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UBC Theses and Dissertations

Accounting : from an information systems perspective 1970

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ACCOUNTING: FROM AN INFORMATION SYSTEMS PERSPECTIVE by VLADIMIR ANATOLE MATVEIEF B.Sc, (Loyola College) University of Montreal 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION IN THE FACULTY OF GRADUATE STUDIES OF THE UNIVERSITY OF BRITISH COLUMBIA, 1970 We accept this thesis as conforming to the required standard Vancouver, Canada In p re sen t i ng t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree tha permiss ion f o r e x ten s i ve copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t t e n pe rm i s s i on . Department of Commerce and Business Administration The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date April 2 3 , 1 9 7 0 ABSTRACT The author extended the synthesis of the s o - c a l l e d accounting spread sheet i n t o a more compact and mathema- t i c a l l y rigorous formulation. This formulation was applied to an example i n the form of a computerized accounting information system. 1 The systematic approach used bridges the communication gap betv/een the accounting profession and the q u a n t i t a t i v e ! oriented computer s p e c i a l i s t s who design computer based accounting systems. The use of tensor a n a l y s i s and coordinate transforma- t i o n s i n accounting theory was also explored. The author be l i e v e s t h i s to be an important area for further research. TABLE OF CONTENTS CHAPTER Page I INTRODUCTION (JUSTIFICATION OF STUDY) . . . . 1 A. Study in perspective . 2 B. Purpose of thesis . . . . . ' . . . . 2 C. Nature of the problem . . . . . . . . *f D. Chapter organization. . k E. Definition of terms 5 II AN OVERVIEW OF THE' FIRM ... . . . . . . 7 A. Behavioral aspects . . 7 B. Structural characteristics . . . . . . 8 C. Problems of coordination 1 0 III ORGANIZATIONAL DEVELOPMENT . . . . . . .13 A. Short and long run considerations . . . . . . . •' . . 1 3 B. The worth of information . Ik- C. Financial information i n perspective. 1 5 D. Conceptual framework for information systems design . 1 6 E. Information systems design . . . . . , 1 7 F. The characteristics of information . . . 2 0 IV ACCOUNTING INFORMATION CHARACTERISTICS . . . 2 2 A. Overview. . • . . 2 2 B. Accounting a c t i v i t i e s 2 3 C. Use of accounting information . . . . . 2 5 CHAPTER Page V THE ACCOUNTING SPREAD SHEET . 2 7 A. Matrix representation 2 7 B. Matrix accounting . . . . . . . . . 2 9 VI EXTENDING THE ACCOUNTING SPREAD SHEET . . . 3 1 A. Role of the extended accounting matrix in the development of accounting information systems . . . . . 31 B. Descriptive analysis of matrix accounting applied to the spread sheet . . 3 2 C. Theoretical analysis of the extended matrix accounting approach . . . 3 5 D. An example . 3 8 VII STATE OF THE ART. ... . . . . . . . . 5 2 A. Simple transactions . . . . . . . . 5 3 B. Arithmetic n-space and transformation of coordinates 5 5 C. Contravariant and covariant tensors . . 5 7 D. Use of coordinate transformations in accounting . . . . . 5 9 VIII CONCLUSIONS . 6 1 A. Summary . . . . 6 1 B. Direction for further research . . . . . 6 2 BIBLIOGRAPHY. . . . . . . . . 6k Appendix one - A computer program for the accounting system example 67 Vita LIST OF FIGURES FIGURE Page 1 The pyramidal structure of an organization 9 2 Managerial authorities developing intelligence functions 16 3 Conceptual approach to systems design . . . . 18 ACKNOWLEDGEMENTS The author wishes to acknowledge the c o n s t r u c t i v e advice and c r i t i c i s m , and the v a l u a b l e support r e c e i v e d from h i s academic teachers: P r o f e s s o r R i c h a r d V. M a t t e s s i c h , P r o f e s s o r C.L. M i t c h e l l , P r o f e s s o r Vance F. M i t c h e l l and P r o f e s s o r Hart- mut J . W i l l . Furthermore, the author thanks h i s w i f e L a r i s s a f o r her a s s i s t a n c e i n w r i t i n g and implementing the computer example developed i n t h i s t h e s i s . I. INTRODUCTION (JUSTIFICATION OF STUDY) This thesis develops specialized insights into computer- ized accounting information systems. The author i s guided by a conceptual framework (Will, 1968) outlining information systems characteristics,of. accoun- ting. Research i n accounting (Mattessich, 1957; 196*t; I j i r i , 1965, 1967; ... ) i s viewed i n the confines of organizational theory (March and Simon, 1958; Cyert and March, 1963; ... ) and some of the accumulated knowledge i s applied. An attempt i s also made to u t i l i z e some of the interdis- ciplinary research within the fields of systems theory, orga- nizational development and information, technology (Ackoff, I960; Blumenthal, 1969; Emery, 1969; Forrester, 1961; Von Neumann, 1955; ... ). Accounting has h i s t o r i c a l l y used information technology of the times to provide the organization with an important component of what i s currently referred to as Management Information Systems. Accounting thought and practice i s essentially steeped in management and systems sciences. "It i s hoped that a better understanding of the informa- tion systems characteristics of accounting w i l l be helpful in developing better information systems 11. (Will, 1968) 2 A. Study i n perspective; Accounting information systems are considered to be e s s e n t i a l e n t i t i e s i n the o v e r a l l framework of manageri- a l l y u s e f u l information systems. From the p r a c t i c a l viewpoint, the author extended the synthesis of the s o - c a l l e d accounting spread sheet (Mat.te- s s i c h , 1957; Kohler, 1963; I j i r i , 1965) i n t o a more com- pact and mathematically rigorous formulation, and applied i t to an example i n the form of a computerized accounting sys- tem. From t h e t h e o r e t i c a l v i e w p o i n t , t h e a u t h o r b e l i e v e s that accounting systems may be i n t e r r e l a t e d through the use of tensors a n d transformation of coordinates. However these thoughts have to b e further researched and applied to an example. B. Purpose of t h e s i s : The contemporary problems of an operational accounting information system can be attacked through the p r a c t i c a l app- l i c a t i o n of i n t e r d i s c i p l i n a r y research. The t h e s i s w i l l i . provide a perspective on the relevance of accoun- 3 ting information to organizations; i i . develop a systematic analysis of financial accounting information from the computer spe- c i a l i s t s viewpoint; i i i . use the extended matrix representation of the accounting spread sheet in generating the f i - nancial statements. A systematic approach i s used to bridge the communica- tion gap between the accounting profession and the quantita- tively oriented computer specialists who develop computer based information systems. The extended accounting spread sheet provides both the accountant and systems analyst with common ground from which to work. . A mathematical expression of accounting gives the sys- tems analyst perspective on the problem, and allows him to l o g i c a l l y apply, information technology and computer science to the computerization of accounting systems. The mathematical expressions and the use of algorithmic techniques may reduce the misunderstandings that arise i n the attempts to computer- ize accounting systems. The accountant , on the other hand, may gain insight into modern information generating technology. The use. of analystical tools and information technology as well as the realization that the systematic procedures of accounting have dimensions not necessarily tied to traditional methods of recording a c t i v i t i e s , w i l l result in the develop- ment of new approaches to accounting information systems. C. Nature of the problem: Both the theoretical and practical facets of the problem have to be considered. Theoretical considerations deal with the i . implications of accounting information systems on organizational development; i i . viewing accounting information systems i n the broader f i e l d of management information systems; The practical considerations depend on the a b i l i t y to develop pragmatic and workable information systems for use .by organizations. D. Chapter organization: Chapters two through four point out that information has important characteristics, and that i t i s a resource u t i l i z e d by a l l organizations. Chapters five and six highlight the specialized insights attained by applying mathematical techniques to the matrix representation of the accounting spread sheet. Chapter six, in particular, applies the findings to a simple accounting sys- 5 tern using periodic inventory valuation. Chapter seven explores the use of tensor analysis and coordinate transformations in accounting theory; the author believes that this i s an important area for further study. Appendix one l i s t s the e x p l i c i t l y programmed version of the accounting system example; i t i s programmed i n the PL/1 computer language, and i s easily extendable to any number of accounts within a given chart of accounts. E. Definition of terms: Accounting spread sheet; a worksheet providing a two-way ana- l y s i s or cla s s i f i c a t i o n and storage of costs or other accoun- ting data. Algorithm; a step-by-step procedure that always yields a so- lution to a problem i n a f i n i t e number of steps. Coordinate; a set of numbers used to specify the location of a point i n space. Endogenous; system dependent (variable). Exogenous: system independent (variable). Pragmatic: concerned with the practical consequences of actions or beliefs. Principal: object or phenomenon measured. Semantic: concerned with the study of meaning i n language. 6 Surrogate: a substitute. Syntactic: concerned with the way i n which elements are com- bined to form classes, sets and numbers. Tensor: a generalization of a vector; may be the result of vector multiplication. Tensor analysis: deals with the study of vector multiplication, and with the manner in which vector products transform from one system of coordinates to another. 