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Accounting : from an information systems perspective Matveief, Vladimir Anatole 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 presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Commerce and Business Administration The University of British Columbia Vancouver 8, Canada Date April 23, 1970 ABSTRACT The author extended the synthesis of the so-called accounting spread sheet into a more compact and mathema tically rigorous formulation. This formulation was applied to an example in the form of a computerized accounting information system. 1 The systematic approach used bridges the communication gap betv/een the accounting profession and the quantitative! oriented computer specialists who design computer based accounting systems. The use of tensor analysis and coordinate transforma tions in accounting theory was also explored. The author be lieves this 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 10 III ORGANIZATIONAL DEVELOPMENT . . ... . .13 A. Short and long run considerations . . . . . . . •' . .13 B. The worth of information  Ik-C. Financial information in perspective. 15 D. Conceptual framework for information systems design .16 E. Information systems design . . . . . ,17 F. The characteristics of information . . . 20 IV ACCOUNTING INFORMATION CHARACTERISTICS . . .22 A. Overview. . • . . 2B. Accounting activities 3 C. Use of accounting information . . . . .25 CHAPTER Page V THE ACCOUNTING SPREAD SHEET . 27 A. Matrix representation 2B. Matrix accounting . . . . ... . .29 VI EXTENDING THE ACCOUNTING SPREAD SHEET ... 31 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 . . 32 C. Theoretical analysis of the extended matrix accounting approach . . . 35 D. An example . 38 VII STATE OF THE ART. ... ... . . . . .52 A. Simple transactions . . . . ... .53 B. Arithmetic n-space and transformation of coordinates 55 C. Contravariant and covariant tensors . . 57 D. Use of coordinate transformations in accounting . . . . . 59 VIII CONCLUSIONS . 61 A. Summary . .  . 61 B. Direction for further research . . . . . 62 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 constructive advice and criticism, and the valuable support received from his academic teachers: Professor Richard V. Mattessich, Professor C.L. Mitchell, Professor Vance F. Mitchell and Professor Hart-mut J. Will. Furthermore, the author thanks his wife Larissa for her assistance in writing and implementing the computer example developed in this thesis. I. INTRODUCTION (JUSTIFICATION OF STUDY) This thesis develops specialized insights into computer ized accounting information systems. The author is guided by a conceptual framework (Will, 1968) outlining information systems characteristics,of. accoun ting. Research in accounting (Mattessich, 1957; 196*t; Ijiri, 1965, 1967; ... ) is viewed in the confines of organizational theory (March and Simon, 1958; Cyert and March, 1963; ... ) and some of the accumulated knowledge is applied. An attempt is also made to utilize 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 historically used information technology of the times to provide the organization with an important component of what is currently referred to as Management Information Systems. Accounting thought and practice is essentially steeped in management and systems sciences. "It is hoped that a better understanding of the informa tion systems characteristics of accounting will be helpful in developing better information systems 11. (Will, 1968) 2 A. Study in perspective; Accounting information systems are considered to be essential entities in the overall framework of manageri-ally useful information systems. From the practical viewpoint, the author extended the synthesis of the so-called accounting spread sheet (Mat.te-ssich, 1957; Kohler, 1963; Ijiri, 1965) into a more com pact and mathematically rigorous formulation, and applied it to an example in the form of a computerized accounting sys tem. From the theoretical viewpoint, the author believes that accounting systems may be interrelated through the use of tensors and transformation of coordinates. However these thoughts have to be further researched and applied to an example. B. Purpose of thesis: The contemporary problems of an operational accounting information system can be attacked through the practical app lication of interdisciplinary research. The thesis will i. provide a perspective on the relevance of accoun-3 ting information to organizations; ii. develop a systematic analysis of financial accounting information from the computer spe cialists viewpoint; iii. use the extended matrix representation of the accounting spread sheet in generating the fi nancial statements. A systematic approach is 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 logically 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 in 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 activities, will 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; ii. viewing accounting information systems in the broader field of management information systems; The practical considerations depend on the ability 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 it is a resource utilized by all 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 is an important area for further study. Appendix one lists the explicitly programmed version of the accounting system example; it is programmed in the PL/1 computer language, and is 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 lysis or classification and storage of costs or other accoun ting data. Algorithm; a step-by-step procedure that always yields a so lution to a problem in a finite number of steps. Coordinate; a set of numbers used to specify the location of a point in 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 in language. 