49 81 91 57 31  48 84 79 07 25 75  22 52 42 01 79 73 09 45 95 79 70 45 53 31 95 92 08 68 12 93 55 52 47 99 27  29-3.2  33-36  37-40  37 p i 29 4 4 48 0 7 55 88 5 0 25 59 5 4 00 59 84 7 7 23 29 1 6 89 02 4 4 54 43  14 7 7  49 49 9 1 46 87 06 27 2 0 66 23 34 82 hh 7 5 30 65 75 11 02 39 41 5 6 00 12 71 79 38 7 3 14 7 1  V P 87 69 77 81 91 79 59 97 87 70 92  K5  66 52 02 62 09 51 75 65 46 2 8 37 0 9  53 88 94 38 31 61 11 77 10  04 10 3^ 36  64  16 78 83 37  Pr  89 61 77 26 71 91 67 03 64 1 9 82 16 9 0 57 99 11 72 39 99 51 69 6 6 00 10 23 59 12 97  31 43  80 33 3k 6 7 5 9 9+ k5 1 3 8 8 81 60 96 24 3 4 04 15 83 24  Twenty-fourth Thousand  1-4 1 2  I5 6  9 10 11 12  ll ll 17 18 19 20 21 22  i 25  Source s  65 91 60 89 31 *+9  99 93 31 76 93 95  14 03 08 40  61 49 43 76 58 37 89 92 16 87 66 88 36 69 09  52 74 09 51 86 81 07 12 31 14  18 99 42 30 24  5-8  9-12  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  79 76 25 39 82 92  ¥ P  89 25 38 90 07 90  89 51 76 83 49 02  69 60 45 05 29 77 80 42 86 49 42 00 99 99  18 03 09 96 09 52 02 60 18 91 21 72 12 09  24 8 5  13-16  17-20  15 67 67 09 35 66 63  M  99 77 13 84 20 57 08 80 89 38 73 H4 47 49 63 19 74 67 64 27 03 11  53 85 60 20 65 56  52 09 15 10 68 35 95  95 98 10 35 86 9 2 82 25 87  5k-  73 09 72 20 91  50 32 95 21 31 28 31 58 28 11 07 61  M8 41  41  50 32 37 69 58 83 13 06  70 83 88 85 97 h-7 31 18 3^ 66  21-24  24 21 02 68 14 64 47 41  96 67 82 3; 51  5  61 7h 89 46 51 91 01 6  _  99 85 S7 56 85 09  M+  84 07  68 65 29 66 44 56 65 05 82 86 66 87  25-28  29-32  33-36  37-40  36 05 85 51 68 18 20 18 10 79 97 71 25 17 21 31  80 57 3^ 29 43 08 13 69 20 24 02 66 53 25 00 24 98 28 21 70 03 65 89 95 09  15  41  12 10 07 15 81 15 86 43  89 79 06 06 83 77 11 51 67 5h  73 55 30 25 01 02 21 87 83 97 10 33 11 82 88  61 51 83 87 76 31 13 75 51 91 06 81 32 65 81 69 56  44 22 7h  46  13 91 25 09  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  M. G. K e n d a l l and B. B. Smith, Tables of Random Sampling Numbers. T r a c t s f o r Computers N o. XXIV. Cambridge: Cambridge U n i v e r s i t y P r e s s , 1951, p.  39  15.  1 H H  - 116 -  APPENDIX I I VALUES OF t FOR GIVEN DEGREES OF FREEDOM (n) AND AT SPECIFIED LEVELS OF SIGNIFICANCE  LEVEL OF SIGNIFICANCE n  1 2 3 4 5  6 7 8 9 10 20  ?° 40  6o 100 00 Source:  ,—i  0.20  0.10  3.078 1.886 1.638 1-533 1.476 1.U40 1.415 1.397 1.383 1.372 1.325 1.310 1.303 1.296 I.289 I.282  6.314  0.05  , ,  0.02  2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.725 1.697 1.684 1.671  12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.086 2.042 2.021 2.000  31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.528 2.457 2.423 2.390  1.645  1.960  2.326  2.920  1.658  I.98O  2.358  ,  Uy  0.01  n  63.657 9.925 5.841 4.604 4.032 3.707 3.