7 II. AN OVERVIEW OF THE FIRM The information systems architect must be aware of the complexities of information systems design. The information system designed w i l l have to take into account the limitations of an organization. These limitations are usually associated with the behavioral aspects of the firm, with the structural characteristics of the firm, and with the problems of coordi- nation. A. Behavioral aspects: The behavioral theory of the firm has been formulated by Cyert and March (1963). Their concepts are very useful i n dea- l i n g with the limitations of information systems within the confines of the organization and subject to i t s relational pec u l i a r i t i e s . Their focal points of uncertainty avoidance, problemis- t i c search, quasi-resolution of conflict, and organizational goals and learning are b r i e f l y outlined, i . Uncertainty avoidance; the dominant coalition negotiates i t s environment by attempting to transform uncertainty and r i s k into certainty equivalents. i i . Problemistic search: the solution i s biased by the urgency with which i t i s needed; i t i s moti- vated by the problem, and may tend to be simple- minded. i i i . Quasi-resolution of conflict; the group or coali- tion of individuals controlling the organization 8 are i n dynamic balance with each other, and the decision rules incorporated into the firm do not provide optimal decisions, but result i n v/hat i s acceptable or feasible. iv. Organizational goals and learning: the reconci- l i a t i o n of the organization to i t s performance w i l l be based on the expectations of the coalitions and their choice of decisions. The response to the dysfunctions and opportunities facing the dominant coalition to some extent leaves the organization dependent on the environment, the coalitions, and their aspi- ration levels. Bounded rationality, resulting from the quasi- resolution of conflict and the environmental uncertainties, tends to emphasize sequential attention to goals. In short, in a situation of bounded rationality, the expectations of a firm and i t s choice of alternative actions w i l l be highly influen- ced by the a v a i l a b i l i t y of information, and will depend on i t s format. B. Structural characteristics: Considerable amount of literature exists on the subject of organizational structure; and only one of the many constructs is presented. The behavioral aspects of the firm can be complemented by a rational, albeit idealized, viev; of i t s structural components 9 depicting the organization as a pyramidal structure with sides representing the various functions (financial, production, mar- keting, ... ) and layered into a policy-oriented apex, an ad- ministrative midsection, and a transactional/operational base (intimately related to the l o g i s t i c s of the.organization). The figure summarizes the main features of the construct, FINANCIAL PRODUCTION MARKETING FIGURE. 1. The pyramidal structure of an organization In very broad terms, one may say that the adaptive and behavioral aspects dominate the upper half of the pyramidal structure, due to required adaptation to unforeseen circum- stances which result i n transitional behavior. The lower half or' 1 technological core' i s more predictable, due to the higher incidence of repetitive behavior and the shorter time spans of control involved. At this level the potential importance of computational information and algorithmic procedures can be 10 emphasized. .... Emery (1969), in considering the hierarchical nature of organizations, the need for interaction among organizational subunits, and the coordination decisions facing the managers and administrators, suggests that the degree of coordination w i l l depend on the costs of improved information technology. Here information technology i s seen affecting organizational structure, and i s considered to be.the interconnecting tissue between organizational subunits. C. Problems of coordination; Emery (1969), using the Simon-Ando model of nearly de- composable systems, applied i t to the organizational hierar- chy. Briefly, interactions between organizational subunits are coordinated through the transmission of information,.and i s the result of planning and/or goal setting. The organiza- tion i s seen factoring i t s global objectives into a hierarchy of subobjectives. He also brings i n the notion of the impli- c i t tradeoff between local and global objectives, and intro- duces the time dimension as the measure of the sub-unit's independence. 11 ... Because of the limited information-handling a b i l i t y 11 of both humans and information processing equipment, the organization must be constituted as a nearly de- composable system. This i s achieved by combining close- l y r e l a t e d a c t i v i t i e s and decoupling them from h i e r a r - c h i c a l l y more distant a c t i v i t i e s . The macro-character- i s t i c s of the organization are governed by r e l a t i v e l y aggregate plans issued by higher l e v e l managers. Within the constraints imposed by t h i s information,.a lower l e v e l manager then pursues h i s (changing) goals more or l e s s independently. - This scheme has the e s s e n t i a l advantage of econo- i mizing on coordination. Higher l e v e l managers adjust lower l e v e l constraints without having to know t h e i r d e t a i l e d i m p l i c a t i o n s . Lower l e v e l managers are r e l a - t i v e l y i s o l a t e d from the r e s t of the organization, and .can carry on t h e i r a c t i v i t i e s without constant atten- t i o n to most of the d e t a i l e d a c t i v i t i e s of other parts of the organization."(Emery, 1969; pp.32-33) The a c t i v i t i e s of the organization provide the managerial l e v e l s with the events to be captured and retained i n the aform of information for p o s s i b l e future use. The need for consis- tent accumulation of managerially u s e f u l information can be s a t i s f i e d by the use of o p e r a t i o n a l l y oriented information systems. The need for coordination of disparate l o c a l a c t i v i - t i e s i s an important factor favoring management information systems designed to f u l f i l l s p e c i f i c o b jectives. H i s t o r i c a l l y , information systems created and used by 12 organizations revolve around v/ell established accounting prac- t i c e s and procedures, which do not require the investment of large monetary funds for t h e i r maintenance. However, the r a p i d i n t r o d u c t i o n of computers i n t o a l l sectors of North American a c t i v i t y , has increased the use of information technology and organized i n t e l l i g e n c e to a l e v e l where one cannot view them as free commodities. The use of information and organized i n t e l l i g e n c e has.' to be considered as... a legitimate factor of production i n v o l v i n g costs of c o l l e c t i o n and dissemination. In summary, information i s found to be an important i n - gredient used by a l l organizations and i t influences t h e i r behavior. Information can be generated and disseminated through the use of information systems, and these to some extent r e - f l e c t the structure of the organization. III. ORGAN!ZATIONAL DEVELOPMENT The approach to organizational development usually i n - volves environmental research, positional audits, i d e n t i f i - cation of :challenges, forecasts on premises previously estab- lished, and proposal of goals or objectives. The descriptive diagnosis based on the current states of the organization i s then used to develop a prescriptive analysis of required or- ganizational climates, ways of work, interpersonal relation- ships, communication, and information systems. Organizational development may require an overall-system, planned-change effort i n order to cope with the alterations needed by the organization. A. Short and long run considerations; The long term aspirations of the organization are assumed to be really those of the dominant coalition members. The mem- bers are expected to give the organization i t s global objec- tives and i t s stated rationality. The verbalized objectives, useful i n guiding the organization's specific a c t i v i t i e s and growth may be called intelligence functions. The objectives and rationality of a firm change with time, and a distinction between short and long run behavior should Ik be made. The short run considerations constrains the i n t e l l i - gence functions, and direct thera to the fulfillment of local objectives through purposeful activity. The long run consider- ations alter the firm's behavior, by requiring i t to conform to the modifying forces of the. environment and to the out- comes of organizational assessment. In practice, the global objectives are revised through periodically issued directives and guidelines. These alter the pseudo-bureacratic conditions within the organization, i t s a c t i v i t i e s and the control and allocation of i t s resources B• The worth1 of information: In the previous chapter, the worth of information was emphasized from several viewpoints. The generation of infor- mation and i t s a v a i l a b i l i t y were found to be influenced by the behavioral aspects of the firm, to the firm's structural cha- r a c t e r i s t i c s , and to the problems of coordination between or- ganizational subunits. It was pointed out that i . information i s the interconnecting tissue bet- ween organizational subunits; i i . information flows are major determinants of orga- nizational structure, and vice versa; i i i . information generation involves costs of collec- tion and dissemination; 15 i v . information can be generated and disseminated through the use of information systems; v. the degree of coordination within a firm i s de- pendent on the costs of improved information technology; v i . a v a i l a b i l i t y of information influences the expec- tations of the firm, and i t s choice of alterna- tives. Under the circumstances, i t i s f e l t that the development of information systems should conform to the overall objec- tives of organizational development. ^ C. Financial information in perspective; Organizational development, among other considerations, concentrates primarily on improving the current state of the organization. In most organizations, wealth determination i s an essential ac t i v i t y . It provides the organization with i n - formation that i s useful i n assessing the financial health of the organization. Financial information, obtained through wealth determi- nation, supplies the firm with indicators measuring both the current state of the organization, and i t s a b i l i t y to survive. The knowledge of financial p r o f i t i b i l i t y and l i q u i d i t y i s the operational goal of wealth and income determination. 16 T h i s knowledge has f o r c e n t u r i e s been pro v i d e d by the double e n t r y , bookkeeping accounting i n f o r m a t i o n sys- tem. I n t h i s p e r s p e c t i v e , f i n a n c i a l i n f o r m a t i o n and o r g a n i - z a t i o n a l development are i n t i m a t e l y r e l a t e d . D. Conceptual framework f o r i n f o r m a t i o n system design; W i l l (1969) developed premises, pragmatic i n nature, which c o n s i d e r i n f o r m a t i o n systems as means of extending managerial c a p a b i l i t i e s . The f o l l o w i n g f i g u r e g r a p h i c a l l y conveys the concept of managerial a u t h o r i t i e s d e f i n i n g and a p p l y i n g i n t e l l i g e n c e func- t i o n s (or processes) w i t h i n the co n f i n e s of o r g a n i z a t i o n a l r a t i o n a l i t y . S c i e n c e & phi l o s o p h y o f v a l u e s \ a n t i c i p a t i o n p{>of p u r p o s e f u l a c t i v i t y r e s o u r c e s -{>in formation knowledge MANAGERIAL AUTHORITY L o c a l goals are de f i n e d , o p e r a t i o n a l g o a l s are set I DEVELOPMENT OF THE (INTELLIGENCE FUNCTIONS; OR PROCESSES O p e r a t i o n a l goals are planned and c o n t r o l l e d through methodologies and r a t i o n a l e s o f pur- p o s e f u l a c t i v i t i e s FIGURE 2.Managerial a u t h o r i t i e s developing i n t e l l i g e n c e f u n c t i o n s . 