6 Surrogate: a substitute. Syntactic: concerned with the way in 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 will 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 in dea ling with the limitations of information systems within the confines of the organization and subject to its relational peculiarities. Their focal points of uncertainty avoidance, problemis-tic search, quasi-resolution of conflict, and organizational goals and learning are briefly outlined, i. Uncertainty avoidance; the dominant coalition negotiates its environment by attempting to transform uncertainty and risk into certainty equivalents. ii. Problemistic search: the solution is biased by the urgency with which it is needed; it is moti vated by the problem, and may tend to be simple-minded. iii. Quasi-resolution of conflict; the group or coali tion of individuals controlling the organization 8 are in dynamic balance with each other, and the decision rules incorporated into the firm do not provide optimal decisions, but result in v/hat is acceptable or feasible. iv. Organizational goals and learning: the reconci liation of the organization to its performance will 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 its choice of alternative actions will be highly influen ced by the availability of information, and will depend on its 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 its 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 logistics 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 in transitional behavior. The lower half or'1 technological core' is 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 will depend on the costs of improved information technology. Here information technology is seen affecting organizational structure, and is 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 it to the organizational hierar chy. Briefly, interactions between organizational subunits are coordinated through the transmission of information,.and is the result of planning and/or goal setting. The organiza tion is seen factoring its global objectives into a hierarchy of subobjectives. He also brings in the notion of the impli cit 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 ability 11 of both humans and information processing equipment, the organization must be constituted as a nearly de composable system. This is achieved by combining close ly related activities and decoupling them from hierar chically more distant activities. The macro-character istics of the organization are governed by relatively aggregate plans issued by higher level managers. Within the constraints imposed by this information,.a lower level manager then pursues his (changing) goals more or less independently. -This scheme has the essential advantage of econo-i mizing on coordination. Higher level managers adjust lower level constraints without having to know their detailed implications. Lower level managers are rela tively isolated from the rest of the organization, and .can carry on their activities without constant atten tion to most of the detailed activities of other parts of the organization."(Emery, 1969; pp.32-33) The activities of the organization provide the managerial levels with the events to be captured and retained in theaform of information for possible future use. The need for consis tent accumulation of managerially useful information can be satisfied by the use of operationally oriented information systems. The need for coordination of disparate local activi ties is an important factor favoring management information systems designed to fulfill specific objectives. Historically, information systems created and used by 12 organizations revolve around v/ell established accounting prac tices and procedures, which do not require the investment of large monetary funds for their maintenance. However, the rapid introduction of computers into all sectors of North American activity, has increased the use of information technology and organized intelligence to a level where one cannot view them as free commodities. The use of information and organized intelligence has.' to be considered as... a legitimate factor of production involving costs of collection and dissemination. In summary, information is found to be an important in gredient used by all organizations and it influences their behavior. Information can be generated and disseminated through the use of information systems, and these to some extent re flect the structure of the organization. III. ORGAN!ZATIONAL DEVELOPMENT The approach to organizational development usually in volves environmental research, positional audits, identifi 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 is 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 in 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 its global objec tives and its stated rationality. The verbalized objectives, useful in guiding the organization's specific activities 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 intelli 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 it 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, its activities and the control and allocation of its 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 its availability were found to be influenced by the behavioral aspects of the firm, to the firm's structural cha racteristics, and to the problems of coordination between or ganizational subunits. It was pointed out that i. information is the interconnecting tissue bet ween organizational subunits; ii. information flows are major determinants of orga nizational structure, and vice versa; iii. information generation involves costs of collec tion and dissemination; 15 iv. information can be generated and disseminated through the use of information systems; v. the degree of coordination within a firm is de pendent on the costs of improved information technology; vi. availability of information influences the expec tations of the firm, and its choice of alterna tives. Under the circumstances, it is felt 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 is an essential activity. It provides the organization with in formation that is useful in 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 its ability to survive. The knowledge of financial profitibility and liquidity is the operational goal of wealth and income determination. 16 This knowledge has for centuries been provided by the double entry, bookkeeping accounting information sys tem. In this perspective, financial information and organi zational development are intimately related. D. Conceptual framework for information system design; Will (1969) developed premises, pragmatic in nature, which consider information systems as means of extending managerial capabilities. The following figure graphically conveys the concept of managerial authorities defining and applying intelligence func tions (or processes) within the confines of organizational rationality. Science & philosophy of values \ anticipation p{>of purposeful activity resources -{>in formation knowledge MANAGERIAL AUTHORITY Local goals are defined, operational goals are set I DEVELOPMENT OF THE (INTELLIGENCE FUNCTIONS; OR PROCESSES Operational goals are planned and controlled through methodologies and rationales of pur poseful activities FIGURE 2.Managerial authorities developing intelligence functions. 