Matrix Accounting Primer
Suppose Pacioli Had a Computer
How Accounting Theory Fits Electronic Media Better Than Paper
We propose that Accounting has always been transaction-oriented and that automation of Accounting records to date has reduced the accountant's ability to work with whole transactions.
Perhaps the inventors of the 'Italian method' had a multidimensional concept of transactions but were restricted to two-dimension paper for a medium. The task of posting is an effective way to reduce a multidimensional event to two-dimension paper.
Replacment of the ledger with the patented index of transactions results in more flexible reports and significantly less process effort.
- Revolutionary visual of accounting flow
- Patterns create information
- Key relationships immediately apparent
- Identify exceptions and major transaction flows
Accountants and Auditors have long known that the journal entries contain information of a different kind from what is found in the ledgers or the trial balance. The method proposed here shifts some of the emphasis of Accounting from trial balance, ledgers, and statements to the journals. In this regard, the method is revolutionary. Parts of the method proposed in this presentation are found in ABACUS, Sept. 1992 and INTERNAL AUDITING, Spring, 1996.
Patterns of behavior is a familiar human term. Patterns of business behavior are partially documented in transactions, which are then partially documented in journal entries. To the extent that these patterns of entries are useful, the index gives us new information. A credit sale is not equal to a cash sale, for instance.
The management and audit of frequent transactions is different from that of infrequent ones. Probably, frequent transactions are well supervised. Here, verification of procedure is important. We know that infrequent transactions are unlikely to be done under a procedure so a signal of frequency is useful to the Accounting manager.
This method helps the Accountant to separate exceptions from the better-organized main operation and to manage them from different viewpoints.
Notice that the Trial Balance is depicted as a horizontal bar. The concept of the Trial Balance being merely a total of journal entries is developed further in Exhibit 3, where the trial balances over time are depicted as horizontal bars of data, above and below the journal activity. For comparison, think of the totals of a cash disbursement spreadsheet, each total is related to one account, dr. or cr..
The working trial balance worksheet, developed perhaps 300 years ago, is at the center of Accounting reporting systems. However, American developments, particularly Funds Flow and Cost Accounting, are awkward on worksheets - we are forced to use a periodic method of subtraction to arrive at these reports.
Funds-flow reports do not fit the worksheet. They appear to relate to tabulations made from the layers of journal entries - the 'other ends' of cash entries for cash-flow reporting, for instance.
Other logic difficulties may be alleviated with this layer design. Financial Accounting appears to be oriented toward ledgers while Managerial Accounting appears to be oriented toward activities or events - the stuff of journal entries.
This index changes the single-entry vs. double-entry debate. The Data-Pattern Index automates the whole double-entry journal rather than the single-entry posting. Double-entry logic can now be preserved in computer form.
- Posting requires relatively expensive sort and copy operations
- SQL is weak working with adjacent records
- Whole transactions not tabulated and indexed
Posting is at the heart of present-day procedure. The manual task is to copy from the journal to the (sorted) ledger. The computer task is to sort the journal and write the individual lines to the ledger.
Sorting is a rising-cost operation, the larger the job, the more costly per unit. Writing computer records is also costly because each written computer record must be checked. Posting is an expensive process in computer terms. Similarly, database joins are an expensive computer process.
The Data-Pattern Index accomplishes the task of posting without sorting or copying onto disk -- and leaves the journal entries intact!
The question is, 'Do we really need to use awkward process to arrive at the working trial balance?'
Figure 1: Transaction Layers
Accountants agree that the journal entry is meaningful in its entirety. Some of the meaning of the full transaction record is lost when the parts are separated. Auditors often look for the 'other end' of journal entries. Auditors try to scan for unusual entries, either in money amount or account construction.
The 'layers' slide shows a portion of a working trial balance with intact journal entries as they are summarized in the Data-Pattern Index. The (vertical) totals of accounts are available for traditional reports via the working trial balance, and the details of transactions are available for flow reports, management accounting, and audit analysis.
What is a layer? It is the total of all occurrences of one journal entry design. A design is usage of the identical accounts, modified by debit and credit, perhaps we can term this an account-side. Regardless of the order of accounts the first operator might select, the software puts all journal entry debits into ascending ledger order, followed by sorted credits. The defined combination is used and permutations are eliminated.