^99 3.355 3.250 3.169  1 2 3 4 5 6 7 8 9 10 2.845 20 2.750 2.704 2.660 60 2.617 120  2.576 00  F r e d e r i c k E. Croxton and Dudley J . Cowden, A p p l i e d Gene r a l S t a t i s t i c s . New York: P r e n t i c e - H a l l , Inc.,1955, PP. 750-751, Appendix I .  APPENDIX I I I OPERATING REVENUE (In m i l l i o n s of d o l l a r s ) Name o f Company  1955  195^-  1 A u t o - S o l e r Co. 2 B a l s a C h i c a O i l Corp. 3 Bausa Machine Tool Company 4 B e l l Company 5 Bischop & Babcock Mfg. Co. 6 Brown McLaren Mfg. Co. 7 Carpenter (L.E.) & Co. 8 Chief Consolidated M i n i n g Co. 9 Cleveland-Sandusky Brewing Corp. 1 0 Consolidated R e t a i l S t o r e s Inc. 1 1 Copper T i r e and Rubber Co. 12 Curtis Lighting 1 3 Davega S t o r e s Corp. 14 Diamond Motor Car Co. 1 5 Dixon (Joseph) Crumble Co. 1 6 E & B Brewing Co.Inc. 17 Flagg U t i c a Corporation 1 8 F l o t i l l P r o d u c t s Inc. 1 9 F l o u r M i l l s o f America, Inc. 2 0 Gerotor May Corporation 2 1 Globe America Corporation  1.56 0.97  1.76  1953  2.68  1952  2.33  1951  1950  19^9  1948  19^7  1946  2.32  1.17 0.87  0.08 O.69  1.08 1.76  1.14 0.58  1.07  1.87  I.63  2.07  1.26  1.31  0.89  O.76  0.71  0.78  3.52  3.88  14.53  5.66  14.85  3.61 16.68  h.99  7.20  6.22  3A7  h.95  4.48  1.06  1.36  1.45  1.80  8.20  8.75  11.52  15.9h  _  13.44  1.91  1.55  1.18  2.98 0.65  4.24  0.91  1.33  1.35  1.59  1.42  1.35  1.28  1.27  1.72  26.49  25.75  28.13  30.02  29.72  23.63  15.03  22.95  17.71  23.82  24.75 25.83  26.38 82.11  17.06 O.98 26.31  IO.38  17.23  10.00 1.61 15.92 18.19  18.23 17.00  37.55  38.63  62.93 108.14  1.30  1.84  1.12  6.65  2.64  37.93 11.63  1.28 1 7 . ^-2  4.85  1.29  2.55  6.80  2.40  1.87  1.57  5.96  79.93 9.62  1.37  13-41 13.26  7.14  3.04  28.84 50.06  3.16  O.83  2.58  3.90  I.63  1.98  1.19  0.95  1.27  1.12  1.45  1.28  29.24 3 1 . 5 1  35.65  31.59  31.62  13.27 5.94 2.60 I.69 2 4 . 3 6 24.75 27.09 21.28  7.77  11.08  11.02  23.31  21.10  3.31  2.02  2.74  10.04 0.97  1.32  —  _  54.70  28.08  1.66  2.58  1.88  10.06  6.07  1.88  14.29  8.62  8.46  93.64  80.58 1 1 5 . 3 0 9 7 . 2 9  -  —  4.30  4.88  4.81  2.35  1.97  8.71  7.50  8.39  7.59  5.66  —  22.69  15.11  -  2.21  41.68  0.79  7.24  2.58  37.47 8.80 0.56  .70  2.35 0.69  O.82 2.11  9.01 O.76  11.55  7.17  0.48  -  9.9^ —  Name o f Company  1955  2 2 Gum Products Inc. 2.11 2 3 Hathaway B a k e r i e s , Inc. 2 2 . 7 3 24 H i l l e r H e l i c o p t e r s 7.74 2 5 Jacob Rupert 49.12 2 6 J e a n n e t t e Glass Company 5.14 2 7 Jessop S t e e l Co. 16.40 28 Lanston I n d u s t r i e s Inc. 2.98 2 9 Longchamps Inc. 7-78 3 0 MacMillan Petroleum Corp. 13.71 3 1 Maguire I n d u s t r i e s , I n c . I.98 3 2 Mandel Brothers Inc. 32.17 3 3 Merrimac Hat Corp. 2.60 3 4 Michigan B a k e r i e s , I n c . 