1? In such an approach, one assumes that rationality is im posed upon the function or process. This is in line with the concept of rationality as being imposed upon the 'world' by the enquirer himself. Such an approach need not seek 'optima-lity' 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 reflect 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 its 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 files. It is felt 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 racteristics, and the idea of measurement is imbedded in them. They (information systems) provide precise causal relations, and serve purposeful needs. The output of information sys tems is reproducible,, repetitive and structured; but its use is not. Information systems design attempts to facilitate the flow of information to, from and through the organizational hierarchy. In practice, they adapt to the operational activi ties of the organization and involve all phases of logistic control. One may emphasize that the control is 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 in 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 filtering out the insignificant information. F. The characteristics of information: What is information? " ... if the notion.of management is 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, reliability, and pre dictability, then the information is considered rele vant. Relevance is thus an indicator of the degree of identity between the information system and the underlying real system. ... It is now possible to call classified 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 is fundamentally a three-dimerisional (pragmatic, semantic, syntactic) con cept is 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 is then considered as the output of data transmutation processes and is 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 in analysing accounting information systems. 22 IV. ACCOUNTING INFORMATION CHARACTERISTICS The operational goals of wealth and income determination are essentially the knowledge of financial profitability and liquidity. The objectives have for centuries been partially satisfied through the use of double entry, bookkeeping accoun ting systems. A. Overview: Accounting systems are pragmatic because the generated information is used in attaining knowledge of financial pro fitability and liquidity. The goal orientation of accounting information is 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 will provide users with consistent methods for recording valuations. Essen tially, the characteristics of accounting systems require that i. surrogate measures of the principals be establ ished; ii. surrogate structure be defined; iii. the states of the surrogate measures be main tained over time; 23 iv, the states of the surrogate measures be alter able by consistent rules. The problem of identifying the principal, when the accounting valuation is the surrogate, is a problem faced by the managerial authorities. They have the option of adopting structure of surrogates, dispensing with them altogether, or altering them. In all cases, the managerial authorities make an attempt to conform to their own objectives, and measure the principal accordingly. The structure of the surrogates is largely dictated by the classifications used in reflecting the principal. Also, goal orientation affects the measuring, recording and processing methodology used in an accounting system. In short, the accounting system is expected to supply relevant informa tion in accordance with the required organizational rationa lity. B. Accounting activities: From an information systems perspective, double entry accounting information has semantic, syntactic and pragmatic dimensions. In fact, from such a perspective, 'double entry' is no longer relevant, as it implies that an amount is re corded twice. Double entry and double classification are im-24 plicit in the structure of computerized accounting systems; peculiar classificational schemes are accepted as distingui shing features of accounting systems, which set them apart from other computerized, non-accounting systems. In light of operational systems theory, accounting acti vities have to be viewed from an internal and external acti vity -viewpoint. The characteristic distinctions between the two types of activity 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 priori 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 in the attempts to reduce accounting in formation systems io algorithms. The problems of human communication faced in describing the attributes of given measurements limit the semantic di mensions of accounting information. Also, the economic goal orientation of accounting information will effectively subor-25 dinate the syntactic dimension of accounting information to the classificational considerations long embedded and insti 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, is an indicator of the affective pressures applied. It is the ability 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 is used to generate the relevant mea sures. Here, the indicators of affective pressures and of the predicted behavior are usually financial in 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 its 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 is a major influencing factor on organizational behavior, and any attempt to clarify accounting system methodology (in information systems perspec tive) will 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 in 1927. The matrix form . is also known to American business account ing under the name of "spread sheet" (Kohler, 1963). Kohler's spread sheet is " a worksheet providing a two-way analysis or recapitulation of costs or other accounting data" and it achieves dual classification with a single entry (Mattessich, 196^; p.90). A. Matrix representation: Mattessich (1937; 196^, pp. 75-77) interpreted every transaction as a separate matrix, in 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 Ijiri (I960; 1963, pp. 82-137) has extended the usefulness of this representation by developing mathematical expressions for it, and by tying it in with li near and goal programming (Charnes, Cooper and Ijiri, 1963). The matrix formulation of the accounting spread sheet is 28 used to relate the " ... fundamental relation (of asset and equity partitioning) ..." (Ijiri, 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 w^.. represent ing the total amount of simple transactions whose debit entries are all made to the ith account and whose credit entries are all made to the jth account, is related to the changes in the asset and equity accounts AU, by the following mathematical expression (Ijiri, I963), ( W - W* ) x e » AU (1) where, V/* is the transpose matrix of V/; e is a column vector, s x 1, whose ele ments are all equal to 1; u is the resultant vector, s x 1, con taining all numerical changes to the beginning balance vector u. Some of the shortcomings of such an exposition lies in 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 final balance vector, u - Au » 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 irritant, 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 