Figure 2: Transaction Layers
The key to our invention is development of a new sparse matrix technique. Five-point journal entries from a 2,000-acount chart (4,000 account-sides) leave immense vacant space in typical matrix methods.
We tally those entry designs which exist. Further, we relate all the designs which post a given account-side, hence the term Data-Pattern Index.
People and businesses specialize and prefer to repeat their operations. The journal entries which record these operations maybe expected to occupy a minute portion of multidimension space and further, the specialized few will tend to repeat often.
Exhibit 1: 13 Journal Entries
Exhibit 1 lists 13 journal entries as might be found in the first textbook exercise, except that compound entries are included as fundamental patterns. The rules over this journal are adapted from many computer packages: all debits precede all credits, more importantly, the selected debits or credits appear in ascending sequence. Three pairs of repeating entries appear.
Notice that compound entries appear in an early example. Also note that entries 4 and 5 have identical account-sides and will be summarized into one item for reporting. The detail, should it be needed, continues in the journal.
These 13 entries will appear in the following slides:
First the remaining of the 13 entries
Second, in the index itself
Third, in a restatement of the Accounting cycle which shows how layers of transaction summaries replace posting and serve as a management aid.
Entries 7 through 13 fill out the journal so that every account is posted, one side or the other.
Entries 12 and 13 illustrate another pair of entries to be combined into a single summary record.
Different patterns of posting have been accumulated for credits to Cash and Accounts Payable, and the debits to Advertising Expense and Supplies Expense.
Exhibit 2: Computer Index
The index shown in Exhibit 2 replaces the ledger. The index organizes the layers of transactions. The first three index records illustrate most of the index usage.
The first line is simply the two lines of the first journal entry shown horizontally. The two ledger postings define the key to the index. There is only one occurrence of this pattern - the tally 1, and the transaction ID, journal entry # 1, is stored in the right-hand column.
The second line illustrate a compound entry. The debit-credit balance can be seen, however, the computer reports out-of-balance conditions on query.
A new concept develops upon inspection of these entries: the precise definition of the accounts in an entry defines a specific line of the index,regardless of number of accounts in the entry. This modification of traditional accounting is the center of the index method. If the firm allows more than one posting to a given account-side in its procedure, the index combines the duplicate postings.
A journal entry defines an 'event' in accounting. The length of the journal entry defines the number of dimensions in multi-dimensional analysis (entry 2 is three-dimensional).
The third line of the index shows the transaction-flow feature in that all entries of a given precise design are totaled into one index record. Note that the two entries 3 and 10 are summarized and their transaction IDs are listed at the right-hand column. Aggregation is a problem in Accounting. This method of aggregation, totals of identical entries, seems to avoid the problems of other methods of aggregation.
Our computer friends will want to substitute the computer location of the journal entry for the entry number - making this structure a true index of entries. The observer is then able to inspect all the identical entries.
The Accounting cycle is restated in Exhibit 3. Note that each index record of Exhibit 2 is present. Each line of the central portion of Exhibit 3 corresponds to an individual index record of exhibit 2.
A table of which summaries contain a given account-side is easily constructed - observe the dollar amounts in the debit or credit half-columns of each account. This table provides two features - the traditional trail of information from the ledger back to the journal and information about the types of journal entries which posted the account. This latter is new information in accounting
Data Patterns are easily found. Searches by account-side are depicted as views of the columns in Exhibit 3. The exact lines of Exhibit 2, the index, appear on this schematic of the account cycle. The summaries selected via an account-side appear as transaction patterns. Study of transaction patterns is helpful in measuring internal control and accounting supervision. If a given account has a large number of patterns, that account is 'complex' and requires more supervision.
The 'other ends' of entries are always available. Transaction flows are always tabulated. Notice that the index is always up-to-date and able to produce reports. The closing process is merely another journal entry to this system.
A number of business problems fit this organization. If the endeavor has a master list - that includes the bill of material processor, product mix, and many data mining problems - this new logic of Accounting also applies.
Auditors have a build-in advantage in this events logic of computing. Auditors have experience in analysis of log information. If we use this advantage, we can lead, rather than follow, the reorganization of business decision logic.
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