7.76 3 5 Mohawk L i q u e r Corp. 3.91 3 6 Morgan's Inc. 4.43 3 7 N a t i o n a l Research Corp. 4 . 2 3 38 N e l s o n ( N . 0 . ) "Company 17-72 3 9 New England Box Company 4.04 40 Oceanic O i l Company 1.88 41 0 » S u l l i v a n Rubber Corp. 6 . 4 8 42 Peck Stow & W i l l o x Co. 2.20 4 3 P l a s t i c Wire and Cable Corp. 8.51 4 4 Plume & Atwood Mfg.Co. 9.63 4 5 P o w d r e l l & Alexander I n c . 6 . 1 9 46 Queen Anne Candy Co. 2.84 4 7 Reis (Robert) & Co. 4.65 48 Reymer & Brothers Inc. 2.25 4 9 Richmond Cedar Works 1.65  195^  1953  2.29 23.94 6.35 52.51 4.62 11.38 4.00 7.99  2.02 26.30 10.37 57.22 4.66 15.58 3-58 8.77  1952  1951  1950  19^9  1948  1947 1946  1.95 2.49 2.20 2.58 4.32 27.62 27.88 2 7 . 3 0 2 6 . 1 9 2 5 . 8 0 2 2 . 1 1 1 9 . 7 8 14.40 6.66 49.83 3 8 . 8 1 3 0 . 3 1 25.80 39.76 43.73 38.63 4.33 4-. 41 3.42 2.71 2.82 3.73 5.52 1 6 . 5 3 1 5 . 2 3 8 . 3 2 6.44 8.89 11.33 11.25 3.14 3.33 3.13 3 . 8 8 3 . 6 6 2 . 1 0 2.46 7.78 7-66 7.90 8.29 8.20  1 4 . 0 1 1 6 . 4 0 1 5 . 9 5 14-.20 1 1 . 8 4 9.48 1 1 . 0 5 9.63 9.00 I . 7 6 2.14 2.33 2.96 2.70 2.68 3.6O 30.70 30.55 32.04 34.29 33.98 35.63 36.33 35.07 27.48 5.99 6.95 7.25 7.68 8 . 7 8 8 . 5 8 8.80 11.93 13-55 7.26 6.09 5.51 4.84 4.25 3.92 4.33 3.61 3-72 3.22 2.92 2.52 2.96 2.75 1.75 3.80 3.31 3 . 2 9 2 . 2 2 1.30 2.28 2.89 3.95 4.02 3.07 H-.63 3 . 5 3 H-.12 2 . 8 2 1.29 1.41 1.16 O.97 1 . 3 2 15.64 2 . 6 8 2 . 9 9 H-.19 4.30 2.81 4.29 3.66 5.55 6.55 7.19 6.75 5.26 6.69 7.36 6.12 2.05 1.09 0.81 0.91 6 . 6 l 6.84 6.61 6.29 5.92 3.97 3.03 4.38 6.20 4.33 5.00 5.00 5.09 4.13 4 . 0 8 5.13 6 . 2 0 8 . 5 7 9.40 6 . 0 6 2.92 2.03 2.31 3.05 9.14 1 0 . 5 1 8 . 2 7 1 0 . 0 6 8 . 8 2 5.46 6.73 6.70 7 . 5 1 1 2 . 8 9 1 5 . 9 5 1 7 . 8 3 2 1 . 6 2 1 8 . 3 1 23.06 21.89 3.27 3.51 3.5*+ 3.07 3.15 3 . 0 5 2 . 0 3 2.92 H-.23 4 . 8 2 4 . 4 1 4.84 4 . 6 9 4 . 4 9 6.16 7.59 2.10 2.68 2.90 2 . 4 l 2.37 2.59 2.47 2.46 1.68 2 . 8 7 2.46 2.85 2.27 2.75 -  2.21 20.57 3.34 9.09 2.22  Name o f Company 5 0 Rochester & P i t t s b u r g Coal Co. 5 1 Rock O l a Mfg. Corp.  5 2 . Ronson C o r p o r a t i o n 53 54 55 56 57 58 59  1955  1954  1953  1952  1951  1950  38.10 4.8l  31.80 4.76  41.95 3-28  42.76  47.88 4.15 3^.63 2.21 4.43 6.97  0.77 2.26  45.77 5.22 32.50 2.76 7.13 6.60 1.10 0.76 1.03 21.85  28.95  Rudy Mfg. Company 3.62 Sandura Company 4.76 Scranton Lace Company 6.41 Seneca F a l l s Machine C o . 1 . 6 0 Shasta Water Company 2.65 Sherman P r o d u c t s , Inc. 4 . 3 1 Sidney Blumenthal & Co.  Inc.  6 0 Standard Commercial Tobacco I n c . 