its diagonal elements. This approach does not detract from the mathematical exposition of Ijiri (1963), and in fact enhances it. B. Matrix accounting: The author.shows that there is considerable potential in the matrix representation for the development of computerized accounting information systems, i. the matrix representation contains the chart of accounts used; 30 ii. the methodology of matrix representation lets one create or define transformation mechanisms for the formulation of one matrix accounting system in 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 in the deve lopment of accounting information systems will be briefly discussed in the first 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, will be descriptively explained. The theoretical formulation is 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 itself to computer programming and to the definition of computer based files. In this respect, it has widespread applicability in 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; ii. as a model bank, the application of mathematical techniques can be viewed as dependent on the ex plicit structural characteristics of the matrix. 32 B. Descriptive analysis of matrix accounting  applied to the spread sheet: Accounting accounts may be diagrarnmatically represented by a number of arrays and extended into matrices. The matrices contain the aggregate information about the status of the accounts of the system. i. Beginning balances; the chart of accounts can be shown to be an array with as many rows or columns as there are accounts. The rows define the debit sides and the columns define the credit sides of the respective accounts (in accordance with the Ijiri notation). Since debiting and crediting of an account by the same transaction is not prac tised, the diagonal, of the resulting matrix can be reserved for the beginning balances of the accounts (this is a breakthrough in the matrix representation of the spread sheet). The beginning matrix TQ is as follows, Credits D B e N. 0 N. I b = To ( 3) i t 0 C s E S 33 ii. Postings: the exogenous transactions, or post ings, are the components w. . developed by Ijiri (1963)> and consist of linear aggregation of one or more similar simple transactions to given non-diagonal elements, 0 0 w. . ij w. . 10 0 w ( k) iii. Accruals and portfolio changes: the exogenous transactions w„ mirror events ocurring in the "real" world. They have been supplemented by endogenous variables to reflect the events im posed upon the system by the rationality and methodology of the specific scheme. These are represented by the a. ,'s first developed in this thesis; these are similar to the w. .'s, except that they are generated through internal compu tation, and according to preset rules, a. . ij a. . i0 0 = A (5) 3k iv. The time dimension: time is implicit in all three matrices, a. at time p , the opening balance is TQ b. at some subsequent time p, , all w. . have been posted for the time period p^ - pQ; 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 all mapped principals for a gi ven accounting system can be contained in the T-matrix, where, . - T =' T * W + A (6) vi. 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 is important to view the T-matrix as consisting of all relevant accounts of an account structure, and not limited to the balance sheet or the income statement accounts. The matrix extrac ted is defined in accordance to the financial state ment requirements, and consists only of those accounts that are of interest. 35 The derived T-matrix is a composite, and is the end re sult of a number of previous operations. It is quite possible to set up non-financial T-matrices preceding the financial T-matrix. As a suggestion, the notion of composite T-matrix (resulting from the amalgamation of several, disparate matrices) can be extended to inventories (opening inventories, issues/ receipts, commitments/on-orders)„ It can also be extended to price and quantity purchased, and to price and quantity sold matrices; as well as to the logistics preceding the account ing measurements. In this respect, accounting and management science inter face, and the multidimensionality of a given simple financial transaction can be utilized to better advantage by both dis ciplines. C. Theoretical analysis of the extended matrix  accounting approach: The need for an extended matrix accounting theory is 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 situa tion. i. Theoretical development of the T-matrix; the T-matrix is 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 is a structure en compassing all of the accounts of the chart of accounts, and is 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.. XX 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 in financial accounting). ii. The algorithm; the outstanding balances are cal culated by means of the following expression T x e = ( TQ + ( T±J - T )) x e = tf (10) where t^. is the ending balance vector, n x 1, whose elements become the components of [ ^ii] °^ tiie i>ollowinS accounting period. iii. Verification of posting; the accuracy of the com putational process is checked by mailing use of the following relationship, en x To = en x T = 0 where T e is the transpose -of a column vector con-n sisting of all elements equal to 1. iv. Changes to the ;T-matrix: a summary aggregation o all changes to the accounting system by entries affecting it are obtained through vector subtrac 38 tion, ' tf - tQ = At (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 is interesting to note that the above approach allows one to think in terms of im posed boundary conditions (the beginning balance T ), and in 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 in 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 in this thesis will be illustrated 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 Shilling-law (1969), and then used to bring out the practicality of the extended theory of matrix accounting. In the example, the statement of Financial Position as of December 31, 19x7 was given as 39 BALANCE SHEET ASSETS EQUITIES Cash on hand 4,000 Accounts receivable 24,000 Inventory 16,000 Furniture 15,000 less Depreciation4,000 11,000-Accounts payable 20,000 Capital stock 35,000 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 capital stock 8 retained earnings 9 sales revenue 10 miscellaneous revenue 11 cost of goods sold 12 administrative expenses 13 miscellaneous expenses 14 summary accounts Initial balances Debit 4,000 24,000 16,000 15,000 Credit 4,000 20,000 35,000 40 The accounting entries to be posted were the following-, 1. Merchandise purchased inventory 98,000 accounts payable 98,000 2. Expenses payable miscel. expenses 19,000 accounts payable 19,000 3. Cash sales cash on hand 45,000 sales revenue 45,000 4. Credit sales 5. Salaries accounts receivable 127,000 sales revenue 127,000 administrative expenses 50,900 cash on hand .s 50,900 6. Accumulated depreciation administrative expenses 1,000 depreciation-furniture 1,000 7. Furniture sold cash on hand 50 furniture 0 8. Gain on sale 9. Write-off cash on hand 30 miscel. revenue 0 depreciation-furniture 350 furniture 350 10. Collection 11. Payments cash on hand 118,000 accounts receivable accounts payable 114,100 cash on hand 12. Ending inventory was determined at $18,000. 