1? In such an approach, one assumes that rationality i s im- posed upon the function or process. This i s i n line with the concept of rationality as being imposed upon the 'world' by the enquirer himself. Such an approach need not seek 'optima- l i t y ' according to some given law, and can instead allow that the rationality be imposed by the managerial authorities in accordance with their inclinations. The managerial authorities are able to obtain goal re- lated knowledge and information by using information handling and system design technology. Figure 3 shows a conceptual approach useful in information systems design. Both figures 2 and 3 r e f l e c t the conceptual framework developed by Will (1969); however, they are this author's interpretations of his work, E. Information systems design: The multifaceted pyramidal structure of an organization suggests that information systems design requires an integrated approach to interfacing the various facets of subunits and the levels of the pyramid. However, the complexity of the orga- nization, and the near decomposability of i t s subunits, vitiates the use of communal information through well-defined, interre- 18 MATT ON ARTIFICIAL EQUIPMENT INPUT IS IDENTIFIED MEASURED CLASSIFIED. STORED INTUITION INSIGHT KNOWLEDGE V NATURAL INTELLIGENCE EQUIPMENT DATA BANKS CREATED DATA AND MODELS ->( BANKS MANAGEMENT iGOAL ORIENTED <]-'INFORMATION I IRETBIEVED VIA l _ . iTHE BANK MANA-I ! GEMENT SYSTEM • * 7 I GOAL RELATED i (KNOWLEDGE MAY1 IBE EXTRACTED 1 I AND USED FOR \ •GOAL RELATED , lACTIVITY I rINFORMATION IF' USED BY THE IN- TELLIGENCE FUN- CTIONS J OPERATIONAL GOALS MAY BE ACHIEVED MODEL BANKS DESIGNED OPERATIONAL [INFORMATION I CAN BE CON- 'DENSED, PRO- | CESSED AND •COMMUNICATED leading to GLOBAL GOAL ACHIEVEMENT FIGURE 3« Conceptual approach to systems design 19 lating data bank f i l e s . It i s f e l t that data banks must be created with the intelligence function in mind and must be oriented toward some objective. Information systems have situational and relative cha- ra c t e r i s t i c s , and the idea of measurement i s imbedded in them. They (information systems) provide precise causal relations, and serve purposeful needs. The output of information sys- tems i s reproducible,, repetitive and structured; but i t s use i s not. Information systems design attempts to f a c i l i t a t e the flow of information to, from and through the organizational hierarchy. In practice, they adapt to the operational a c t i v i - ties of the organization and involve a l l phases of l o g i s t i c control. One may emphasize that the control i s not normally exercised by recurring caricatures of managers (as profit maximizers), but by individuals whose goal formulation incor- porates besides risk and uncertainty, the typical human i n - clinations and ambitions that cannot be assumed away in the •design and development of information systems. Current information technology permits one to create data and model banks for use throughout the organization. The data banks can provide the users with information on financial demographic, simulative, and economic factors, among others. 20 The model bank can transform raw, unaggregated data (as well as information), into operationally useful information, while f i l t e r i n g out the insignificant information. F. The characteristics of information: What i s information? " ... i f the notion.of management i s related to such intelligence tasks as goal formulation (consisting of goal planning and goal setting), and goal (achieve- ment) control, such insights ought to be related to the concept of information. ... If the information system reflects the real system perfectly;, such that goal pursuit and goal attainment can be determined with a high degree of accuracy, r e l i a b i l i t y , and pre- d i c t a b i l i t y , then the information i s considered rele- vant. Relevance i s thus an indicator of the degree of identity between the information system and the underlying real system. ... It i s now possible to c a l l c l a s s i f i e d phenomena or their surrogates (measurements).data and to relate this data definition to the pragmatic definition of information by postulating that the data descriptions (data names) selected for the measurements reflect the goal systems such that goal variables and parameters are identifiable within goal-sub-goal relations. ... To realize that information i s fundamentally a three-dimerisional (pragmatic, semantic, syntactic) con- cept i s simple but to incorporate this insight into an 21 information systems definition means to apply the structural and procedural systems notions to the con- cepts of information. Information i s then considered as the output of data transmutation processes and i s identical to desired knowledge which provides insights into a problem or a particular problem solution ..." (Will, Dec,1969; Management Science, pp.Bl69-7U The pragmatic, semantic and syntactic dimensions of infor- mation are useful i n analysing accounting information systems. 22 IV. ACCOUNTING INFORMATION CHARACTERISTICS The operational goals of wealth and income determination are essentially the knowledge of financial p r o f i t a b i l i t y and l i q u i d i t y . The objectives have for centuries been pa r t i a l l y satisfied through the use of double entry, bookkeeping accoun- ting systems. A. Overview: Accounting systems are pragmatic because the generated information i s used in attaining knowledge of financial pro- f i t a b i l i t y and l i q u i d i t y . The goal orientation of accounting information i s also relevant as an indication of the identity between the surrogate ..and the mapped principal. The goal orientation of an overall accounting system determines to a large measure the processing flow of double entry accounting entries. The accounting systems w i l l provide users with consistent methods for recording valuations. Essen- t i a l l y , the characteristics of accounting systems require that i . surrogate measures of the principals be establ- ished; i i . surrogate structure be defined; i i i . the states of the surrogate measures be main- tained over time; 23 i v , the states of the surrogate measures be alter- able by consistent rules. The problem of identifying the principal, when the accounting valuation i s the surrogate, i s a problem faced by the managerial authorities. They have the option of adopting structure of surrogates, dispensing with them altogether, or altering them. In a l l cases, the managerial authorities make an attempt to conform to their own objectives, and measure the principal accordingly. The structure of the surrogates i s largely dictated by the classifications used i n reflecting the principal. Also, goal orientation affects the measuring, recording and processing methodology used i n an accounting system. In short, the accounting system i s expected to supply relevant informa- tion in accordance with the required organizational rationa- l i t y . B. Accounting a c t i v i t i e s : From an information systems perspective, double entry accounting information has semantic, syntactic and pragmatic dimensions. In fact, from such a perspective, 'double entry' i s no longer relevant, as i t implies that an amount i s re- corded twice. Double entry and double cl a s s i f i c a t i o n are im- 24 p l i c i t in the structure of computerized accounting systems; peculiar c l a s s i f i c a t i o n a l schemes are accepted as distingui- shing features of accounting systems, which set them apart from other computerized, non-accounting systems. In li g h t of operational systems theory, accounting a c t i - v i t i e s have to be viewed from an internal and external a c t i - vity -viewpoint. The characteristic distinctions between the two types of act i v i t y are significant in information system design. External accounting entries are based on events occur ing outside of the boundaries of the system, and must be con- sidered to be the exogenous variables that alter the states of the surrogates. The internal accounting entries, on the other hand, may be generated on an a p r i o r i goal oriented assumption. These assumptions may reflect the expressed one- to-one correspondences between states of the surrogates (accounts) whose levels are altered to reflect accruals and adjustments. The use of exogenous and endogenous variables are extremely useful i n the attempts to reduce accounting i n - formation systems i o algorithms. The problems of human communication faced i n describing the attributes of given measurements lim i t the semantic d i - mensions of accounting information. Also, the economic goal orientation of accounting information w i l l effectively subor- 25 dinate the syntactic dimension of accounting information to the cla s s i f i c a t i o n a l considerations long embedded and i n s t i - tutionalized into various chart of accounts. C. Use of accounting information; Global objectives are necessarily vague, and they have to be reduced to surrogates capable of measure. Measured surro- gates are then used to assess the fulfillment of local objec- tives relating to the overall goals. i I The adaptibility of organizational behavior to changes in response to local goals, i s an indicator of the affective pressures applied. It i s the a b i l i t y to generate behavioral changes originally predicted, v/hich result in the success of stated objectives, that has to be measured. In both cases, accounting information i s used to generate the relevant mea- sures. Here, the indicators of affective pressures and of the predicted behavior are usually financial i n nature. Accounting information provides the base for much of the systematic planning attempted. It ensures that members of an organization are supplied with periodic, factual and search- ing analyses on the behavior of the organization. It offers administrators with alternative allocations of resources, and focuses on key behavioral and/or performance problems affect- 26 ing the well-being of the organization and of i t s dominant coalition. Accounting, measurement has dominated the rationality of most economically oriented organizations, by providing the managerial authorities with reliable financial information with which to assess their performance. The use of accounting information i s a major influencing factor on organizational behavior, and any attempt to c l a r i f y accounting system methodology (in information systems perspec- tive) w i l l add to the study of organizational development. 27 V. THE ACCOUNTING SPREAD SHEET According to Mattessich (1964)> the idea of presenting accounting in matrix form can be traced to Gomberg's "geo- metrical" presentation of bookkeeping methods back i n 1927. The matrix form . i s also known to American business account- ing under the name of "spread sheet" (Kohler, 1963). Kohler's spread sheet i s " a worksheet providing a two- way analysis or recapitulation of costs or other accounting data" and i t achieves dual c l a s s i f i c a t i o n with a single entry (Mattessich, 196^; p.90). A. Matrix representation: Mattessich (1937; 196^, pp. 75-77) interpreted every transaction as a separate matrix, i n order to " reveal the structural relations of accountancy in terms of a general: and universally accepted language (of mathematics)". As a result, accounting matrices have become more fre- quently referenced; and I j i r i (I960; 1963, pp. 82-137) has extended the usefulness of this representation by developing mathematical expressions for i t , and by tying i t i n with l i - near and goal programming (Charnes, Cooper and I j i r i , 1963). The matrix formulation of the accounting spread sheet i s 28 used to relate the " ... fundamental relation (of asset and equity partitioning) ..." ( I j i r i , 1963, p.90) to a square matrix W identified with the so-called spread sheet of double- entry accounting. The square matrix W, s x s, with elements ŵ.. represent- ing the total amount of simple transactions whose debit entries are a l l made to the i t h account and whose credit entries are a l l made to the jth account, i s related to the changes i n the asset and equity accounts AU, by the following mathematical expression ( I j i r i , I963), ( W - W* ) x e » A U ( 1 ) where, V/* i s the transpose matrix of V/; e i s a column vector, s x 1, whose ele- ments are a l l equal to 1; u i s the resultant vector, s x 1, con- taining a l l numerical changes to the beginning balance vector u. Some of the shortcomings of such an exposition l i e s i n the convenient but unnecessary restriction of the chart of accounts to the Asset and Equity portion of an accounting system's chart of accounts. The beginning balances are stored separately from the 29 matrix W, and the current balances are calculated by adding two different vectors u and Au to obtain u, the f i n a l balance vector, u - A u » u (2) Other methods employed by Kemeny, et al.