6 1 S t y l o n Corp. 6 2 1 2 t h S t r e e t Store 6 3 U n e x c e l l e d Chemical Corp. 64 V i c t o r P r o d u c t s Corporation 6 5 Wayne Screw Products Co. 6 6 Wilson Brothers 6 7 Yolande C o r p o r a t i o n  22.7^-  24.42  3.26 3.56 5.82 3.46 1.93 3.56  18.49  26.48  3«56 3.84 6.65 4.07 0.54 3.73  3.79  28.46  2.14  5.35 7.02 3.72 0.47 3 A 3  24.19  25.96  31.34  2.35 2.15  5-39 6.05 3.77  3.56 3-90 3.65  12.84 2.16 4.12  12.46 4.57  1.21  4.68  8.45  6.06  6.63  1.64  1.11  20.39 2.23  19.51 2.29  2.64  1949  1948  5.15 32.13 I.87  28.82  4.92  6.84  0.75 0.89 1.75 15.89  VI  2  2.65  3.86 9.08 O.63 0.92  2.51  21.85  8.12 18.18 2.36  3.95 11.00 1.39  7.10 0.77 1.12 2.12  0.13 1.13 1.15  21.94  22.26  5T26  16.13  5^74  5.37  3.85  4.83  6.16  10.81 1.21  10.07  5.70  1.30 I6.96 3.54  13.28  4.49  4.82  5T08  5.27  5^65  6.35  3.60  2.72  2.38  8.40  7.82  8.49  9.59  8.14  1.82  1.68 21.11 2.26  1.96  1.32  24.09 2.82  21.88 2.73  0.99 16.73 2.85  21.10 2.78  1946  6.66  3.15  1.25  1947  3..26  16.42  3.47  1.03 2.85  APPENDIX IV OPERATING COSTS ( i n m i l l i o n s of d o l l a r s ) Name o f Company  1955  1 Auto S o l e r Company 2 B a l s a C h i c a O i l Corp. 1.08 3 Baush Machine Tool Company 1.77 4 B e l l Company 9.49 5 Bishop <&f Babcock Mfg.Co,. 8.29 1.23 6 Brown McLaren Mfg. Co. 7 Carpenter (L.E.) & Co. 6.42 8 Chief Consolidated Mining Co. 1.22 9 Cleveland-Sandusky Brewing Co. 1.41 1 0 Consolidated R e t a i l Stores Inc. 28.21 11 Cooper T i r e and Rubber Co. 22.71 12 Curtis Lighting 2.71 24.20 1 3 Davega-Stores Corp. 14- Diamond T. Motor Car.Co,.37.71 1 5 Dixon (Joseph) Crumble Co. 10.76 16 E & B Brewing Co. I n c . 1.30 17 F l a g g U t i c a C o r p o r a t i o n 16.88 18 F l o t i l l P r o d u c t s I n c . 15.87 1 9 F l o u r M i l l s o f America, Inc. 38.34 2 0 Gerotor May Corp. 1.71 2 1 Globe America Corp. 6.02 5  1954  1953  1952  1951  1950  1949  1948  1947  1946  1.55 0.96  2.24 0.74  1.96 0.72  2.01 0.68  1.09 1.08  0.84 0.72  0.97 0.80  0.89 0.57  0.84 ,0.39  3.08 13.12 5.07 1.36 4.82  3.10 14.16 6.67 2.11 4.33  4.54 15.69 5.97 1.59 5.88  2.96 15.90 3-53 1.28 6.83  1.61 13.72  1.93  1.31  1.88  3- £ 1.08 3.28  1.55 12.13 2.83 0.67 2.21  3.79 0.84 2.81  7.07 0.81 2.77  2.37 0.68 3.67  .35  1.15  1.18  1.62  1.57  1.40  1.75  1.14  0.85  1.46  1.26  1.18  1.15  1.61  1.26  1.22  1.09  1.07  25.97  27.68  29.42  28.03  28.19  30.20  33.34  29.43  29.04  14.84 2.57 25.01 26.32  21.93 2.07 26.21 80.25  16.77 1.08 26.16 77.61  16.65 2.88 27.47 48.22  12.16 2.44 23.35 26.59  6.22 1.61 23.57 21.09  7.80 2.45 21.57 35.68  IO.76 2.34 19.01 38.63  9.92 1.93 21.46  9.4o 1.4o 16.09 17.46  10.04 1.29 18.10 16.96  9.56 8.87 14.56 13.57  11.00 0.50  8.61 I.09  7.28 1.02  8.67 0.86  9.84 1.90  9.37 0.80  9.07  9.72  39.20 2.22 7.21  6 8 . 0 2 107.85 4.36 4.09 8.12 6.88  mm  2  _  —  13.44  12.17  92.79 4.41. 7.53  7 9 . 3 6 :1 1 3 . 