41 118,000 114,100 The above information is enough to generate the finan cial statements from. In order the calculations are reason ably clear to follow, all the relevant vectors and matrices v/ill be explicitly listed. Referring to equation (8), t.. and e'.. are defined .ii ii in the following manner,( in OOO's ) 4 t. . ii 24 16 0.0 15 20 35 0 0 0.0 0 0 0 and, ( in units ), k2 11 -1 si 0.0 -1 0.0 -1 -1 -1 The matrix multiplication for x gives the TQ matrix with the following values in 000's, T. 24 16 15 0.0 -4 -20 o;o -35 0 0 0 0 0 The matrix V/ is 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 pQ, the matrix TQ was ge- ; nerated in 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 will go on until such time p^ when the financial statements are requested. At p^ the closing inventory valuation will be required, in order that the closing entries can be made; the endogenous mat-rix A is 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 = 16-18 -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 in terms of the component matrices T , V/ and A. It is now assumed that the principles have been sufficiently well outlined, and the attention will be focused on the T-raatrix as defined in equa tion ( 6). The T-matrix, at time p,, will have the folowing elements 45 l 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 0 0 0 96 0 50.9 1 0 19 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 all active accounts, ( T - TT ) x e = Atint (14) and can be applied to the revenue and expense account numbers 9, 10, 11, 12 and 13. The outstanding balances in these accounts will then be transfered by means of endogenous tran saction entries into the summary account number 14. 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 0 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) is applied to the summary account number 14, in order to deter mine the retained earnings balance. The balance is then used to create the last 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, it is clear that the T-matrix has at this moment all 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 is 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 in the T-matrix, the calculation of (T-TT)xe = At.nt (14) will provide one with an intermediate vector whose components are the net transaction balances of all exogenously activated accounts. The components of the matrix ( T - T ) are not ex plicitly shown in this discussion. They are similar to the components of a matrix developed further in the section, and shown on page 50. The net transaction balances of all 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 will result in 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 will be noted that the accounts involved in the Income Statement have zero beginning balances. This is because they are aggregation of entries to accounts that are set to zero at the end of an accounting period. The traditional trial ba lance and adjusted trial 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 all the endogenous transactions have been posted. The entries at the time of the determination of the balance sheet are arranged in 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 all 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 in printing out the balance sheet (and in supplying the T-matrix with a new set of beginning balances for the following period). The elements of(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 -°96 -96 50.9 1 -51.9 19 -15.13 472->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 will 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 tical 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 in accordance with the way the aggregate will be used. Though the determination of ration ality is not a problem of accounting per se, the reflected rationality requires explicit 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 tivities involving measurement in general. They are seen as being independent of the particular coordinate system used in describing, classifying and aggregating them. Mathematical analysis allows one to develop alternative coordinate systems, or if they already exist, provide an explicit formulation of a coordinate system in 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 in accoun ting is commented upon. 53 •A. simple transactions: Events are recorded in 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; it is quite clear that the account structure encompasses the sum total of the one-to-one reciprocal correspondences between all dimen sions Of all 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, is not unique. It is quite possible that the amount A i k have different dimensions xJ and x in 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 in 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, it cannot be changed by the accounting system used in recording the transaction. 54 If the valuation ofvthe assets is recorded through amounts A exogenous to the accounting system, then the linear aggregate of accounting quantities is governed by' the inputs to the given accounting system, and the valuation is reflected through the specific account structures used, however, the valuation will remain unchanged or invariant. The linear aggregate of $100. will 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 its sum total will 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 explicit formulation of one coordinate system in terms of another can be made avai lable through the specification of coordinate transformation equations. Sections B and C of this chapter v/ill introduce the conc epts of arithmetic n-space, transformation of coordinates, co-variant and contravariant tensors, all of which may be rele vant to accounting theory. 