(1962) use additional rows and columns of the matrix for the beginning and ending balances. In either case, the computerization of the accounting matrix presents a minor i r r i t a n t , due to the separation of the beginning balances from the transaction entries. The author has formulated a set of mathematical express- ions that allow the beginning balances to be incorporated into the accounting matrix through the use of i t s diagonal elements. This approach does not detract from the mathematical exposition of I j i r i (1963), and in fact enhances i t . B. Matrix accounting: The author.shows that there i s considerable potential i n the matrix representation for the development of computerized accounting information systems, i . the matrix representation contains the chart of accounts used; 3 0 i i . the methodology of matrix representation le t s one create or define transformation mechanisms for the formulation of one matrix accounting system i n terms of another. In non-technical words, more than one spread sheet matrix can be used, their interdepencies can be mathematically for- mulated, and subsequently computerized. 31 VI. EXTENDING THE ACCOUNTING SPREAD SHEET The role of the extended accounting matrix i n the deve- lopment of accounting information systems w i l l be briefly discussed i n the f i r s t section. In the second section the specialized insights of the author, obtained by applying mathematical techniques to the matrix representation of the accounting spread sheet, w i l l be descriptively explained. The theoretical formulation i s then given in the third section. A. Role of the extended accounting matrix in the development of accounting information systems: The extended accounting matrix lends i t s e l f to computer programming and to the definition of computer based f i l e s . In this respect, i t has widespread applicability i n the deve- lopment of accounting information systems. Also, the matrix representation of an accounting system has data and model bank characteristics, i . as a data bank, the elements of a matrix can be viewed as storage devices, retaining information on the accounts of the system; i i . as a model bank, the application of mathematical techniques can be viewed as dependent on the ex- p l i c i t structural characteristics of the matrix. 32 B. D e s c r i p t i v e a n a l y s i s of matrix accounting a p p l i e d to the spread sheet: Accounting accounts may be diagrarnmatically represented by a number of a r r a y s and extended i n t o m a t r i c e s . The m a t r i c e s c o n t a i n the aggregate i n f o r m a t i o n about the s t a t u s of the accounts of the system. i . Beginning balances; the chart of accounts can be shown to be an a r r a y w i t h as many rows or columns as there are accounts. The rows d e f i n e the d e b i t s i d e s and the columns def i n e the c r e d i t s i d e s of the r e s p e c t i v e accounts ( i n accordance w i t h the I j i r i n o t a t i o n ) . Since d e b i t i n g and c r e d i t i n g of an account by the same t r a n s a c t i o n i s not p r a c - t i s e d , the diagonal, of the r e s u l t i n g matrix can be reserved f o r the beginning balances of the accounts ( t h i s i s a breakthrough i n the m a t r i x r e p r e s e n t a t i o n of the spread s h e e t ) . The beginning matrix T Q i s as f o l l o w s , C r e d i t s D B e N. 0 N. I b = T o ( 3) i t 0 C s E S 3 3 i i . P o s t i n g s : the exogenous t r a n s a c t i o n s , or post- i n g s , are the components w. . developed by I j i r i ( 1 9 6 3 ) > and c o n s i s t of l i n e a r aggregation of one or more s i m i l a r simple t r a n s a c t i o n s to given non- diagonal elements, 0 0 w. . i j w. . 10 0 w ( k) i i i . A c c r u a l s and p o r t f o l i o changes: the exogenous t r a n s a c t i o n s w „ m i r r o r events o c u r r i n g i n the " r e a l " world. They have been supplemented by endogenous v a r i a b l e s to r e f l e c t the events im- posed upon the system by the r a t i o n a l i t y and methodology of the s p e c i f i c scheme. These are represented by the a. ,'s f i r s t developed i n t h i s t h e s i s ; these are s i m i l a r to the w. .'s, except t h a t they are generated through i n t e r n a l compu- t a t i o n , and a c c o r d i n g to p r e s e t r u l e s , a. . i j a. . i0 0 = A (5) 3k iv. The time dimension: time i s implicit i n a l l three matrices, a. at time p , the opening balance i s T Q b. at some subsequent time p, , a l l w. . have been posted for the time period p^ - p Q; c. at time p^, the accruals and portfolio changes are made. v. The composite T-matrix; by, superimposing (through matrix addition) the contents of the three matrices' T V/ and A the author arrives at a single matrix o, ,. called the T-matrix. This matrix consists of the accounts of the system and reflects changes to them (both endogenous and exogenous). In other words, the set of a l l mapped principals for a g i - ven accounting system can be contained i n the T- matrix, where, . - T =' T * W + A ( 6 ) v i . Matrix extraction; subsets of the mapped principals can be extracted' from the T-matrix. They are then used to arrive at the traditional financial state- ments. It i s important to view the T-matrix as consisting of a l l relevant accounts of an account structure, and not limited to the balance sheet or the income statement accounts. The matrix extrac- ted i s defined in accordance to the financial state- ment requirements, and consists only of those accounts that are of interest. 3 5 The derived T-matrix i s a composite, and i s the end re- s u l t of a number of previous operations. I t i s quite possible to set up non-financial T-matrices preceding the f i n a n c i a l T - matrix. As a suggestion, the notion of composite T-matrix ( r e s u l t i n g from the amalgamation of several, disparate matrices) can be extended to inventories (opening inventories, issues/ r e c e i p t s , commitments/on-orders)„ I t can also be extended to price and quantity purchased, and to price and quantity sold matrices; as w e l l as to the l o g i s t i c s preceding the account- ing measurements. In t h i s respect, accounting and management science i n t e r - face, and the multidimensionality of a given simple f i n a n c i a l transaction can be u t i l i z e d to better advantage by both d i s - c i p l i n e s . C . Theoretical analysis of the extended matrix accounting approach: The need for an extended matrix accounting theory i s dictated by the lack of a consistent approach to accounting from an operational computer information system perspective. The equations formulated by the author help remedy the s i t u a - t i o n . i . Theoretical development of the T-matrix; the T- matrix i s an ordered array of amounts consisting 36 of aggregated accounting entries on the off-diago- nal elements, and of opening balances on the main diagonal elements. The T-matrix i s a structure en- compassing a l l of the accounts of the chart of accounts, and i s an n x n element matrix. The n stands for the total number of accounts within a given chart of accounts, T = T. + N ( 7) where t. . t. . xx e 1.. xx = W + A = [ w. . ) + f a. . ] ( 8) ( 9) ( 9a) Key to symbols used: T - T_ -N t.. X X e'.. XX the T-matrix the opening balance matrix the transactions entry matrix, con- sisting of off diagonal ( i / j) ele- ments the unsigned opening balance matrix, consisting only of the diagonal ( i = j) elements unit matrix, with positive diagonal elements for assets and expenses, ne- gative for equity, revenue and summary accounts 37 w. . 10 a. . 10 the exogenous transactions matrix ( i ft 0) the endogenous transactions matrix ( i * 0) (where the transactions refer to the usual account- ing entries used i n financial accounting). i i . The algorithm; the outstanding balances are cal- culated by means of the following expression T x e = ( T Q + ( T ± J - T )) x e = t f (10) where t^. i s the ending balance vector, n x 1, whose elements become the components o f [ ̂ i i ] °^ t i i e i > o l l o w i n S accounting period. i i i . Verification of posting; the accuracy of the com- putational process i s checked by mailing use of the following relationship, en x To = en x T = 0 where T e i s the transpose -of a column vector con-n sisting of a l l elements equal to 1. i v . Changes to the ;T-matrix: a summary aggregation o a l l changes to the accounting system by entries affecting i t are obtained through vector subtrac 38 tion, ' t f - t Q = A t (12) The equations ( 7 ) , (10), (11) and (12) form the core of the author's theoretical development of the extended matrix approach to accounting systems. It i s interesting to note that the above approach allows one to think in terms of im- posed boundary conditions (the beginning balance T ), and i n terms of so-called natural boundary conditions (the chart of account structure). The concepts of "boundary" are quite im- portant from a systems viewpoint, and help to isolate i n one's mind the essential characteristics of an accounting informa- tion system. D. Example of an accounting information system for computers; The findings and analysis presented i n this thesis w i l l be i l l u s t r a t e d by an example. The example represents a simple accounting system that uses periodic inventory valuation. It was extracted from a popular textbook by Gordon and S h i l l i n g - law (1969), and then used to bring out the pr a c t i c a l i t y of the extended theory of matrix accounting. In the example, the statement of Financial Position as of December 31, 19x7 was given as 3 9 BALANCE SHEET ASSETS EQUITIES Cash on hand 4,000 Accounts receivable 24,000 Inventory 16,000 Furniture 15,000 l e s s Depreciation4,000 11,000- Accounts payable 20,000 Capital stock 3 5 , 0 0 0 55,000 55,000 and the chart of accounts was defined as follows, Account number Account name 1 cash on hand 2 accounts receivable 3 inventory 4 furniture 5 depreciation-furniture 6 accounts payable 7 c a p i t a l stock 8 retained earnings 9 sales revenue 1 0 miscellaneous revenue 1 1 cost of goods sold 1 2 administrative expenses 1 3 miscellaneous expenses 1 4 summary accounts I n i t i a l balances Debit 4 , 0 0 0 2 4 , 0 0 0 16,000 15,000 Credit 4,000 20,000 35,000 4 0 The accounting e n t r i e s to be posted were the following-, 1. Merchandise purchased i n v e n t o r y 9 8 , 0 0 0 accounts payable 9 8 , 0 0 0 2. Expenses payable m i s c e l . expenses 1 9 , 0 0 0 accounts payable 1 9 , 0 0 0 3. Cash s a l e s cash on hand 4 5 , 0 0 0 s a l e s revenue 4 5 , 0 0 0 4. C r e d i t s a l e s 5. S a l a r i e s accounts r e c e i v a b l e 1 2 7 , 0 0 0 s a l e s revenue 1 2 7 , 0 0 0 a d m i n i s t r a t i v e expenses 5 0 , 9 0 0 cash on hand .s 5 0 , 9 0 0 6. Accumulated d e p r e c i a t i o n a d m i n i s t r a t i v e expenses 1 , 0 0 0 d e p r e c i a t i o n - f u r n i t u r e 1 , 0 0 0 7 . F u r n i t u r e s o l d cash on hand 50 f u r n i t u r e 50 8. Gain on s a l e 9. W r i t e - o f f cash on hand 30 m i s c e l . revenue 30 d e p r e c i a t i o n - f u r n i t u r e 350 f u r n i t u r e 350 10. C o l l e c t i o n 11. Payments cash on hand 118,000 accounts r e c e i v a b l e accounts payable 114,100 cash on hand 12. Ending i n v e n t o r y was determined a t $18,000. 