3 0 2.06 4.25 6.63 5.27  -  _  93.47 2.04 9.26  —  _  —  —  50.44 2.66 6.21  —  28.88 2.00 2.50  Name o f Company 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  1955  Gum P r o d u c t s Inc. I.98 Hathaway B a k e r i e s I n c . 2 3 . 2 1 H i l l e r Helicopters 7.77 Jacob Ruppert 49.02 Jeannette Glass Company 4 . 7 6 Jessop S t e e l Co. 14.67 Lanston I n d u s t r i e s , I n c . 3.14 Longchamps I n c . 8.02 M a c M i l l a n Petroleum Corp. 13.55 Maguire I n d u s t r i e s , I n c . 1 . 9 4 Mandel B r o t h e r s Inc. 32.77 Merrimac Hat Corp. 2.69 Michigan Bakeries,Inc. 7.52 Mohawk L i q u e r Corp. 3.71 Morgan's Inc. 4.31 N a t i o n a l Research Corp. 4.73 Nelson ( N . 0 . ) Company 17.56 New England Box Company 3 . 8 3 Oceanic O i l Company 1.40 0 ' S u l l i v a n Rubber Corp. 6.43 Peck Stow & Wilcox Co. I.96 P l a s t i c Wire and Cable Corp. 7-76 Plume & Atwood Mfg. Co. 9 . 9 1 P o w d r e l l & Alexander I n c . 5 . 8 9 Queen Anne Candy Co. 2.72 R e i s (Robert) & Co. 4.55 Reymer & B r o t h e r s I n c . 2.25 Richmond Cedar Works 1.66 Rochester & P i t t s b u r g C o a l Co. 37.71 Rock O l a Mfg. Corp. 4.44  1954  1953  1952  2.17 1.90 24.26 25.02 6.46 9 . 7 0 51.59 56.16 4.30 4.22 1 1 . 1 9 14.06 4.45 3.20 7.64 8 . 6 1  2.40 26.70 12.42 48.56 3.99 13.83 2.70 7.71  2.19 26.92 6.11 39.06 4.35 12.56 2.60 7.45  1 3 . 9 5 1 6 . 4 51 5 . 3 4 2.06 1.66 2.16 3 1 . 9 1 3 1 . 8 5 33.11 5.82 6.82 7.12 7 . 2 0 6.13 5.66 3.43 3.44 3.20 3.3* 3 . 2 8 2.23 4.54 3.53 3.97 15.85 2.72 2.73 6.41 3.67 5.44 1.28 0.91 O.87 6.27 6.53 6.24 4.40 4.52 4.51  1951  1950  1949  1948  2.53 25.92  3.07 25.05  4.73 24.30  3246 3.49 7.74 2.47 7.46  28.03 2.80 7.29 2.70 7.93  13.41 2.72 33.78 7.48 4.79 2.83 1.76 2.40 3.91 6.84 0.62 5.82 4.51  11.65 2.94 34.02 8.52 4.15 2.39 2.47 1.33 2.61 6.41  1947  1946  21.24  18.39  39.76 2.84 9.51 2.38 7.97  42.85 3.31 12.03 1.55  35.80 4.17 11.56 1.83  9.60 3.47 35.05 8.41 3.71 2.92 3.06 1.34 2.19 5.27  10.40 4.41 35.47 8.79 4.06 2.61 3.71 1.18 2.56 6.16  ,9.06  8.45  33.36 11.59  26A5 12.02  2.11 3.62 1.17  3.09 2.81 1.38  6A4  5A7  5?44 3.89  4.00 4.13  2.89 4.67  4.12  5^80  2.34 6.62 20.37 2.10 6.16 2.36  3.29 6.43 17.99 3.10 7.59 2.29  2.05  5.59 7.57 9.08 9.86 8.5613.55 3.12 3.25 4.23 4 . 8 2 2.28 2 . 6 7 I.39 3.23  7.94 8.26 16.98 3.26 4.41 2.75 2.55  5.23 9.26 17.64 2.87 4.84 2.42 2.59  2.79 8.54 20.67 2.85 4.69 2.38 2.21  2.11 6.23 18.60 2.92 4.49 2.58 2.61  32.43 40.54 4.49 3.81  41.40 4.13  45.34 4.74  43.22 5.34  4.84  5.46  6.59  -  14.87 2.97 9.09 1.95  3.68  Name o f Company  1955  5 2 Ronson C o r p o r a t i o n 26.35 5 3 R u d y Mfg. Company 3.72 5 4 Sandura Co. 4.59 5 5 S c r a n t o n Lace Company 6.36 5 o Seneca F a l l s Machine Co. 1 . 