55 B. Arithmetic n-space and, transformation of coordinates; The intention here is 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 is partly based on the position of points in space that is not necessarily three-dimensional ( a manifold of points ), and partly on the ana lysis of numbers defined through point positions in space. By replacing lengths and magnitudes by positions carries with it a purely spatial and no longer material conception of ex tension. , In three dimensional space, a point is 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 in 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 in locating an n-diraensional point within a space of n-dimensions. Any set of objects which can be placed in a one-to-one reciprocal correspondence with an arithmetic n-space, will 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 ) , if y1 - y1 (x^x2, ... xn) i = 1,2, ... n (IS) and assuming that x1 can be solved for, so that x1 = x1 (y1^2, ... y11) i - 1,2, ... n (ife) where y^nd x1 are single valued. Then the point P can be put into correspondence with the n-tuple (y^y2, ... y11). The point P has not changed, but a new method for attaching numbers to the point has been made available. The equation (15) is called a transformation of coordinates system of equations, and results in a new coordi nate system being defined. 57 Contravariant and covariant tensors: The abstracts spatial development of the variable rela tion-values between points relies in 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. 12 n In general, any set of n quantities A ,A , ..... AX in a coordinate system (x\x2, ... xn) can be related to n other quantities A.\A2, ...AN in another coordinate system (x\x2,-... xn) 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 first rank, or of the first order. Similarly, n quantities A-^A^, ... Aft in a coordinate 2' X 2 ii system (x ,x , ... x ) relate to n other quantities 5-^,1 » "^2 xi • ••.A in another coordinate system (x"~,x , ...x ) by the 58 transformation equations A. P A q A q P = 1,2, n (18) which are defined as the components of a covariant vector or covariant tensor of the first rank or first order. The tensor is not just the set of components in one co ordinate' system, but an abstract quantity which is represented nents AH or A^. If, for example, the components of a contra-variant tensor are known in one coordinate system, then the components are known in all other allowable systems by the equation (IT-). The coordinate system does not give a new vec tor, it changes the components of the same vector; in other words, the contravariant tensor is an invariant under a co ordinate transformation (an object of any kind which is not changed, by transformations of coordinates is called an in variant). in each coordinate system (x ,x", xn) 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 if it is supplemented by the definition of numbers through point-positions in 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 in describing and aggre gating them mathematically. Their invariance permits tensor analysis to be applied to the theory of accounting. 12 n _i _2 _vi As an example, let (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, x1 = x1 (x1,^2, ... xn) i = 1.2, n or, x1 (x^x2, i = 1,2, n (20) Once the relations are defined, an explicit 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 in more than one coordinate system, and thus it may be expressed in the components of the contravariant or covariant tensors of the first rank. . The amount of the entry is independent of the particular chart of accounts used, or imposed upon it. 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) will be needed in order to create accounting informa tion systems. 61 VIII. CONCLUSIONS The thesis drew .upon existing knowledge, and added to it by extending the application of computerized accounting sys tems. The tangible contributions made to accounting from an information systems perspective are summarized in the first 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 stics of the firm, and to the problems of coordi nation facing an organization; ii. information systems generated in conformance v/ith the objectives of organizational development; iii. the characteristics of information and information systems. The thesis then ' i. traced the development of the accounting spread sheet in matrix form; ii. 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 its (matrix) appli cability to computerized accounting information systems; iii. applied the findings and analysis to a simple com puterized accounting system using periodic inven tory valuation; iv. explored the use of tensors and coordinate trans formation equations in the field of accounting. B• Direction for further research: The systematic development of accounting systems for com puters will help i. bridge the communication gap between the account ing profession and the quantitatively oriented computer specialists; ii. improve the quality of the documentation available on existing computerized accounting systems; iii. 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 it will help clarify 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 cit and implicit formulation of structural relationships bet ween accounting systems should be attempted. Examples of auch relationships will 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 in Cost Accounting: a discipline in transition", Boston: Houghton Mifflin Co. Blumenthal, S.H., 1969, "Management Information Systems", Engle wood Cliffs: 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 Cliffs: Prentice-Hall Inc. Cyert,R.M.,and J.G. March, 1965, "A Behavioral Theory of the Firm", Englewood Cliffs, N.J.: Prentice-Hall Inc. Dearden,J., 1962, "Cost and Budget Analysis", Englewood Cliffs, 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 Cliffs, N.J.,Prentice-Hall Inc. 65 Ijiri, Y.,1967, "The Foundations of Accounting Measurement; a mathematical, economic and behavioral enquiry", Englewood Cliffs, .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 Cliffs, N.J.: Prentice-Hall, Inc. Lass, H., 1950, "Vector and Tensor Analysis", New York: McGraw-Hill Book Co.,Inc. Likert, R. ,1961, "New Patterns of Management", New York: Mc Graw-Hill Book Co.,Inc. , March, J.G. & H.A. Simon, 1958, "Organizations", New York: John 1 Wiley and Sons Marin, J., 1967, "Design of Real-time Computer Systems", Engle wood Cliffs, K.J.: Prentice-Hall Inc. Mattessich, R., 1964, "Accounting and Analytical Methods", Home-wood, 111.,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 Gordon, M.J. & Shillinglaw, 1969, 11 Accounting: a managerial approach", (4th ed.), Homewood,111: Richard D. Irwin Inc. Simon, H.A., 1945, "Administrative Behavior",(2nd ed.), N.Y.: The Free Press (1965) Thompson, J.D., 1967, "Organizations in Action", New York: Mc Graw-Hill Book Co. Webster, E., 1964, "How to win the business game", Harmonds-worth; Penguin 3ooks 66 Will, H.J.,1969, "A Critical Analysis of the Assumptions Under lying Selected Managerial Accounting Models: An in formation systems approach", Ph.D. dissertation, University of Illinois,111. ,1969, "Management Information Systems", Faculty of Commerce and Business Administration, The University of British 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 FILES */ 2 1 DCL TRANMST FILE OUTPUT ; /* TRANSACTION TAPE,STREAM I/O * / 3 1 ' OCL SYSIN FILE 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) CHAR(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 llllllllllM. 