41 118,000 114,100 The above i n f o r m a t i o n i s enough to generate the f i n a n - c i a l statements from. In order the c a l c u l a t i o n s are reason- a b l y c l e a r to f o l l o w , a l l the r e l e v a n t v e c t o r s and matrices v / i l l be e x p l i c i t l y l i s t e d . R e f e r r i n g to equation ( 8 ) , t . . and e'.. are defined . i i i i i n the f o l l o w i n g manner,( i n OOO's ) 4 t. . i i 24 16 0 . 0 15 2 0 35 0 0 0 . 0 0 0 0 and, ( i n units ), k2 11 -1 s i 0.0 -1 0.0 -1 -1 -1 The matrix multiplication for x gives the T Q matrix with the following values i n 000's, T. 24 16 15 0.0 -4 -20 o ; o -35 0 0 0 0 0 The matrix V/ i s formed by direct entries of the w. .'s into the respective positions of the matrix, 43 w. .= 3-0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 0 118 .05 0 98 0 .35 0 114.1 0 50.9 19 0 8 9 10 11 12 13 14 45 .03 127 0 0 0 0 0 At the beginning of the period p Q, the matrix T Q was ge- ; nerated i n accordance with the structural peculiarities of the chart of accounts. During the interval between p and p., tran- o 1 eaction entries were entered into the W matrix. This w i l l go on un t i l such time p^ when the financial statements are requested. At p^ the closing inventory valuation w i l l be required, i n order that the closing entries can be made; the endogenous mat- r i x A i s then generated. The ending inventory valuation of $18,000 allows one to form the endogenous transaction entry number 13 as follows, COST OF GOODS SOLD = BEGINNING INVENTORY - ENDING INVENTORY - PURCHASES (13) or, CGS = 1 6 - 1 8 -98 = 96 and 13. Cost of goods sold valuation cost of goods sold 96,000 inventory 96,000 Up to here, the matrix T was discussed i n terms of the component matrices T , V/ and A. It i s now assumed that the principles have been sufficiently well outlined, and the attention w i l l be focused on the T-raatrix as defined i n equa- tion ( 6). The T-matrix, at time p,, w i l l have the folowing elements 4 5 l 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 1 4 1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 1 4 4 1 1 8 .05 4 5 . 0 3 2 4 1 2 7 16 98 1 5 . 3 5 - 4 1 1 4 . 1 - 2 0 - 3 5 0 0 0 9 6 0 5 0 . 9 1 0 1 9 0 0 At this point, the mathematical expression, equation ( 1 ) , can be expressed in terms of A t ± t > an intermediate vector consisting of net transaction balances of a l l active accounts, ( T - T T ) x e = A t i n t ( 1 4 ) and can be applied to the revenue and expense account numbers 9, 1 0 , 1 1 , 1 2 and 1 3 . The outstanding balances i n these accounts w i l l then be transfered by means of endogenous tran- saction entries into the summary account number 1 4 . The closing entry transactions are as follows, 46 14. Closing entry - sales revenue sales revenue 172,000 summary account 172,000 15. Closing entry - misc. revenue misc. revenue 30 summary account 30 16. Closing entry - cost of goods sold summary account 96,000 c.g.s. 96,000 17. Closing entry - administrative expenses summary account 51,900 admin, expenses 51,900 18. Closing entry - miscel. expenses summary account 19,000 misc. expenses 19,000 After the closing entries are made, the equation (14) i s applied to the summary account number 14, i n order to deter- mine the retained earnings balance. The balance i s then used to create the l a s t entry, 19. Transfer to retained earnings summary account 5,130 retained earnings 5,130 Though the above outline does no more than skim through the mechanics of an accounting system using periodic inventory valuation, i t i s clear that the T-matrix has at t h i s moment a l l the entries required to generate the new balance sheet, and 47 that the income statement was available as soon as the cost of goods sold was known. In fact,-the computerized version of the example, stores the balances of the revenue and expense accounts as they become known, This i s an important point, since endogenous transactions are created through an iterative process. Assuming, for the moment, that the endogenous transactions 14 through 19 have not yet been recorded i n the T-matrix, the calculation of ( T - T T ) x e = A t . n t (14) w i l l provide one with an intermediate vector whose components are the net transaction balances of a l l exogenously activated accounts. The components of the matrix ( T - T ) are not ex- p l i c i t l y shown i n this discussion. They are similar to the components of a matrix developed further i n the section, and shown on page 50. The net transaction balances of a l l activated accounts are given by At. ., and are as follows, 48 -1.92 9 2 -.40 -.65 -2.90 0 0 •172 -.03 96 51.9 19 0: the vector components -172, -.03 are net balances of the reve- nue accounts; similarly, 96, 51.9 and. 19 are the net balances of the expense accounts (in 000's), and the difference between the linear aggregation of the accounts w i l l result i n an amount equal to the retained earnings. The income statement, can therefore be generated, INCOME STATEMENT SALES REVENUE Less COST OF GOODS SOLD 96,000 ADMINISTRATIVE EXP 51,900 MISCELLANEOUS EXP 19,000 166,900 INCOME prior to extraordinary item Gain on MISCELLANEOUS REVENUE 172,000 5 , ioo 30 5,130 49 It w i l l be noted that the accounts involved in the Income Statement have zero beginning balances. This i s because they are aggregation of entries to accounts that are set to zero at the end of an accounting period. The traditional t r i a l ba- lance and adjusted t r i a l balance can also be made available from the T-matrix. But because they are essentially worksheets, and convenient only to manual processing of accounting infor- mation, they have been bypassed in the computerized informa- tion systems context. 1 Now we return to the T-matrix where a l l the endogenous transactions have been posted. The entries at the time of the determination of the balance sheet are arranged i n the T-matrix in the following manner, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 4 118 .05 45 .03 24 127 16 98 15 .35 -4 114.1 -20 -35 172 .03 96 50.9 1 19 5.13 96 51.9 19 50 where the entries into account number 14 are a l l endogenously derived entries a. the application of equation (10) to the T-raatrix generates the ending balance vector t^, whose ele- ments are then used i n printing out the balance sheet (and i n supplying the T-matrix with a new set of beginning balances for the following period). The elements o f ( T + ( T. . - T.. )) are shown below, 9 10 11 12 15 14 4 118 .05 -114.1 45 .03 ' -50.9 -118 24 127 16 98 -96 -.05 15 -.35 .35 -4 -1 114.1 -98 -20 . -19 -35 -5.13 -45 -127 !72 -.03 -°3 96 -96 50.9 1 -51.9 19 -19 5.13 472->03 96 51.9 19 Multiplying the above T-matrix by a row vector e, gives the following vector t 51 2.08 33 18 14.6 -4.65 -22.9 -35 -5.13 0 0 0 0 0 0 The statement of Financial Position as of December 31, 19x8 w i l l be given as • BALANCE SHEET ASSETS Cash on hand 2,080. Accounts receivable 33,000 Inventory 18,000 Furniture 14,600 less Depreciation 4,650 9,950 EQUITIES Accounts payable 22„90Q Capital stock 35,000 Retained earnings 5,130 63,030 63,030 52 VII. STATE OF THE ART Accounting theory has evolved primarily out of the prac- t i c a l application of accounting systems to help managements to cope with real world problems. Thus for an accounting va- luation scheme to be successful, the particular method of aggregation must be chosen i n accordance with the way the aggregate w i l l be used. Though the determination of ration- a l i t y i s not a problem of accounting per se, the reflected rationality requires e x p l i c i t structural relationships to emerge; and hence the value of mathematical analysis in deve- loping computerized accounting information systems. Accounting transactions can be viewed as reflecting ac- t i v i t i e s involving measurement in general. They are seen as being independent of the particular coordinate system used i n describing, classifying and aggregating them. Mathematical analysis allows one to develop alternative coordinate systems, or i f they already exist, provide an expli c i t formulation of a coordinate system i n terms of another, subject to coordinate transformation equations, and consistent with information sys- tems technology. The rest of the chapter explores some of the qualities of tensors, and of transformation coordinates. Their use i n accoun- ting i s commented upon. 53 •A. simple transactions: Events are recorded i n accounting systems by assigning debit and credit dimensions to the amount reflecting the event. The debit and credit dimensions assigned are restricted by the account names used within an.account structure; i t i s quite clear that the account structure encompasses the sum total of the one-to-one reciprocal correspondences between a l l dimen- sions Of a l l accounts, for that given accounting system. The interrelatedness existing between the amount A, the debit and credit dimensions x^ and x*c, and the account struc- ture, i s not unique. It i s quite possible that the amount A i k have different dimensions x J and x i n different accounting systems. For example, debit cash and credit inventory as ver- sus debit cash and credit sales revenue. In other words, the simple accounting transactions involving amount A are indepen- dent of the accounting system imposed upon the amount A. The accounting system used i n classifying and aggregating the transactions can then be looked upon as a specific coordinate system reflecting certain structural characteristics. It also follows that in amount A reflects a valuation of a principal, i t cannot be changed by the accounting system used in recording the transaction. 54 If the valuation of vthe assets i s recorded through amounts A exogenous to the accounting system, then the linear aggregate of accounting quantities i s governed by' the inputs to the given accounting system, and the valuation i s reflected through the specific account structures used, however, the valuation w i l l remain unchanged or invariant. The linear aggregate of $100. w i l l always equal $100 in spite of any chart of accounts used. Let the set of arrayed numbers, representing the linear aggregate of accounting quantities, within a given account structure, be such that i t s sum total w i l l equal the linear aggregate' of an another accounting system. When this condition holds, then the sets of arrayed numbers from the different accounting systems, using the same input transaction amounts A, can be subjected to coordinate transformation, and inter- relating their account structures. The explic i t formulation of one coordinate system i n terms of another can be made avai- lable through the specification of coordinate transformation equations. Sections B and C of this chapter v/il l introduce the conc- epts of arithmetic n-space, transformation of coordinates, co- variant and contravariant tensors, a l l of which may be rele- vant to accounting theory. 