Double-Entry Bookkeeping

The foundation of accounting, double-entry bookkeeping, is often introduced to students in an imprecise, pedagogical manner, intended to ease the learner in into the topic by means of analogies, etc.  But actually it's much easier to understand if it's presented as it truly is: a set of definitions can then be shown to satisfy some simple mathematical identities. Once I discovered this in 2007, it was an incredibly intellectually satisfying moment and has served me very well in understanding financial statements over the years. So forget the thick textbook and just read the below.

A succinct and mathematically precise summary of bookkeeping—alla Veneziana, "in the Venetian manner", i.e. double-entry bookkeeping

- Financial statements are a set of three documents which summarize an economic entity’s activities. They can be constructed entirely from just two sources: (1) a “chart of accounts” and (2) a list of “transactions”.
- A chart of accounts is just a list of names each of which is called an "account", each of which is assigned one of five categories: Asset, Liability, Equity, Revenue, and Expense.
- Three special accounts always exist for every company: Cash (an Asset account), Retained Earnings (an Equity account), and Share Capital (an Equity Account).
- Each economic event (called a "transaction") at a company consists of a date, an amount, a debit account, and a credit account (i.e. two of the above accounts).  (The amount is the same for the debit and the credit.)
- All accounts start at 0, and debits are (+) to Asset and Revenue accounts and (-) to all others.  Credits are the opposite.
- The first transaction in every company must be a credit to Share Capital with an amount >0.  Normally the debit account for this transaction is Cash.
- Debits and credits are never associated with the Retained Earnings account, but instead with the Revenue and Expense accounts.  Retained earnings captures all revenue and expense transactions.

Financial Statements:
1. For a given date, the balance sheet is a list of all Asset, Liability, Equity accounts.  For each account, the sum of all debits and credits for that account for transactions dated on or before the date is shown. The special account, Retained Earnings, is the cumulative sum of all transactions impacting the revenue and expense accounts up to that date.
2. For a given date range, the profit and loss statement is a list of all Revenue and Expense accounts and the sum of all credits and debits during that date range.  (including both dates -> e.g. if from 1 Jan to 31 Dec, it will include all days in the calendar year) The sum of all these figures between the start and end dates is a number called the Profit.
3. For a given date range, the cash flow statement breaks down the change to the "Cash" account.  To do this, we list the change in ALL balance sheet accounts (i.e. Asset, Liability, and Equity) OTHER than cash.  Since on each date the balance sheet must sum to 0, this is equivalent.

Observations:
- Note that the change in the Retained Earnings account is precisely the Profit shown in the profit and loss statement.
- A cash flow statement can be thought of as a restatement of the balance sheet in terms of differences, with a focus on the CASH account. Another way to think of it is cash and retained earnings are additional categories, and there are no revenue or expense categories.  So categories are C, OA, L, RE, OE. In this formulation, balance sheet shows all categories, C+OA=L+RE+OE P&L shows changes to all retained earnings accounts. CF statement shows changes to all accounts OTHER than CASH.