99' ;  12 1 DCL DV2 (18) PIC'SIZZlllllllM .9 9' ; 13 1 L DV3 (18) PIC'S2Z111111ZZV.99« ; 14 1 DCL DAT LI PIC999999' ; \b 1 L DEB I T_ACCOUNT " PIC'99' ; "" ""' 16 1 DCL CREDIT_ACCOUNT PIC'99' ; 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 L 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) PIC SZZZZZZZZZZV.99' ; 2 I 1 CCL SUM PIC'SZZZZZZZZZZV.99' ;  28 1 UCL Fl CHAR177) ; 29 1 DCL F2 CHAR(52) ; 30 1 L 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« IMITO) ; 35 1 DCL ASSET.EOUIT (18) PIC'SZZZZZZZZZZV.99' ; 36 1 L CONST CHAR130) INIT(' •) ; 3 7 I DO I = 1 TO 13 PROGRAM ACCT L- V.MATVEIEF MARCH 1970 */ PAGE 3 STMT LEVEL NEST -- - -- - - -•- - •— - -V 3 a ! 1 ROW NO (I) = 0 ; f 1 1 SIGN_OIAGU) = • • ; 40 1 1 NAME S(I ) = • ' ; 41 1 1 C I AG_ EL EM ENTS ( I ) = 0 ; 42 1 1 DVI (I) = o ; "•" 43 1 ' 1 0 v 2 ( I) = o ; 44 1 1 DV31 I) = 0 : 45 1 1 iNCOME_STMl(1) = 0 ; 46 1 1 ASSET_EOUIT(I) = 0 ; 47 1 1 ENO ; t8 1 DO I = 1 TO 18 ; 49 1 1 00 J = 1 TO 18 ; 5C 1 2 MATRIXlI.J) =0 ; 5 1 1 2 tNU ; 52 1 1 END : 53 1 CM ENDFILE (SYS IN) GOTO A20 ; ' " " /* START MAIN PROCEDURE */ /* READ CONTROL CARD */ 55 I PUT EDIT ( ********************************************* , '* INPUT DATA TO ACCOUNT PROGRAM ** , '* ASSETS AND EQUITIES FOR BALANCE SHEET *• , (X( 30),A, SKIP(2),X(30) ,A,SKIP(2) ,X(30) «A,SKIP(2) , X(30 ) , A ) ; 5 c 1 PUT SKIP!4) ; 5 7 1 GET EDIT (MATR!X_SIZE, M0_CARDS_DIAG,INITI AL_RUN, DAT E_OF_STMT,Fl ) (F(2),F(2),A(1),F(6),A(69)) ; 58 1 PUT DATA (MATRIX_SIZE, NO_CARD S_DI AG »INITIAl RUN, GAT E_OF_STM T ) ; /* INITIAL_RUN = 1 FOR CREATING MASTER BLANK 0 THE R Wl SE <•/ 55 1 IF I NI TI AL_RUN = • • THEN GOTO A05 ; ~" /* READ IN NAMES */ 6 1 1 PUT SK1P(4) ; 62 1 M = MA rR I X_SI ZE ; 63 T L = N0_ CAR DS_U I AG ; " ' -- -- - - - ---- — — • " —~o — -64 1 DO I = 1 TC M : 65 1 1 GET EDIT ( ROW_NG (1), S1GN_DI AG(I) , NAM ES( 1) . F2 ) ( F(2) , A(l), A(25) , A(52J ) ; 6 6 1 I PUT DATA { POW_NO (I), S I GN_D IAG( I ), NAM ES( I) ) ; 67 1 1 PUT SKIPll) ; 68 1 1 END ; ' f /* PrSLKiRAf ACCT L.- V.MATVEIEF MARCH 1970 */ PAGE 4 STMT LEVEL NEST • • -- • — - . . ~ -V /* READ IN DIAGONAL ELEMENTS - 6 ELEMENTS ON EACH CARD */ f 69 7C 7 1 72 73 1 1 Kl = 1 ; K2 = 6 ; DO I = 1 TO L ; GET EDIT((DIAG_ELEMENTS (K) DO K= Kl TO K2 ) ,F3 ) (16) F112.2) , A(8) ) ; Kl = K2 + 1 ; '- -74 75 76 77 j 1 1 K2 = K2 + 6 ; END ; PUT SKIP14) ; PUT CAT A ( { 01AG_ELEMENTS(K > DO K = 1 TO M ) ) ; -- • •- ; - - -78 79 80 8 1 82 i /* PUT DI AGONAL_ELEMENTS INTO MATRIX WITH CORRECT SIGNJS */ DO I = 1 TU M ; IF S I GN_DI AG ( I ) = 'N' THEN MATRIX(I ,1) = DI AG_ E LE ME NT S (I 3 * (-1 ) ; " ELSE MATRIXil,I)= DIAG_ELEMENTS(I) ; DIAG_ELEMENTS(I) = MATRIX(l.I) ; - - • • - - - -83 84 1 END ; PUT PAGE ; 85 1 A05 : /* READ IN TRANSACTION CARDS */ GET EDIT (DATEl.OEBIT_ACCOUNT,CREDIT_ACCOUNT,AMOUNT,REF, 86 87 ' 1'"' - -EXPLANATION ,F4 ) ( F(6), F(2), F(2), F(12,2) , A(3), A(20) , A135) ) ; PUT DATA IDATEl.DEBIT_ACCOUNT« C REDIT_ACC0UNT,AMOUNT, EXPLANATION ) ; PUT SKIP(2) : . — o a 90 9 1 9 2 93 AlO : IF DEBIT_ACCOUNT = CRED IT_ACCOUNT THEN GOTO AlO ; CALL BQOWT R_T R AN ; MATRIXIQEBlT_ACCOUNT, CREDIT_ACCOUNT) = AMOUNT ; GOTU AO 5 ;' " OVl (CREDIT_ACCOUNT) = AMOUNT ; ..... . ... . ..... 94 95 96 \ A 20 : C AT t AREA = CATE1 ; GOTU A05 ; PUT EDIT ( •«*#***>?--;'**>>=>***»*<'*#***********<>*****>:•«***=»• , •*# OUTPUT DATA FROM ACCOUNT PROGRAM *' , '** ASSETS AND EQUITIES FCR BALANCE SHEET *« , H 97 1 •** INCOME STATEMENT *' , (PAGE,SKIP(2),X(30) , A , SKI P ( 2) ,X(30) ,A,SKIP(2), X(30),A,SKIP(2),X(30),A,SKIP(2),X{ 30),A ) ; PUT SKIP(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 SKIP14) ; PUT DATA [(( MATRIX(I.J) CQ J=l TO M) DO 1= 1 TO M ) ) ; TIFT 1 05 106 10 7 108 10 9 DO I = 1 To M ; INCOME_STMT(I) -END ; PUT SKIP(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 ((( MATRIX!I,J) CO J=l TO M) DO 1= 1 TO M )J ; PUT SKIP!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 (({ MATRIX(I.J) DO J=l TO M) DO 1= 1 TO M )) ; 11 3 ) IS 117 11 8 119 120 12 1 122 123 "PUTSKIPI4) ; PUT DATA ((DV2(I) DO I = I TO M ) ) ; CALL GOOFIN_DI AG ; PUT EDIT ( END PRODUCT OF ACCOUNT PROGRAM **#**' V ****** ASSETS AND EQUITIES FOR BALANCE SHEET', ( PAGE, X(30),A, SK IP12 ) ,X(30 ),A,A ) PUT SKIP(4) ; PUT DATA ((CV3(I) DO I = 1 TO M J); CALL H00FIi\_MATRIX ; 11=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 II =2 THEN CONST= ' 3 AS E D ON T (F)' ; PUT EDIT ('STATEMENT OF FINANCIAL POSITION ( AS OF' , 'DEC.31 .1970)* , CONST, 'BALANCE SHEET' , •A S SE TS ($)» , •£ OU IT I E. S . ($)' ) /* PROGRAM ACCT U. " V.MATVEIEF MARCH 1970 */ PAGE 6 STMT LEVEL NEST (PAGE. X(30).A.A. X(4). A. SKIP(4)t 138 139 140 X (50 ) , A, SKIP ( 4 ) , X(27) , A, X(48) , A ) ; PUT SKIPI2) ; PUT EDIT (NAMESd ) , AS S ET_ ECU IT (1 ), NAMES(6J, ASSET_E0UIT (6) ) (R( F MLB) ) ; PUT EDIT ( NAMES12) , ASSET_EQUIT(2) ) ( R (FMLB) ) PUT EDIT ( NAMES(3), ASSET_EOUIT(3), NAMES(7) , ASSET_EOUIT( 7) ) IR (FMLB) ) ; PUT EDIT ( NAMES(4), ASSET_EOUIT(4) ) ( R (FMLB) ) ; PUT EDIT (NAME S(5) > ASSET_E0UIT(5), N AMES(8), ASSET_EQUI T( 8) ) ( R(FMLB)) ; F y LB= FM2 ; PUT EDIT ( '  , • DO I = 1 TO 5 ; A S SE T_T OT A L = ASS ET_T OT AL + ASS ET_EQU IT I I ) END ; DO I = 6 TO 3 ; E 0 UI T_ TOT AL = ECU IT_TOT AL + ASSET_EOUIT (I) ) (R1FMLB)) END ; PUT EDIT ( AS S ET_TOTAL. EOUIT_TOTAL) ( SKIP(2), X(40), P'SZ2ZZZZ2ZZZV.99' , X(4t>), P' SZZZZZZZZZZV.99 ' ) ; DO I =1 TO M ; AS SE T_EOU 1 T( I ) •= DV31I) ; 155 156 158 159 A35 : END ; IF 11= 2 THEN GOTO A35'; GOTU A 30 ; PUT EDIT ( 'STATEMENT OF FINANCIAL POSITION ( AS OF' 'DEC.31.1970)'. CONST, •INCOME STATEMENT*J TP~AGE, X(30),A,A, X ( 4 T, A, SKIP! 4 T 160 161 162 153 X(50) FMLB = FM3 : FMLB2 = FM4 ; PUT EDIT ( NAME S(9) , PU T CO If ( N AM ES( 11 ), ,A, SKIP(4)) INCUME_STMT(9) ) (R(F MLB2) ) 1NCOME_STMT! 11) ) (R(FMLB) ) PTJTTIJTT ( NAMES f 12 ) , 1NCUM E_STMT(12)) fRTFML B ) F PUT EDIT ( NAMES! 13),1NCUME_STMT( 13)) (R(FMLB)) AS S ET_T 0T AL = 1NCOM E_S TMT( 11) + INCOME_STMT! 12) INCOME_STMTl13) ; EOUIT_TOTAL = 1NCOME_STMT(9) + ASSET_TCTAL ; NE T_ I NC OME = E QU I T_T OT AL + INCOM E_STMT ( 10 ) ; •O PUT EDIT ( ' . ' ) tSKIP(2).X(40),A) ; PUT EDIT (ASSET_TOTAL) (SKIP(2),X(40),P'SZ22Z2222ZZV.99• ) ; PUT EDIT ('INCOME PRIOR TO EXTRAORDINARY ITEM', EQUIT _TOTAL) (SKIP(2). X(10),A, X(56), P'SZZZZZZZZZZV.99• ) ; PUT E DIT( NAMES (10), INCOME_STMT( 10 I ) (R(F MLB2) ) ; 169 1 70 171 172 /* PROGRAM ACCT L.