55 B. Arithmetic n-space and, transformation of coordinates; The intention here i s not to emphasize a serai-Euclidean method of ideally representing measureable magnitudes; but to point out that the idea of magnitude and of perceived dimen- sions of the geometric tradition can be superseded by the ab- stract, spatial development of the variable relation-values between points in space. This geometry i s partly based on the position of points in space that i s not necessarily three- dimensional ( a manifold of points ), and partly on the ana- l y s i s of numbers defined through point positions in space. By replacing lengths and magnitudes by positions carries with i t a purely spatial and no longer material conception of ex- tension. , In three dimensional space, a point i s a set of three values determined by specifying a particular frame of refe- rence or coordinate system. The Cartesian, the cylindrical and the spherical coordinate systems are the most commonly used frame of references. With.them, the same point can be expressed i n terms of (x, y, z), or (x, r, 9 ) , or (r, 0 , 0). Also the three frames of reference are mathematically related to each other by derived sets of equations. Coordinate systems of more than three dimensions follow 56 by analogy, and may be used i n locating an n-diraensional point within a space of n-dimensions. Any set of objects which can be placed i n a one- to-one reciprocal correspondence with an arithmetic n-space, w i l l result in a coordinate system. The one-to-one correspon- dence between the elements or points of the n-space and the arithmetic n-space used, can be chosen in many ways, and ref- lects the nature of the problem. As an example, consider a point P corresponding to the n- 1 2 n tuple (x ,x , ... x ) , i f y 1 - y 1 ( x ^ x 2 , ... x n) i = 1,2, ... n (IS) and assuming that x 1 can be solved for, so that x 1 = x 1 ( y 1 ^ 2 , ... y11) i - 1,2, ... n (ife) where y^nd x 1 are single valued. Then the point P can be put into correspondence with the n-tuple ( y ^ y 2 , ... y 1 1). The point P has not changed, but a new method for attaching numbers to the point has been made available. The equation (15) i s called a transformation of coordinates system of equations, and results i n a new coordi- nate system being defined. 57 Contravariant and covariant tensors: The abstracts spatial development of the variable r e l a - tion-values between points r e l i e s i n part on the theory of . tensor analysis. In this section, the definitions of contra- variant and covariant tensors are given, and related to the previous section on coordinate.transformations. 1 2 n In general, any set of n quantities A , A , ..... A X i n a coordinate system ( x \ x 2 , ... x n) can be related to n other quantities A . \ A 2 , . . . A N i n another coordinate system (x\x 2,- ... x n) by the transformation equations ax ^ a* q q-1 p = 1,2, ... n (1?) which are defined as the components of a contravariant vec- tor or contravariant tensor of the f i r s t rank, or of the f i r s t order. Similarly, n quantities A-^A^, ... Aft i n a coordinate 2' X 2 ii system (x ,x , ... x ) relate to n other quantities 5-̂ ,1 » "^2 xi • ••.A i n another coordinate system (x"~,x , ...x ) by the 58 transformation equations A. P A q A q P = 1,2, n ( 1 8 ) which are defined as the components of a covariant vector or covariant tensor of the f i r s t rank or f i r s t order. The tensor i s not just the set of components i n one co- ordinate' system, but an abstract quantity which i s represented nents A H or A^. If, for example, the components of a contra- variant tensor are known i n one coordinate system, then the components are known i n a l l other allowable systems by the equation (IT-). The coordinate system does not give a new vec- tor, i t changes the components of the same vector; in other words, the contravariant tensor i s an invariant under a co- ordinate transformation (an object of any kind which i s not changed, by transformations of coordinates i s called an i n - variant). i n each coordinate system (x ,x", x n) by the set of compc- 59 D. Use of coordinate transformations in accounting: If accounting measurements are not perceived only in terms of magnitude and dimensions of the geometric tradition, and i f i t i s supplemented by the definition of numbers through point- positions i n space, a purely spatial conception of accounting systems may be attempted. Such a formulation would be of major importance to accounting theory. Accounting entries of the simple type are independent of the particular coordinate system, used i n describing and aggre- gating them mathematically. Their invariance permits tensor analysis to be applied to the theory of accounting. 1 2 n _ i _2 _ v i As an example, l e t (x ,x , ... x ) and (x ,x , ... ) be coordinates of a point in two different frames of reference, and accepting the existence of n-dimensional space, n indepen- dent relationships between the coordinates of the two systems can be set up, x 1 = x 1 (x 1,^ 2, ... x n) i = 1.2, n o r , x 1 ( x ^ x 2 , i = 1,2, n (20) Once the relations are defined, an expli c i t and mathematically valid methodology becomes available to accounting encompassing the accounting spread sheet, the incidence matrix and the net- 60 work formulation. The accounting equation (Assets = Equity) mirrors a given accounting entry i n more than one coordinate system, and thus i t may be expressed i n the components of the contravariant or covariant tensors of the f i r s t rank. . The amount of the entry i s independent of the particular chart of accounts used, or imposed upon i t . The structural and functional considerations of the chart of accounts can be dis- tinguished from the purely algorithmic.processing of the tran- saction- entries. The application of structural and procedural systems notions to the concepts of information (accounting or other) w i l l be needed i n order to create accounting informa- tion systems. 61 VIII. CONCLUSIONS The thesis drew .upon existing knowledge, and added to i t by extending the application of computerized accounting sys- tems. The tangible contributions made to accounting from an information systems perspective are summarized in the f i r s t section. A discussion of the systematic development of accoun- ting systems for computers and directions for further research and development conclude the thesis. A. Summary The thesis provided perspective on i . the relevance of accounting information to orga- nizations, by directing the reader's attention to •the behavioral aspects and structural characteri- st i c s of the firm, and to the problems of coordi- nation facing an organization; i i . information systems generated i n conformance v/ith the objectives of organizational development; i i i . the characteristics of information and information systems. The thesis then ' i . traced the development of the accounting spread sheet in matrix form; i i . enhanced the mathematical exposition of matrix 62 accounting by formulating a new series of mathe- matical expressions that synthesized the previous work in the area, and extended i t s (matrix) appli- c a b i l i t y to computerized accounting information systems; i i i . applied the findings and analysis to a simple com- puterized accounting system using periodic inven- tory valuation; i v . explored the use of tensors and coordinate trans- formation equations in the f i e l d of accounting. B• Direction for further research: The systematic development of accounting systems for com- puters w i l l help i . bridge the communication gap between the account- ing profession and the quantitatively oriented computer specialists; i i . improve the quality of the documentation available on existing computerized accounting systems; i i i . focus attention of the practitioners to the advan- tages of using mathematically developed algorithms. The matrix representation can be extended to a number of areas closely related to the accounting process. Non financial T-matrices can be defined and incorporated with the financial T-matrix. This interface between accounting and management science should be exploited, since i t w i l l help c l a r i f y their common objectives, and improve the understanding of accounting 63 as an important ingredient of management science. The use of the matrix representation for accounting sys- tems operating on common input data, can allow the interdepen- dencies between the accounting systems to be mathematically formulated, and computerized. This practical area of research can be applied to existing accounting systems. Finally, expli- c i t and implicit formulation of structural relationships bet- ween accounting systems should be attempted. Examples of auch relationships w i l l do much to advance the use of tensors and coordinate transformations. 64 BIBLIOGRAPHY Ansoff, H.I. (Sd.), 1969, "Business Strategy", London: Penguin Books Anton,H.R. & P.A.Firmin (Eds.), 1966, "Contemporary Issues i n Cost Accounting: a discipline in transition", Boston: Houghton M i f f l i n Co. Blumenthal, S.H., 1969, "Management Information Systems", Engle- wood C l i f f s : Prentice-Hall, Inc. Charnes,A.,W.Cooper and Y. Ijiri,1963,"Breakeven Budgeting and Programming to Goals", Journal of Accountancy,1,1, pp.16-44. Churchman, C.W., 1961,"Prediction and Optimal Decision: philo- sophical issues of a science of values", Englewood C l i f f s : Prentice-Hall Inc. Cyert,R.M.,and J.G. March, 1965, " A Behavioral Theory of the Firm", Englewood C l i f f s , N.J.: Prentice-Hall Inc. Dearden,J., 1962, "Cost and Budget Analysis", Englewood C l i f f s , N.J.: Prentice-Hall Inc. Driebeek,N.J., 1969, Applied Linear Programming", Reading, Mass: Addison-Wesley Publishing Co. Emery, J.C., 1969, Organizational Planning and Control Systems", London: Collier-Macmillan Ltd. ,(Ed.), 1969, "Systems Thinking", London: Penguin Books Forrester, JJI. ,1961,"Industrial Dynamics", New York: John V/iley & Sons Galbraith, J.K., 1967, "The New Industrial State", New York: The New American Library (Signet Books), Inc. Germain, C.B., 1967, "Programming the IBM 360", Englewood C l i f f s , N.J.,Prentice-Hall Inc. 65 I j i r i , Y.,1967, "The Foundations of Accounting Measurement; a mathematical, economic and behavioral enquiry", Englewood C l i f f s , .N.J.: Prentice-Hall Inc. , 1965, "Management Goals and Accounting for Control", "Amsterdam, Holland; North-Holland Publishing Co. Kohler, E.L., 1963, "A Dictionary for Accountants", (3rd ed.), Englewood C l i f f s , N.J.: Prentice-Hall, Inc. Lass, H., 1950, "Vector and Tensor Analysis", New York: McGraw- H i l l Book Co.,Inc. Likert, R. ,1961, "New Patterns of Management", New York: Mc- Graw-Hill Book Co.,Inc. , March, J.G. & H.A. Simon, 1 9 5 8 , "Organizations", New York: John 1 Wiley and Sons Marin, J., 1967, "Design of Real-time Computer Systems", Engle- wood C l i f f s , K.J.: Prentice-Hall Inc. Mattessich, R., 1 9 6 4 , "Accounting and Analytical Methods", Home- wood, 1 1 1 . ,Richard D. Irwin, Inc. , 1957, "Towards a General and Axiomatic Founda- tion of Accountancy - with an introduction to the matrix formulation of accounting systems", Account- ing Research, Vol.8, No. 4 (London; Oct,1957) pp.328- 55 Ralston,A. & H.S.Wilf, I960, "Mathematical Methods for Digital Computing", New York; John Wiley & Sons G o r d o n , M.J. & Shillinglaw, 1 9 6 9 , 11 Accounting: a managerial approach", ( 4 t h ed.), Homewood,111: Richard D. Irwin Inc. Simon, H.A., 1 9 4 5 , "Administrative Behavior",(2nd ed.), N.Y.: The F r e e Press (1965) Thompson, J.D., 1 9 6 7 , "Organizations in Action", New York: Mc- Graw-Hill Book Co. Webster, E., 1 9 6 4 , "How t o win the business game", Harmonds- worth; Penguin 3 o o k s 66 Will, H.J.,1969, "A C r i t i c a l Analysis of the Assumptions Under- lying Selected Managerial Accounting Models: An i n - formation systems approach", Ph.D. dissertation, University of Illinois,111. ,1969, "Management Information Systems", Faculty of Commerce and Business Administration, The University of B r i t i s h Columbia, Canada Appendix one; A computer program for the accounting system exam; (Please refer to chapter VI, section D) A A A A A A A A A A A A A *** ******* ******* ******** *** ** ******* * * * * * * * * * * * * * * * * * * * ***** ********* *** ****** ******** ***** ** ********* * SIMON FR AS ER UN IVE*SITY * v ** ** £* ** ** ** ** ** ** ** ** ** * * /** ** ** ** ** ** ** ** ** * C3MPUHNG CENTRE * * * * * ** ** ** ** ** ** ** * ********* ** ** ** ********* ** ** **** * * ** ******* ** ** ** ********* ** ** **** * MVT RE L 17 ** ** ** ** ** ** ** ** ** ** ** ** * ft ** ** ********* ********* ** ** ** ********* ********* * JUNE 1969 * ** ** ******* ******* ** ** ** ********* ******* * * * * * * * * * * * * * * * * * * * * * *** ******** ** ** ********* ****** ********* ********* ** ** ***** ******** ** ** ********* ****** ********* ********* *** *** ** ** ** ** ** ** ** ** ** * * * * * * * * ** ** ** ** ** ** ** ** ** * * * * * * * ** ** ** ** ** ****** ** ****** ****** ** * ** ********* ** ** ** ****** ** ****** ****** * * ** ********* ** ** £* ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** *** ********* ****** ********* ** ** ** * * * * ** * ********* ****** ********* ** ********* ********* ******* ********* ***** ***** ******* ********* ** ********* ********* ********* ********* ******* ******* ********* ********* *** ** ** *** ** ** ** ** ** ** *# **' '** ** ** ** ** ** ' " '"' ** ** *** * * ** ** ** ** * * ** ** ** ** ** ** **** ******** ******* ******* ** ** ** ** ******* * * ** ** ****** ********* ******* ******* ** ** ** ** ** ******* ** ** ** *** ** ** ** ** ** ** ** ** ** ** ** ** ** *** ** ** ** ** ** ** ** ** ** ** *• ** ****** ** ********* ********* ** ******* ******* ********* ** ***** * ** ******* ******* ** ***** ***** ******* ** * *** ** * * ****** ********* * ON Co ******* ** ********* ********* ** ** ** ** ** ** *** ** ** ** ** ** ********* ******* ******** ** ******** ******* ** ** ** ** ** ** * * * * * * ** ** <<* ** ** ********* ********* ********* ****** /* PROGRAM ACCT L.~ V.MATVEIEF MARCH 1970 */ PAGE 2 STMT LEVEL NEST /* PROGRAM ACCT - V.MATVEIEF MARCH 1970 */ 1 AOOACCT: PRGC OPTICNS (MAIN) ; /* DECLARE INPUT AND OUTPUT FI L E S */ 2 1 DCL TRANMST F I L E OUTPUT ; /* TRANSACTION TAPE,STREAM I/O * / 3 1 ' OCL SYSIN F I L E INPUT ; /* CARD INPUT,STREAM 1/3 */ A 1 DCL SYSPRINT FILE OUTPUT ; /* PRINT OUTPUT,STREAM I/O */ /* DECLARE STORAGE AREAS */ 5 1 DECLARE F M LB LABEL ; 6 1. DECLARE FKLB2 LABEL ; 7 1 DCL ROW_N0 (18) PIC'99' ; 8 1 CCL S1GN_ DI AG (18) C H A R ( l ) ; 9 1 DCL NAMES (18) CHAR(25) ; 10 1 CCL 01AG_ELEMENTS( 18) PIC'S11 111 1111IV.99* ; I 1 1 1JCL DV1 118) PIC 'S l l l l l l l l l l M . 99' ; 12 1 DCL DV2 (18) P I C ' S I Z Z l l l l l l l M .9 9' ; 13 1 DCL DV3 (18) PIC'S2Z111111ZZV.99« ; 14 1 DCL DAT LI P I C 9 9 9 9 9 9 ' ; \b 1 DCL DEB I T_ACCOUNT " PIC'99' ; "" ""' 16 1 DCL CREDIT_ACCOUNT P I C ' 9 9 ' ; 1 7 1 OCL AMOUNT PIC 'SZZZZZZZZZZV.99* ; 18 1 OCL RE F CHAR(3) ; 19 1 CCL EXPLANATION CHAR(20) ; 20 1 DCL OATEAREA PIC'999999' ; 21 1 DCL INCOME_STMT (18) PIC * SZZZZZZZZZZV.99* ; 22 1 CCL (M AT RI X_S IZ E, M) PIC'99« ; 2 3 1 DCL ( NQ_C A RD S_D I AG , L ) ' PIC'99' ; 2h 1 DCL INIT1AL_RUN CHAR(l) ; 25 1 CCL DAT E_OF_ST MT PIC'99/99/99* ; 26 1 DCL MATRIX( 18,18) P I C SZZZZZZZZZZV.99' ; 2 I 1 CCL SUM PIC'SZZZZZZZZZZV.99' ; 28 1 UCL F l CHAR177) ; 29 1 DCL F2 CHAR(52) ; 30 1 DCL F3 CHAR(8 ) ; 31 . 1 DCL F4 CHAR(35 J ; 32 I "DECLARE A S SE T_ TO TA L PIC'SZZZZZZZZZZV.99' INITIO) ; 33 1 DECLARE EQU 1T_T0T AL PIC 'SZZZZZZZZZZV.9 9' INITIO) ; 3<, 1 DECLARE NET_INCOMb P1C' S LI III11Z ZZV .99« I M I T O ) ; 35 1 DCL ASSET.EOUIT (18) PIC'SZZZZZZZZZZV.99' ; 36 1 DCL CONST CHAR130) I N I T ( ' •) ; 3 7 I DO I = 1 TO 13 P R O G R A M A C C T L - V . M A T V E I E F M A R C H 1 9 7 0 * / P A G E 3 S T M T L E V E L N E S T -- - -- - - -•- - •— - - V 3 a ! 1 ROW NO ( I) = 0 ; f 1 1 S I G N _ O I A G U ) = • • ; 4 0 1 1 NAME S ( I ) = • ' ; 41 1 1 C I AG_ EL EM E N T S ( I ) = 0 ; 4 2 1 1 DVI ( I) = o ; " • " 4 3 1 ' 1 0 v 2 ( I) = o ; 44 1 1 DV31 I ) = 0 : 4 5 1 1 i N C O M E _ S T M l ( 1 ) = 0 ; 4 6 1 1 A S S E T _ E O U I T ( I ) = 0 ; 4 7 1 1 ENO ; t8 1 DO I = 1 TO 1 8 ; 49 1 1 00 J = 1 TO 18 ; 5C 1 2 M A T R I X l I . J ) = 0 ; 5 1 1 2 tNU ; 5 2 1 1 END : 5 3 1 CM E N D F I L E ( S Y S I N ) GOTO A 2 0 ; ' " " / * S T A R T M A I N P R O C E D U R E * / / * R E A D C O N T R O L C A R D * / 5 5 I PUT E D I T ( * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * , ' * I N P U T D A T A TO A C C O U N T P R O G R A M * * , ' * A S S E T S AND E Q U I T I E S FOR B A L A N C E S H E E T * • , ( X ( 3 0 ) , A , S K I P ( 2 ) , X ( 3 0 ) , A , S K I P ( 2 ) , X ( 3 0 ) « A , S K I P ( 2 ) , X ( 3 0 ) , A ) ; 5 c 1 P U T S K I P !4) ; 5 7 1 GET E D I T ( M A T R ! X _ S I Z E , M 0 _ C A R D S _ D I A G , I N I T I A L _ R U N , DAT E _ O F _ S T M T , F l ) ( F ( 2 ) , F ( 2 ) , A ( 1 ) , F ( 6 ) , A ( 6 9 ) ) ; 5 8 1 P U T D A T A ( M A T R I X _ S I Z E , N O _ C A R D S _ D I AG » I N I T I A l R U N , GAT E_OF_STM T ) ; / * I N I T I A L _ R U N = 1 FOR C R E A T I N G M A S T E R B L A N K 0 THE R Wl SE <•/ 5 5 1 I F I NI TI A L _ R U N = • • T H E N GOTO A 0 5 ; ~" / * R E A D IN N A M E S * / 6 1 1 PUT S K 1 P ( 4 ) ; 6 2 1 M = MA rR I X _ S I ZE ; 6 3 T L = N 0 _ CAR D S _ U I AG ; " ' - - -- - - - - - - - — — • " — ~ o — - 6 4 1 DO I = 1 TC M : 6 5 1 1 G E T E D I T ( ROW_NG (1), S1G N _ D I A G ( I ) , NAM E S ( 1) . F 2 ) ( F ( 2 ) , A ( l ) , A ( 2 5 ) , A ( 5 2 J ) ; 6 6 1 I PUT D A T A { POW_NO ( I ) , S I GN_D I A G ( I ) , NAM E S ( I ) ) ; 6 7 1 1 PUT S K I P l l ) ; 6 8 1 1 END ; ' f / * P r S L K i R A f A C C T L . - V . M A T V E I E F M A R C H 1 9 7 0 * / P A G E 4 S T M T L E V E L N E S T • • -- • — - . . ~ - V / * R E A D I N D I A G O N A L E L E M E N T S - 6 E L E M E N T S O N E A C H C A R D * / f 6 9 7 C 7 1 7 2 7 3 1 1 K l = 1 ; K 2 = 6 ; D O I = 1 T O L ; G E T E D I T ( ( D I A G _ E L E M E N T S ( K ) D O K = K l T O K 2 ) , F 3 ) ( 1 6 ) F 1 1 2 . 2 ) , A ( 8 ) ) ; K l = K 2 + 1 ; '- - 7 4 7 5 7 6 7 7 j 1 1 K 2 = K 2 + 6 ; E N D ; P U T S K I P 1 4 ) ; P U T C A T A ( { 0 1 A G _ E L E M E N T S ( K > D O K = 1 T O M ) ) ; - - • •- ; - - - 7 8 7 9 8 0 8 1 8 2 i / * P U T D I A G O N A L _ E L E M E N T S I N T O M A T R I X W I T H C O R R E C T S I G N J S * / D O I = 1 T U M ; I F S I G N _ D I A G ( I ) = ' N ' T H E N M A T R I X ( I , 1 ) = D I A G _ E L E M E N T S ( I 3 * ( - 1 ) ; " E L S E M A T R I X i l , I ) = D I A G _ E L E M E N T S ( I ) ; D I A G _ E L E M E N T S ( I ) = M A T R I X ( l . I ) ; - - • • - - - - 8 3 8 4 1 E N D ; P U T P A G E ; 8 5 1 A 0 5 : / * R E A D I N T R A N S A C T I O N C A R D S * / G E T E D I T ( D A T E l . O E B I T _ A C C O U N T , C R E D I T _ A C C O U N T , A M O U N T , R E F , 8 6 8 7 ' 1 ' " ' - - E X P L A N A T I O N , F 4 ) ( F ( 6 ) , F ( 2 ) , F ( 2 ) , F ( 1 2 , 2 ) , A ( 3 ) , A ( 2 0 ) , A 1 3 5 ) ) ; P U T D A T A I D A T E l . D E B I T _ A C C O U N T « C R E D I T _ A C C 0 U N T , A M O U N T , E X P L A N A T I O N ) ; P U T S K I P ( 2 ) : . — o a 9 0 9 1 9 2 9 3 A l O : I F D E B I T _ A C C O U N T = C R E D I T _ A C C O U N T T H E N G O T O A l O ; C A L L B Q O W T R _ T R A N ; M A T R I X I Q E B l T _ A C C O U N T , C R E D I T _ A C C O U N T ) = A M O U N T ; G O T U A O 5 ; ' " O V l ( C R E D I T _ A C C O U N T ) = A M O U N T ; ..... . ... . ..... 9 4 9 5 9 6 \ A 2 0 : C A T t A R E A = C A T E 1 ; G O T U A 0 5 ; P U T E D I T ( • « * # * * * > ? - - ; ' * * > > = > * * * » * < ' * # * * * * * * * * * * * < > * * * * * > : • « * * * = » • , • * # O U T P U T D A T A F R O M A C C O U N T P R O G R A M * ' , ' * * A S S E T S A N D E Q U I T I E S F C R B A L A N C E S H E E T * « , H 9 7 1 • * * I N C O M E S T A T E M E N T * ' , ( P A G E , S K I P ( 2 ) , X ( 3 0 ) , A , S K I P ( 2 ) , X ( 3 0 ) , A , S K I P ( 2 ) , X ( 3 0 ) , A , S K I P ( 2 ) , X ( 3 0 ) , A , S K I P ( 2 ) , X { 3 0 ) , A ) ; P U T S K I P ( 4 ) ; /* PROGRAM ACCT L.~ V.MATVEIEF MARCH 1970 * / PAGE 5 STMT LEVEL NEST 98 P UT CAT A < IDV 1(1) DO I = 1 TO M ) ) ; 99 100 101 10 2 103 CALL C00SUBVAR1 ; CALL DOOACCT_ALGOR ; PUT EDIT ( ' * « * * * MATRIX AFTER 1ST ACCOUNTING ALGORITHM * « * * * • ) (PAGE, X (30 ),A ) ; PUT SK IP14) ; PUT DATA [ ( ( M A T R I X ( I . J ) CQ J = l TO M) DO 1= 1 TO M ) ) ; T I F T 1 05 106 10 7 108 10 9 DO I = 1 To M ; INCOME_STMT(I) - END ; PUT S K I P ( 4 ) ; PUT DATA { ( DV2 CALL E 00 SUB VAR2 0V2 ( I ) ( I ) DO I = 1 TO M ) ) ; 110 1 1 1 112 1 13 114 CALL DOOACC T_ALGGR ; PUT EDIT ( ' * « * * * MATRIX AFTER 2ND ACCOUNTING ALGORITHM (PAGE , X(30) ,A J ; _ PUT SK IP<4) ; PUT DATA ( ( ( M A T R I X ! I , J ) CO J = l TO M) DO 1= 1 TO M )J ; PUT SK IP !4 ) ; PUT CAT A ( (CV2( I ) 00 1 = 1 TO M ) ) ; CALL F00SUBVAR3 ; CALL DOOACC T_ALGOR ; PUT EDIT ( MATRIX AFTER 3RD ACCOUNTING ALGORITHM **#**•) (PAGE , X(30) ,A ) ; PUT DATA (({ M A T R I X ( I . J ) DO J = l TO M) DO 1= 1 TO M )) ; 11 3 ) IS 117 11 8 119 120 12 1 122 123 " P U T S K I P I 4 ) ; PUT DATA ( ( D V 2 ( I ) DO I = I TO M ) ) ; CALL GOOFIN_DI AG ; PUT EDIT ( END PRODUCT OF ACCOUNT PROGRAM * * # * * ' V * * * * * * ASSETS AND EQUITIES FOR BALANCE S H E E T ' , ( PAGE, X ( 3 0 ) , A , SK IP12 ) ,X(30 ) ,A,A ) PUT S K I P ( 4 ) ; PUT DATA ( ( C V 3 ( I ) DO I = 1 TO M J ) ; CALL H00FIi\_MATRIX ; 1 1 = 0 : DO I = I TO M ; A30 A SSL T_tU)Ul T( I ) = EN U ; ASSE T_TOTA L = 0 EOUIT_TOTAL = 0 FMLB = FM1 ; DIAG_ELEMENTS( I ) 134 135 137 II = II + 1 ; IF I I = 2 THEN CONST= ' 3 AS E D ON T ( F ) ' ; PUT EDIT ( 'STATEMENT OF F INANCIAL POSITION ( AS OF' , ' DEC .31 . 1 970 ) * , CONST, 'BALANCE SHEET' , •A S S E T S ( $ ) » , •£ O U I T I E. S . ( $ ) ' ) / * P R O G R A M ACCT U. " V . M A T V E I E F M A R C H 1 9 7 0 * / P A G E 6 S T M T L E V E L N E S T ( P A G E . X ( 3 0 ) . A . A . X ( 4 ) . A . S K I P ( 4 ) t 1 3 8 1 3 9 1 4 0 X ( 5 0 ) , A , S K I P ( 4 ) , X ( 2 7 ) , A , X ( 4 8 ) , A ) ; PUT S K I P I 2 ) ; P U T E D I T ( N A M E S d ) , AS S ET_ ECU IT (1 ) , N A M E S ( 6 J , A S S E T _ E 0 U I T ( 6 ) ) ( R ( F M L B ) ) ; PUT E D I T ( N A M E S 1 2 ) , A S S E T _ E Q U I T ( 2 ) ) ( R ( F M L B ) ) P U T E D I T ( N A M E S ( 3 ) , A S S E T _ E O U I T ( 3 ) , N A M E S ( 7 ) , A S S E T _ E O U I T ( 7) ) I R ( F M L B ) ) ; PUT E D I T ( N A M E S ( 4 ) , A S S E T _ E O U I T ( 4 ) ) ( R ( F M L B ) ) ; P U T E D I T ( N A M E S ( 5 ) > A S S E T _ E 0 U I T ( 5 ) , N A M E S ( 8 ) , A S S E T _ E Q U I T( 8) ) ( R ( F M L B ) ) ; F y L B = FM2 ; P U T E D I T ( ' ' , • DO I = 1 TO 5 ; A S SE T_T OT A L = A S S ET_T OT A L + A S S ET_EQU IT I I ) END ; DO I = 6 TO 3 ; E 0 UI T_ TOT AL = E C U IT_TOT AL + A S S E T _ E O U I T ( I ) ) ( R 1 F M L B ) ) END ; PUT E D I T ( AS S E T _ T O T A L . E O U I T _ T O T A L ) ( S K I P ( 2 ) , X ( 4 0 ) , P ' S Z 2 Z Z Z Z 2 Z Z Z V . 9 9 ' , X ( 4 t > ) , P ' S Z Z Z Z Z Z Z Z Z Z V . 9 9 ' ) ; DO I = 1 TO M ; AS SE T_EOU 1 T( I ) •= D V 3 1 I ) ; 1 5 5 1 5 6 1 5 8 1 5 9 A 3 5 : END ; I F 1 1 = 2 T H E N GOTO A 3 5 ' ; GOTU A 3 0 ; P U T E D I T ( ' S T A T E M E N T OF F I N A N C I A L P O S I T I O N ( AS O F ' ' D E C . 