One way to develop an appreciation for the power and beauty of doubleentry is to derive consistent transaction vectors, i.e., start with financial statements and derive the transaction amounts that could have generated the statements. Working backward to uncover transactions (the inverting exercise) complements the more traditional approach of working forward from transactions to financial statements. In addition, the approach highlights a fundamental accounting activity: aggregation. Financial statements summarize a firm's transactions using only a relatively small number of account balances. A consequence of aggregation is that there are infinite consistent transaction vectors. However, because these infinite solutions are all prepared in accordance with double‐entry, they are linked to each other in a systematic fashion. We show how a directed graph representation of the accounting system can be used as a parsimonious means of characterizing all consistent transaction vectors. As the number of accounts and transactions are increased, the inverting exercise becomes tedious if one does not make use of the directed graph. To emphasize this point, the inverting exercise is conducted using a set of published financial statements. We also discuss the issue of picking the most likely transaction vector from the set of consistent transaction vectors. The authors have used this note in undergraduate, M.B.A., and Ph.D. classes. For the Ph.D. class, the note has been supplemented by the more rigorous analyses in the linear algebra literature and the accounting literature.
Skip Nav Destination
Article navigation
1 August 2000
Research Article|
August 01 2000
Estimating Transactions Given Balance Sheets and an Income Statement Available to Purchase
Anil Arya, Associate Professor;
Anil Arya, Associate Professor
Ohio State University.
Search for other works by this author on:
John C. Fellingham, Professor;
John C. Fellingham, Professor
Ohio State University.
Search for other works by this author on:
Douglas A. Schroeder, Associate Professor
Douglas A. Schroeder, Associate Professor
Ohio State University.
Search for other works by this author on:
Online ISSN: 1558-7983
Print ISSN: 0739-3172
American Accounting Association
2000
Issues in Accounting Education (2000) 15 (3): 393–411.
Citation
Anil Arya, John C. Fellingham, Douglas A. Schroeder; Estimating Transactions Given Balance Sheets and an Income Statement. Issues in Accounting Education 1 August 2000; 15 (3): 393–411. https://doi.org/10.2308/iace.2000.15.3.393
Download citation file:
Pay-Per-View Access
$25.00