8 9 5 7 Shasta Water Company 2.64 58 Sherman P r o d u c t s , I n c . 3 . 8 9 59 Sidney Blumenthal & Co. 2 4 . 3 0 6 0 Standard Commercial Tobacco Co. 4.92 6 1 S t y l o n Corp. 4.78 6 2 1 2 t h S t r e e t Store 3.86 6 3 U n e x c e l l e d Chemical C o r p . 1 . 4 4 64 V i c t o r P r o d u c t s Corp. 6.29 6 5 Wayne Screw Products Co. 1 . 6 6 66 Wilson Brothers 20.11 6 7 Yolands C o r p o r a t i o n 2.27  1954  1953  1952  1951  24.97 3.03 3.89 5.98 2.91 1.85 3.31 19.78  24.97 3 0 . 2 1 2 8 . 4 9 3.37 2.19 2.23 4.21 5.48 4.91 6.46 6 . 9 6 6.90 2.03 3.13 2.86 0.9+ 0.48 0.80 1.84 3.22 3.01 23.92 2 5 . 3 0 28.65  3.26 3.48 3.78 4.61 7.01 1.13 19.^4 2.37  11.89 11.45 2.13 1.30 4.23 4.72 8.97 6.52 8.09 7.22 1.69 1.41 20.96 21.07 2.77 2.34  2.35 2.00 4.77 3.71 7.67 1.64 23.86 2.86  1950  1949  1948  1947  1946  26.05 23.74 2.79 1.93 6.62 5.00 6.23 6.32 0.98 0.75 0.80 0.80 1.29 1.90 19.59 16.01  19.85 2.44 3.23 7.85 0.69 0.82 2.06 21.15  12.59 2.18  3.62 1.52  3.01  6.01 4.53 0.80 0.43 1.08 1.05 1.70 1.43 21.33 19.98  4.29  3.51  6.25  15.65  5.04 5.20 2.71 2.45 8.77 7.89 1.21 0.90 21.11 16.86 2.72 2.81  5A1  5T48  5^06  4.47 9.68 1.07 15.96 3.14  4.86 5.39 8.44 4.54 1.10 0.86 16.46 12.53 3.11 2.41  APPENDIX V OPERATING PROFITS ( i n m i l l i o n s of d o l l a r s )  1955  195^  1953  1952  1951  0.13 1. Auto S o l e r Company -0.11 2 B a l s a Chica O i l Corp. 0.03 3 Baush Machine Tool Co. 4 B e l l Company -1.29 5 Bishop &"Babcock Mfg.Co,. 0.46 6 Brown McLaren Mfg. Co. -0.11 0.23 7 Carpenter (L.E.) & Co. 8 Chief Consolidated Mining Co. -0.16 C 9 l e v e l a n d Sandusky Brewing Corp. 0.04 10 C o n s o l i d a t e d R e t a i l Stores, Inc. -1.72 11 Cooper T i r e and Rubber Co. 0.93 12 C u r t i s L i g h t i n g -0.13 Davega Stores Corp. -0.38 14 Diamond Motor Car Company 0.22 15 Dixon (Joseph) Crumble Co. 0.87 -0.02 16 E & B Brewing Co.Inc. 17 F l a g g U t i c a C o r p o r a t i o n 0.54 18 F l o t i l l P r o d u c t s , I n c . 1.36 19 F l o u r M i l l s o f America,Inc. -0.79 -0.41 20 Gerotor May Corp. 21 Glove America Corp. -0.17 22 Gum P r o d u c t s I n c . 0.13 23 Hathaway B r e w e r i e s , I n c . -0.42  0.21  0.44  0.37  0.31  Name o f Company-  -0.07 0.44 -1.60 -0.08 -0.07 0.13  1950  1949  -0.01  0.01  -0.24  0.15  -0.27  0.02  0.23  -o.o4  0.09  0.10  0.12  0.11  0.01  -0.22  0.45  0.60  0.89  1.05  1.31  0.19  -0.02  1.02 -0.02 0.17  , 0.89 0.15  1.06 0.16 1.37  1.11 -0.28 0.16 0.08 1.01 1.18  -0.49  1.86  2.32  1.84  0.50  0.60  0.34 0.28  0.06 0.50 -1.15 -0.31  -0.26  0.21 -0.17  0.73  0.13 0.04  -0.57 -3.09 -0.38 0.21 0.59 -0.41 0.12  -0.32  0.10  -0.10  0.29 0.52 0.62 0.12 -0.45 O.38 0.92  19V7  1946  0.08 o.o4 0.11 0.25 0.23 -0.19 -0.03 -0.04 0.01 0.09 0.26 0.08 0.14 -0.05 .0.32 — — 2.22 1.31 -^0.09 0.15 0.45 