~ V.MATVEIEF MARCH 1970 */ PAGE STMT LEVEL NEST 173 1 174 175 176 177 PUT EDIT! '. .' ) 1 SKIP(2) , X ( 100 ), A) PUT EDITl'NET INCOME', NET_INCOME) ISK1PU ),X(10) ,A,X(80), P'SZZZZZZZZZZV.99' ) ; FM1 : FORMAT ( SKIP12), X ( 10) , A, X(5), P« SZZZZZZZZZZV.'99', X(16), A, X(5), P'SZZZZZZZZZZV.99' ) ; FM2 : FORMAT ( SKIPI2), X(40), A, XI46), A) ; FM3 : FORMAT ( SKIP12), X(10) ,A, X(5), P•SZZZZZZZZZZV.99' ) 173 FM4 FURMAT ( SKIPl2) , X( 10) X<65), P' SZZZZZZZZZZV.99 ' ) 179 180 BOOWT R_T RAN : PROC : /* WRITE A TRANSACTION RECORD */ PUT FILE (TRANMST) EDIT {DAT El,DE3 IT_ACCOUNT,CREDIT_ACCOUNT, AMOUNT, REF, EXPLANATION) 18 1 ( F(6), F(2), F(2), F(12,2) , A(3), A(20) ) END 8 00wTR_TRA N 182 COOSUBVAR1 PROC 1 83 184 185 186 /* VARIABLE SU3R0UI I NE 1 - MATRIX (11,3) */ MATRIX! 11,3) = MATRIX(11,3) + MATRIX(3,3) + MATRIXI3.6) - DV1 ( 3) ; __ AMOUNT = MATRIX 111,3) ; DATE 1 = DATEAREA ; REF ' ' ; TFT 188 E X PLANA TIC N = 'COST OF GOODS SOLD' CALL B 00WTR_ TRAN ; 189 END C00SUBVAR1 14C 1 DCOACCT_ALGOR : PROC ; /* ACCOUNTING ALGORITHM */ 191 2 DO I = 1 TQ M ; 1'J? ? 1 D V 2( I) = 0 ; 193 2 1 END ; 194 2 DO 1=1 TC M ; 195 2 1 SUM= o ; 196 2 1 00 J=l TO M ; 197 2 2 IF 1= J THEN GOTO 005 ; 19 9 ?. 2 SUM= SUM . + MATRIXII.J) - MATRIX(J.I) ; 200 ?. 2 DO5 :END ; 20 1 2 1 0V2 ( I) = SUM : 202 2 1 EN D ; 203 2 END DOO ACCT_ALGO R ; 204 1 E 00 SUB VAR 2 : PROC ; /* VARIABLE SUBROUTINE 2 */ r /* PROGRAM ACCT L.- V.MATVEIEF MARCH 1970 */ PAGE 8 STMT LEVEL NEST -- • -- — -V 205 2 MATR IX{ 9, 14 ) = - DV2( 9) ; ( 206 207 208 209 21 0 21 1 2 2 2 2 2 2 DATE 1 = DA TEARE A ; REF = ' • ; EXPLANATION = 'CLOSING ENTRY - REV ; DEB I T_ACCUUN T = 9 : CRE0IT_ACCOUNT= 14 ; AMCUNT = -DV2 19) ; -- -~: - ---..... — •- - -212 ... 2 CALL BOOW TR_ TRAN ; 213 2 14 215 2 2 2 MATR IX(10 ,14 )= - DV2110) ; " ~ DEBI T_ACCCUNT = 10 ; AMOUNT = - DV2( 10) ; " 2U 2 CALL BOO W T R_T RAN ; 217 218 219 2 2 2 MATRIX ( 14,11) = 0V2U1) ; EXPLANATION = 'CLOSING ENTRY - EXP' ; DEBIT_ACCOUNT = 14 ; - .. ... 220 22 1 22 2 2 2' 2 CREUIT_ACCOUNT = 11 ; AMOUNT = DV2111) ; CALL BOOW TR_TRAN ; ..... .  . _ . . . 223 2 MATR IX( 14, 12) = DV2( 12) ; 224 225 226 2 2 2 CRE01 T_ACCGUM = 12 ; AMOUNT = 0V2 (12) ; CALL BOOWT R_TRAN ; 227 2 MATRIXU4.13) = DV2113) ; 228 229 230 2 2 2 CRfcDIT_ACCOUNT= 13 ; AMOUNT = DV2C13) ; CALL B GOk TR_TRAN ; 231 2 END E00SUBVAR2 ; 23? 233 234 235 1 2 2 2 F00SUBVAR3 : PROC ; /* SUBROUTINE VARIABLE 3 */ MA.IR1 X( 14,8) = - DV2 I 14} ; EXPLANATION = 'EARNINGS' ; AMOUNT = -DV2 f14) ; - -•• - - --0 2 J6 2 CALL B0OWTR_TRAN ; 237 2 END F 00 SUB VA R3 ; /* PROGRAM ACCT L.- V.MATVEIEF MARCH 1970 */ PAGE STMT LEVEL NEST 238 239 240 241 2 2 2 GOO F 1N_D1 AG /» FINAL VALUES GF DIAGONALS */ PROC ; DO 1=1 TO M ; DV3 II) = MATRIX (1,1) + DV2(I) ; END ; 24 2 END GOOF IN_DI AG ; 243 244 245 24 6 247 HOO FIN_MATRI X : MA TR IX DO 1=1 MATRIX END ; PROC ; = o ; TO M ; (I.I) = /* FINAL MATRI X */ DV3 II) 248 249 END END HOOF IN_MA TRIX AOOACCT ; ON A****************************************** * INPUT DATA TO ACCOUNT PROGRAM * * ASSETS AND ECUITIES FOR BALANCE SHEET * ********************************************* MA TRIX_SIZE= 14 N0_CARDS_0IAG=03 IN ITIAL_RU N=' 1' DATE_OF_STMT=31/12/70; RCW_NC(1)=01 S IGfsLCI AG(1)=« • NAM E S( 1 )='CASH ON HAND i * » <UW..NOI 2) =02 SIG N_ 01 AG ( 2 ) =1 ' NAMES(2 )=•ACCOUNTS RECEIVABLE i RCW_.\'C (3 )=03 S IGN_ DI AG(3 ) = 1 ' NAMES!3)='INVENTORY t • • RGW_NG(4)=04 SIGN.CI AG(4)=' « NAMES(4)='FURNITURE 1 ; R C'W_Nl)( 5 ) =0 5' "S IGN_U I AG t b ) =' N' NAMES(5)=• DEPRECIAT ION - FURN i * i RCW_N0(6)=06 S 1GN_0IAG(6)=1N * NAMES!6)='ACCOUNTS PAYABLE i -* ROW.Nii! 7) =C7 SIGN.DIAG(7)=* N' NAMES (7 )=•CAPITAL STOCK i > ROw_Ni! ( 8 )= C 3 SIGN_D1AG(8)='N' NAMES(3)='RETAINED EARNINGS " R G»v_NC ( 9 ) =09 SIGN_CIAG(9)=*N» NAMES! 9 )=' SALES REVENUE a • f ROw.NCH10)=10 S IG N_ DI AG (10)=' N • NAMES(10 )='MISC REVENUE ROW_NG( 11 ) = U S i GN_0I AG( 11)= ' ' NAMES(111 ='COST OF GOODS SOLD 1 • ROiv.NO! 12) =1 2 S IGM_0IAG(12 )=' ' NAMES! 12)= 'ADMINISTRATIVE EXP 1 • f ROW„NO( 1 3)=13 SIGN_DI AG(13)=' ' NAMES(13)=•MISCELLANEOUS EXP 1 • t RGH_NC! 14) = 14 SIGN_ DI AG I 14 ) = ' ' NAMES! 14)=•SUMMARY - REV £ EXP • . D I AC_ EL EMENT S ( 1 )= + 4000.00 DIAG_ELEMENTS(2)=+ 24000.00 DI AG_ ELEMENTS!3)=+ 16000.00 01 AG_F LE ME NIS(4)= + lbOOO.OO DI A G_ ELEME NTS ( 5) = + "" 4000. 00 DI AG_ ELEMENTS 16)= + 20000.00 01AGJELEMENTS(7) = + 3500C.CO DIAG.ELEMENTS (8 )=+ .0 DIAG_ ELEMENTS!9)= + . 00 01AG_ ELEMENT S( 10 ) = + .00 DIAG_ELEMENTS(11)=+ .00 DI AG. ELEMENTS(12)=+ .00 OlAG_ELEMENTS<13)=+ " .00 DIAG_ELEMENTS( 14)=+ .00; - •-- - - — -— - - ' - •-• • =010169 DEBIT. ACCUUNT= 03 CREDIT_ ACCOUNT = 06 AMOUNT= 93000.00 EXPLANATI0N= 'MERCHANDISE PJRCHASD' ; DATEl =02 0169 ' DEB I T_ ACCOUNT= 13 CRE DIT_ ACCOUNT =06 AMOUNT= + .19000.00 E XP L A NA TI ON = ' MI SC E XP PAYABLE ... • ; UATE1 V =0 30 169 C E B I T_ ACCUUNT= 01 CREDIT_ ACCOUNT = 09 AMOUNT= + 45000.00 EX PLANATION= •CASH SAL ES '; /DATEl =040169 DEBIT. ACCCUNT= 02 CR ED IT_ ACCOUNT = 09 AMOUN T= 127000.00 EXPLANATI 0N = •CREDIT SALES '; DAT El =050169 DEBIT. ACCOUNT= 12 CREDI T_ ACCOUNT =01 AMOUNT= 50900.00 EXPL ANAT ION = 'SALARIES. EXPENSE DATEl =0o0169 DEB IT. ACCOUNT= 12 CR ED I T_ ACCOUNT = 05 AMOUNT= 1000.00 EXPLANATI0N= ' ACCUM DEPRECI AT ION •; OATE 1 =0701o9 DEB I T_ ACCOUNT= 01 CRECIT_ ACCOUNT =04 AMOUN T = + 50.00 E XP LANA TI0N = 'FURNITURE SOLD DATEl =070169 DEB IT_ ACCUU.MT= 01 - CREDIT_ ACCOUNT = 10 __AMOUNT = + 30.00 EX PLANATION = • GAIN ON FUR^J SOL0 • ; OATE 1 =C7C169 DEBIT. ACCCUNT= 05 CR£CIT_ ACCOUNT = 04 AMOUN T= 350. 00 E XPLANATI0N= •ACCUM DEP ONF'JRN DEL* 1 DAT El =0801o9 DEBIT. ACCOUNT= 01 CREDI T_ ACCOUNT =02 AMOUNT= + 118000.00 EXPL ANAT I0N = •COLLECTION OF CASH *; DATEl =090169 DEBIT. ACCOUNT= 06 CR E D I T_ ACCOUNT = 01 AMOUNT= + 114100.00 ' - i, i, EXPLANATI0N= •PAYMENTS TO SJPPLIER'; DATEl =3IC169 DE3I T_ ACCQUNT= 03 CREDIT. ACCOUNT =0 3 AMOUNT= + 18000.00 EXPLAN4 TION= •ENDING INVENTORY •; -- - - ~- -- - - - ... . .. . -N3 Co f STATEMENT OF FINANCIAL POSITION i AS OFDEC.31.19&J) BALANCE SHEET r ASSETS it) - - - E Q U IT I E S li) CASH ON HANO + 4CO0.OO ACCOUNTS PAYABLE — 20000.00 ACCOUNTS RECEIVABLE + 24000 .00 _ , . . \ ._. _ INVENTORY + 16000.00 CAPITAL STOCK - 35000.00 FURNITURE 15000.00 DEPRECIATION - FURN 4000.00 RETAINED EARNINGS + .00 — + 55000.00 55000 .00 -• --• •- ^ • — ;-- •'--o VO - - • • • STATEMENT OF FINANCIAL POSITION t AS OFDEC.31.1970) BASED ON TIF) INCOME STATEMENT SALES REVENUE COST OF GOODS SOLD ADMINISTRATIVE EXP 172000.00 96000 .00 519CC.CO MISCELLANEOUS EXP 19000 .00 166900.00 INCCME PRICR TU EXTRAORDINARY ITEM MISC REVENUE 5100.00 30.00 NET INCOME 5130.00 Co O ' STATEMENT OF { FINANCIAL POSITION ( AS OFOEC.31.1970) BALANCE SHEET BASED ON TCFJ - - . f ASSETS ( $ J E Q U I TJ E S 1$) CASH tiU HAND + ACCOUNTS RECEIVABLE + INVENTORY + 2C30.00 ACCOUNTS PAYABLE 33000 .00 _ 18CC0.00 CAPITAL STOCK _ 22900.00 35000.00 • -— FURNITUREDEPRECIATION - FURN -14600.00 465 0.00 RETAINED EARN IN GS 5130.00 + 63030.00 63030 .00 - - —• , . , _ 

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