3 1 . 1 9 7 0 ) ' . C O N S T , • I N C O M E S T A T E M E N T * J T P ~ A G E , X ( 3 0 ) , A , A , X ( 4 T, A , S K I P ! 4 T 1 6 0 1 6 1 1 6 2 1 5 3 X ( 5 0 ) FMLB = F M 3 : F M L B 2 = FM4 ; PUT E D I T ( NAME S ( 9 ) , PU T CO I f ( N AM E S ( 11 ) , , A , S K I P ( 4 ) ) I N C U M E _ S T M T ( 9 ) ) ( R ( F M L B 2 ) ) 1 N C O M E _ S T M T ! 11) ) ( R ( F M L B ) ) P T J T T I J T T ( N A M E S f 12 ) , 1NCUM E _ S T M T ( 1 2 ) ) f R T F M L B ) F PUT E D I T ( N A M E S ! 1 3 ) , 1 N C U M E _ S T M T ( 1 3 ) ) ( R ( F M L B ) ) AS S ET_T 0T AL = 1NCOM E_S TMT( 11) + I N C O M E _ S T M T ! 1 2 ) I N C O M E _ S T M T l 1 3 ) ; E O U I T _ T O T A L = 1 N C O M E _ S T M T ( 9 ) + A S S E T _ T C T A L ; NE T_ I NC OME = E QU I T_T OT AL + INCOM E_STMT ( 1 0 ) ; •O P U T E D I T ( ' . ' ) t S K I P ( 2 ) . X ( 4 0 ) , A ) ; PUT E D I T ( A S S E T _ T O T A L ) ( S K I P ( 2 ) , X ( 4 0 ) , P ' S Z 2 2 Z 2 2 2 2 Z Z V . 9 9 • ) ; PUT E D I T ( ' I N C O M E P R I O R TO E X T R A O R D I N A R Y I T E M ' , E Q U I T _ T O T A L ) ( S K I P ( 2 ) . X ( 1 0 ) , A , X ( 5 6 ) , P ' S Z Z Z Z Z Z Z Z Z Z V . 9 9 • ) ; PUT E D I T ( N A M E S ( 1 0 ) , I N C O M E _ S T M T ( 10 I ) ( R ( F M L B 2 ) ) ; 1 6 9 1 70 1 7 1 1 7 2 / * P R O G R A M A C C T L.~ V . M A T V E I E F M A R C H 1 9 7 0 * / PAGE S T M T L E V E L N E S T 1 7 3 1 1 7 4 1 7 5 176 1 7 7 P U T E D I T ! ' . . ' ) 1 S K I P ( 2 ) , X ( 1 0 0 ) , A ) PUT E D I T l ' N E T INCOME', NET_INCOME) I S K 1 P U ) ,X (10 ) , A , X ( 8 0 ) , P ' S Z Z Z Z Z Z Z Z Z Z V . 9 9 ' ) ; FM1 : FORMAT ( S K I P 1 2 ) , X ( 10) , A, X ( 5 ) , P« S Z Z Z Z Z Z Z Z Z Z V . ' 9 9 ' , X ( 1 6 ) , A, X ( 5 ) , P ' S Z Z Z Z Z Z Z Z Z Z V . 9 9 ' ) ; FM2 : FORMAT ( S K I P I 2 ) , X ( 4 0 ) , A, X I 4 6 ) , A) ; FM3 : FORMAT ( S K I P 1 2 ) , X (10 ) ,A , X ( 5 ) , P • S Z Z Z Z Z Z Z Z Z Z V . 9 9 ' ) 173 FM4 FURMAT ( S K I P l 2 ) , X( 10) X < 6 5 ) , P' S Z Z Z Z Z Z Z Z Z Z V . 9 9 ' ) 179 1 8 0 BOOWT R_T RAN : PROC : / * WRITE A TRANSACTION RECORD * / PUT F I L E (TRANMST) EDIT {DAT E l , D E 3 IT_ACCOUNT,CREDIT_ACCOUNT, AMOUNT, REF, EXPLANATION) 18 1 ( F ( 6 ) , F ( 2 ) , F ( 2 ) , F ( 1 2 , 2 ) , A ( 3 ) , A ( 2 0 ) ) END 8 00wTR_TRA N 1 8 2 C O O S U B V A R 1 P R O C 1 8 3 1 8 4 1 8 5 1 8 6 / * V A R I A B L E S U 3 R 0 U I I N E 1 - M A T R I X ( 1 1 , 3 ) * / M A T R I X ! 1 1 , 3 ) = M A T R I X ( 1 1 , 3 ) + M A T R I X ( 3 , 3 ) + M A T R I X I 3 . 6 ) - DV1 ( 3 ) ; _ _ A M O U N T = M A T R I X 1 1 1 , 3 ) ; D A T E 1 = D A T E A R E A ; R E F ' ' ; T F T 1 8 8 E X P L A N A T I C N = ' C O S T O F GOODS S O L D ' C A L L B 0 0 W T R _ T R A N ; 1 8 9 E N D C 0 0 S U B V A R 1 1 4 C 1 D C O A C C T _ A L G O R : P R O C ; / * A C C O U N T I N G A L G O R I T H M * / 1 9 1 2 DO I = 1 T Q M ; 1'J? ? 1 D V 2( I ) = 0 ; 1 9 3 2 1 E N D ; 1 9 4 2 DO 1 = 1 T C M ; 1 9 5 2 1 SUM= o ; 1 9 6 2 1 0 0 J=l T O M ; 1 9 7 2 2 I F 1 = J T H E N G O T O 0 0 5 ; 19 9 ?. 2 SUM= SUM . + M A T R I X I I . J ) - M A T R I X ( J . I ) ; 2 0 0 ?. 2 DO5 : E N D ; 2 0 1 2 1 0 V 2 ( I ) = SUM : 2 0 2 2 1 EN D ; 2 0 3 2 E N D DOO A C C T _ A L G O R ; 2 0 4 1 E 0 0 S U B VAR 2 : P R O C ; / * V A R I A B L E S U B R O U T I N E 2 * / r / * PROGRAM ACCT L.- V . M A T V E I E F MARCH 1 9 7 0 * / P A G E 8 STMT L E V E L N E S T -- • - - — - V 2 0 5 2 MATR IX{ 9 , 14 ) = - DV2( 9) ; ( 2 06 2 0 7 208 2 0 9 21 0 21 1 2 2 2 2 2 2 DATE 1 = DA TEARE A ; REF = ' • ; E X P L A N A T I O N = ' C L O S I N G ENTRY - R E V ; DEB I T _ACCUUN T = 9 : C R E 0 I T _ A C C O U N T = 14 ; AMCUNT = - D V 2 19) ; -- -~ : - ---..... — •- - - 2 1 2 ... 2 CALL BOOW TR_ TRAN ; 2 1 3 2 14 2 1 5 2 2 2 MATR I X ( 1 0 , 1 4 )= - D V 2 1 1 0 ) ; " ~ DEBI T_ACCCUNT = 10 ; AMOUNT = - DV2( 10 ) ; " 2 U 2 C A L L BOO W T R_T RAN ; 2 1 7 2 1 8 2 1 9 2 2 2 M A T R I X ( 1 4 , 1 1 ) = 0 V 2 U 1 ) ; E X P L A N A T I O N = ' C L O S I N G ENTRY - E X P ' ; D E B I T _ A C C O U N T = 14 ; - .. ... 2 2 0 22 1 22 2 2 2' 2 C R E U I T _ A C C O U N T = 11 ; AMOUNT = D V 2 1 1 1 ) ; C A L L BOOW TR_TRAN ; . . . . . .  . _ . . . 2 2 3 2 MATR IX( 14 , 12 ) = DV2( 12) ; 2 2 4 2 2 5 2 2 6 2 2 2 CRE01 T _ A C C G U M = 12 ; AMOUNT = 0 V 2 ( 1 2 ) ; CALL BOOWT R_TRAN ; 2 2 7 2 M A T R I X U 4 . 1 3 ) = D V 2 1 1 3 ) ; 2 2 8 2 2 9 2 3 0 2 2 2 CR fcD IT_ACCOUNT= 13 ; AMOUNT = D V 2 C 1 3 ) ; C A L L B GOk T R _ T R A N ; 231 2 END E 0 0 S U B V A R 2 ; 2 3 ? 2 3 3 2 3 4 2 3 5 1 2 2 2 F 0 0 S U B V A R 3 : PROC ; / * S U B R O U T I N E V A R I A B L E 3 * / MA.IR1 X( 1 4 , 8 ) = - DV2 I 14} ; E X P L A N A T I O N = ' E A R N I N G S ' ; AMOUNT = - D V 2 f 1 4 ) ; - -•• - - - -0 2 J6 2 CALL B0OWTR_TRAN ; 2 3 7 2 END F 0 0 SUB VA R3 ; / * P R O G R A M A C C T L.- V . M A T V E I E F M A R C H 1 9 7 0 * / PAGE S T M T L E V E L N E S T 2 3 8 2 3 9 2 4 0 2 4 1 2 2 2 GOO F 1 N _ D 1 A G / » F I N A L V A L U E S G F D I A G O N A L S * / P R O C ; DO 1 = 1 T O M ; D V 3 I I ) = M A T R I X ( 1 , 1 ) + D V 2 ( I ) ; E N D ; 24 2 E N D G O O F I N _ D I A G ; 2 4 3 2 4 4 2 4 5 2 4 6 2 4 7 HOO F I N _ M A T R I X : MA TR IX DO 1 = 1 M A T R I X E N D ; P R O C ; = o ; T O M ; ( I . I ) = / * F I N A L M A T R I X * / D V 3 I I ) 2 4 8 2 4 9 E N D E N D H O O F I N _ M A T R I X A O O A C C T ; ON A * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * I N P U T D A T A TO A C C O U N T P R O G R A M * * A S S E T S A N D E C U I T I E S F O R B A L A N C E S H E E T * ********************************************* M A T R I X _ S I Z E = 1 4 N 0 _ C A R D S _ 0 I A G = 0 3 I N I T I A L _ R U N = ' 1 ' D A T E _ O F _ S T M T = 3 1 / 1 2 / 7 0 ; R C W _ N C ( 1 ) = 0 1 S I G f s L C I A G ( 1 ) = « • N A M E S ( 1 ) = ' C A S H O N H A N D i * » < U W . . N O I 2 ) = 0 2 S I G N_ 0 1 A G ( 2 ) = 1 ' N A M E S ( 2 ) = • A C C O U N T S R E C E I V A B L E i R C W _ . \ ' C ( 3 ) = 0 3 S I G N _ D I A G ( 3 ) = 1 ' N A M E S ! 3 ) = ' I N V E N T O R Y t • • R G W _ N G ( 4 ) = 0 4 S I G N . C I A G ( 4 ) = ' « N A M E S ( 4 ) = ' F U R N I T U R E 1 ; R C ' W _ N l ) ( 5 ) = 0 5 ' "S I G N _ U I A G t b ) = ' N ' N A M E S ( 5 ) = • D E P R E C I A T I O N - F U R N i * i R C W _ N 0 ( 6 ) = 0 6 S 1 G N _ 0 I A G ( 6 ) = 1 N * N A M E S ! 6 ) = ' A C C O U N T S P A Y A B L E i -* R O W . N i i ! 7 ) = C 7 S I G N . D I A G ( 7 ) = * N ' N A M E S ( 7 ) = • C A P I T A L S T O C K i > R O w _ N i ! ( 8 ) = C 3 S I G N _ D 1 A G ( 8 ) = ' N ' N A M E S ( 3 ) = ' R E T A I N E D E A R N I N G S " R G » v _ N C ( 9 ) = 0 9 S I G N _ C I A G ( 9 ) = * N » N A M E S ! 9 ) = ' S A L E S R E V E N U E a • f R O w . N C H 1 0 ) = 1 0 S I G N _ D I A G ( 1 0 ) = ' N • N A M E S ( 1 0 ) = ' M I S C R E V E N U E R O W _ N G ( 1 1 ) = U S i G N _ 0 I A G ( 1 1 ) = ' ' N A M E S ( 1 1 1 = ' C O S T OF G O O D S S O L D 1 • R O i v . N O ! 1 2 ) =1 2 S I G M _ 0 I A G ( 1 2 ) = ' ' N A M E S ! 1 2 ) = ' A D M I N I S T R A T I V E E X P 1 • f R O W „ N O ( 1 3 ) = 1 3 S I G N _ D I A G ( 1 3 ) = ' ' N A M E S ( 1 3 ) = • M I S C E L L A N E O U S E X P 1 • t R G H _ N C ! 1 4 ) = 1 4 S I G N _ D I A G I 1 4 ) = ' ' N A M E S ! 1 4 ) = • S U M M A R Y - R E V £ E X P • . D I A C _ E L E M E N T S ( 1 )= + 4 0 0 0 . 0 0 D I A G _ E L E M E N T S ( 2 ) = + 2 4 0 0 0 . 0 0 D I A G _ E L E M E N T S ! 3 ) = + 1 6 0 0 0 . 0 0 0 1 A G _ F L E M E N I S ( 4 ) = + l b O O O . O O D I A G_ E L E M E N T S ( 5 ) = + "" 4 0 0 0 . 0 0 D I A G _ E L E M E N T S 1 6 ) = + 2 0 0 0 0 . 0 0 0 1 A G J E L E M E N T S ( 7 ) = + 3 5 0 0 C . C O D I A G . E L E M E N T S ( 8 ) = + . 0 0 D I A G _ E L E M E N T S ! 9 ) = + . 0 0 0 1 A G _ E L E M E N T S ( 1 0 ) = + . 0 0 D I A G _ E L E M E N T S ( 1 1 ) = + . 0 0 D I A G . E L E M E N T S ( 1 2 ) = + . 0 0 O l A G _ E L E M E N T S < 1 3 ) = + " . 0 0 D I A G _ E L E M E N T S ( 1 4 ) = + . 0 0 ; - • - - - - — - — - - ' - •- • • = 0 1 0 1 6 9 D E B I T . A C C U U N T = 0 3 C R E D I T _ A C C O U N T = 0 6 AMOUNT= 9 3 0 0 0 . 0 0 E X P L A N A T I 0 N = ' M E R C H A N D I S E P J R C H A S D ' ; D A T E l = 0 2 0 1 6 9 ' D E B I T_ A C C O U N T = 1 3 CRE D I T _ ACCOUNT =06 AMOUNT= + . 1 9 0 0 0 . 0 0 E XP L A NA TI ON = ' MI SC E XP P A Y A B L E . . . • ; U A T E 1 V =0 3 0 1 6 9 C E B I T_ A C C U U N T = 0 1 C R E D I T _ A C C O U N T = 0 9 AMOUNT= + 4 5 0 0 0 . 0 0 EX P L A N A T I O N = • C A S H S A L ES ' ; / D A T E l = 0 4 0 1 6 9 D E B I T . A C C C U N T = 0 2 CR ED IT_ ACCOUNT = 0 9 AMOUN T= 1 2 7 0 0 0 . 0 0 E X P L A N A T I 0 N = • C R E D I T S A L E S ' ; DAT E l = 0 5 0 1 6 9 D E B I T . A C C O U N T = 12 C R E D I T_ A C C O U N T =01 AMOUNT= 5 0 9 0 0 . 0 0 E X P L A N A T ION = ' S A L A R I E S . E X P E N S E D A T E l = 0 o 0 1 6 9 D E B I T . ACCOUNT= 12 CR ED I T_ A C C O U N T = 0 5 AMOUNT= 1 0 0 0 . 0 0 E X P L A N A T I 0 N = ' A C C U M D E P R E C I AT ION • ; O A T E 1 = 0 7 0 1 o 9 D E B I T_ A C C O U N T = 01 C R E C I T _ ACCOUNT =04 AMOUN T = + 5 0 . 0 0 E XP L A N A T I 0 N = ' F U R N I T U R E SOLD D A T E l = 0 7 0 1 6 9 DEB IT_ ACCUU.MT= 0 1 - C R E D I T _ A C C O U N T = 10 __AMOUNT = + 3 0 . 0 0 EX P L A N A T I O N = • G A I N ON FUR^J S O L 0 • ; O A T E 1 = C 7 C 1 6 9 D E B I T . A C C C U N T = 0 5 C R £ C I T _ ACCOUNT = 0 4 AMOUN T= 3 5 0 . 0 0 E X P L A N A T I 0 N = • A C C U M D E P O N F ' J R N D E L * 1 DAT E l = 0 8 0 1 o 9 D E B I T . A C C O U N T = 0 1 C R E D I T_ A C C O U N T =02 AMOUNT= + 1 1 8 0 0 0 . 0 0 E X P L A N A T I 0 N = • C O L L E C T I O N OF C A S H * ; D A T E l = 0 9 0 1 6 9 D E B I T . ACCOUNT= 0 6 CR E D I T_ A C C O U N T = 0 1 A M O U N T = + 1 1 4 1 0 0 . 0 0 ' - i, i, E X P L A N A T I 0 N = • P A Y M E N T S TO S J P P L I E R ' ; D A T E l = 3 I C 1 6 9 D E 3 I T_ A C C Q U N T = 0 3 C R E D I T . ACCOUNT =0 3 AMOUNT= + 1 8 0 0 0 . 0 0 E X P L A N 4 T I O N = • E N D I N G I N V E N T O R Y • ; - - - - ~ - - - - - - . . . . . . . -N3 Co f S T A T E M E N T O F F I N A N C I A L P O S I T I O N i A S O F D E C . 3 1 . 1 9 & J ) B A L A N C E S H E E T r A S S E T S it) - - - E Q U I T I E S li) C A S H O N H A N O + 4 C O 0 . O O A C C O U N T S P A Y A B L E — 20000.00 A C C O U N T S R E C E I V A B L E + 2 4 0 0 0 . 0 0 _ , . . \ ._. _ I N V E N T O R Y + 1 6 0 0 0 . 0 0 C A P I T A L S T O C K - 35000.00 F U R N I T U R E + 1 5 0 0 0 . 0 0 D E P R E C I A T I O N - F U R N 4 0 0 0 . 0 0 R E T A I N E D E A R N I N G S + .00 — + 5 5 0 0 0 . 0 0 55000 .00 - • --• •- ^ • — ;-- •'- -o VO - - • • • S T A T E M E N T O F F I N A N C I A L P O S I T I O N t A S O F D E C . 3 1 . 1 9 7 0 ) B A S E D ON TIF) I N C O M E S T A T E M E N T S A L E S R E V E N U E C O S T OF G O O D S S O L D A D M I N I S T R A T I V E E X P 172000.00 9 6 0 0 0 . 0 0 5 1 9 C C . C O M I S C E L L A N E O U S E X P 1 9 0 0 0 . 0 0 1 6 6 9 0 0 . 0 0 I N C C M E P R I C R T U E X T R A O R D I N A R Y I T E M M I S C R E V E N U E 5100.00 30.00 N E T I N C O M E 5130.00 Co O ' S T A T E M E N T O F { F I N A N C I A L P O S I T I O N ( A S O F O E C . 3 1 . 1 9 7 0 ) B A L A N C E S H E E T B A S E D O N T C F J - - . f A S S E T S ( $ J E Q U I T J E S 1 $ ) C A S H tiU H A N D + A C C O U N T S R E C E I V A B L E + I N V E N T O R Y + 2 C 3 0 . 0 0 A C C O U N T S P A Y A B L E 3 3 0 0 0 . 0 0 _ 1 8 C C 0 . 0 0 C A P I T A L S T O C K _ 2 2 9 0 0 . 0 0 3 5 0 0 0 . 0 0 • - — F U R N I T U R E + D E P R E C I A T I O N - F U R N - 1 4 6 0 0 . 0 0 4 6 5 0 . 0 0 R E T A I N E D E A R N IN GS 5 1 3 0 . 0 0 + 6 3 0 3 0 . 0 0 6 3 0 3 0 . 0 0 - - — • , . , _

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