1.10 -0.02 -0.10 -0.02 0.01 0.01 0.01 Q...03 -0.19 -0.23 -0.06 0.23  0.02  0.78 1.12 0.65 0.37 -0.84 0.78 0.53 0.25 -0.06 0.39 O.32 0.29 0.15 0.08 0.31  1948  0.05  0.10  0.36  0.21  2.31  2.16  2.58  -0.23 0.29 1.74  0.32  1.10  1.79  3.05  1.23  0.55 0.40 -0.04 0.13 0.20 -0.33 -0.23 -0.30  0.07  0.20  0.57  -  1.67  2.12  0.19  -  0.23 -0.10  -  -0.45 -1.26  0.24  2.09  -  —  0.28  -  0.52 —  —  0.85 1.22 2.00 3.82 4.26 -0.80 0.10 -0.09 -0.38 -0.08 -0.12 o.4o 0.86 0.96 0.39 0.80 -0.14 -0.62 — — 0.30 •-0.33 -0.49 - o . 4 l 0.96 1.38 1.14 1.50 0.87 1.39  Name o f Company  1955  24 H i l l e r H e l i c o p t e r s -0:03 25 Jacob Rupert 0.10 26Jeannette Glass Company 0.38 27 Jessop S t e e l Co. 1.73 28 Lanston I n d u s t r i e s , I n c . -0.16 29 Longchamps I n c . -0.24 30 M a c M i l l a n Petroleum Corp. 0.16 31 Maguire I n d u s t r i e s , I n c . o.o4 32 Mandel B r o t h e r s , I n c . -0.60 33 Merrimac Hat Corp. -0.09 34 Michigan B a k e r i e s , I n c . 0.24 35 Mohawk L i q u e r Corp. 0.20 36 Morgan s I n c . 0.12 37 N a t i o n a l Research Corp. -6.5O 38 Nelson (N.O.) Company 0.16 39 New England Box Company 0.21 0.48 40 Oceanic O i l Company 41 0 ' S u l l i v a n Rubber Corp. 0.05 0.24 42 Peck Stow & Wilcox Co. 4 3 P l a s t i c Wire & Cable Corp. 0.75 44 Plume & Atwood Mfg. Co. -0.28 45 P o w d r e l l & Alexander I n c . 0.30 46 Queen Anne Candy Comoany 0.12 47 Reis (Robert) & Co. 0.10 48 Reymer & B r o t h e r s , I n c . 0.00 49 Richmond Cedar Works -0.01 50 Rochester & P i t t s b u r g Coal Co. 0.39 51 Rock O l a Mfg. Corp. 0.37 52 Ronson C o r p o r a t i o n 2.60 53 Rudy Mfg. Company -0.10 54 Sandura Company 0.17 1  1954  1953  1952  1951  0.67 0.92 1.06 0.32 0.44 0.19 1.52 -0.45 0.38 0.16 0.35 0.06 -0.05 . 0.10 -0.02 -1.21 -1.30 0.17 0.13  0.55 -0.25 0.06 2.67  -0.04  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  0.18 0.31 O.49  •0.06 0.37 0.60  0.42 1.28 0.35 0.29 0.47 0.58  0.65 -0.66 0.26 -0.02 0.01 -0.36  0.01 •1.03 0.28 -0.23 0.15 .0.09  0.80 0.15 0.20 -0.12 -0.01 0.26  1.41  1.36 •0.34 •1.75 •0.05 •0.13  2.54 •0.59 6.14  -0.11  0.06 0.18 -0.07 0.09  -0.21 -0.01  0.77  0.34 -0.19 0.61  0.Q6  -1.05 0.15 0.03 0.18 0.29 -0.63 0.27  -0.55  0.23 -0.33  -o.o4  0.28 0.01 0.00  0.11  1.00  -0.53  1.51 0.19  -0.37  0.14  1.46  0.73  0.21  0.79  0.24 0.51 0.20 0.05 0.09  -0.46  O.83  •0.02  •0.48  1950  1949  1948  -2.23 -0.09 -0.85 1.18  0.00 -0.02 -0.62 1.28 0.23 0.65 -0.81 0.86 0.01 0.27  1947  1946  0.88  -0.70 0.55  2.83 1.35 -0.31 0.63  0.57  0.55  1.71 0.34  1.31 1.53  -0.36 -0.20  0.71 0.26 -0.06  0.92  0.65  0.26  o.4o  2* ~  -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  O.36  -0.12 -0.79 0.58 0.17 0.21 o.o4 -0.17 -0.07  1.69 0.62 0.34 -0.01 0T48  0.28 0.13 0.28 0.95 0.30 -0.08  rO.03  0.14  0.2^ 0.02 1.73 0.53  0.14 0.46  0.42 —  -  -  0.40  -  _  - —  -0.05 -0.83 -0.77 -0.29 0.13 -0.19 0.01  -0.03 0.11 2.69 -0.07 -0.30 0.11  -0.24 0.27 3.90 -0.18 0.67 0.17  5.70 0,37 1.53 0.27  0.31 6.45 8.39 •0.03 -0.06 0.51 -0.08  0.06 8.97 0.21 0.63  1.53 5.59 0.18  0.27 3.38 -0.13  -0.01  0.06 2.55  •0.12  0.14  —  —  —  -  0.16  —  —  -  Name o f Company 55 5o 57 58 59 60 61 62 63 64 65 6o 67  1955  S c r a n t o n Lace Company 0.05 Seneca F a l l s Machine C o . - 0 . 2 9 Shasta Water Company 0.01 Sherman P r o d u c t s , I n c . 0.42 Sidney Blumenthal & Co• l n c . -1.56 Standard Commercial Tobacco Co. 0.47 S t y l o n Corp. 1.27 1 2 t h S t r e e t Store -0.09 U n e x c e l l e d Chemical C o r p - 0 . 2 3 V i c t o r P r o d u c t s Corp. -0.23 Wayne Screw Products Co. 0 . 0 4 Wilson Brothers 0.25 Yolands C o r p o r a t i o n -0.04  1954  1953  1952  1951  1950  •0.16 0.55 0.08 0.25  0.19 0.94 0.00 0.51  0.06 0.86 •0.01 0.42  0.07 0.61 •0.03 0.42  0.37 0.12 0.04 0.26  0.52 0.00 0.09 -0.15  1.23 -0.06 0.10 0.45  1.09 -0.03 0.04 0.42  0.73 -0.30 0.08 -0.28  -1.29  0.27  2.69  2.26  -0.22  0.70  0.61  2.28  0.00 0.15 0.05 •0.11 0.82 0.32 0.23  0.14  0.20  -0.25  0.41  0.48  0.04 0.01 0.82 0.11 0.77 0.01  0.07 -0.07 0.25 0.09 -0.13 0.04  0.24 -0.62 1.13 0.14 0.46 0.33  0.26 -0.03 I.63 0.20 0.50 0.43  0.31 0.77 1.16 0.17 0.75 0.44  0.30 0.42 •0.13 0.07 •O.38 -0.02 0.07 •0.08  0.95 0.03 •0.11 •0.52 0.31 0.13 0.20 0.01  0.66 1.01 •0.05 -0.15 -0.17 0.60 0.27  o.o4  -0.08  •o.o4  1949  1948  1947  1946  - 126 -  APPENDIX VI As was mentioned i n chapter IV, f o r t r a n programming was used to a s s i s t i n a r r i v i n g a t the v a l u e s o f the c o n s t a n t s , a and b i n the e q u a t i o n o f the s t r a i g h t l i n e t r e n d , y = a + bx.  The data were submitted t o the UBC  computing c e n t r e i n the manner shown i n the F o r t r a n Form i n the next page.  Coding  The output of data i s as g i v e n i n  Tables IV and V i n chapter IV.  UBC  Computing Centre  Programmer c STATEMENT 0 N NO. T  c  1  2 3 4  5  6  FORTRAN  FORTRAN STATEMENT 7 8  9  FORM  Date__  Page  of IDENTIFICATION  >>  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  •  5 6  1  •  4  0  •  1  1  •  1  •  •?  0  •  2 1  1 9 5 5 1 9 2  2  •  7 6 6 8  2  •  2 4  0  •  44  2  •  1  •  96  0  «  7  1 9 5 1 1 9 5 0 1 9 49  2  •  2  2  •  0 1  0  •  1  1  •  1 7  1  •  0 9  0  •  0 8  0 • 8 0  0  • 8  4  0  •  1 9 48 1 9 47 1 9 46  1  •  0 8  0  •  9 7  0  •  04 1 l  1  •  0 • 8 9  0  •  2  1  •  1 4 0 7  0  0  •  2  1 9 5 5 1 9 5 4  CODING  *  8  4  E N D  S  A  A U T  L  0  C 0 S T  •  S  0L E R  P R 0 P I T rt  0  •  \  —  — I  

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