Tags: finance

Double Entry Accounting

July 31, 2022

The rules are deceptively simple.

Rule #1: Assets = Liabilities + Equity

This equality must hold after you close the period.

Rule #2: Debits = Credits for every transaction.

This is why this is called “double-entry” accounting. Every time money moves, there is one entry for the account that is debited and one entry for the account that is credited.

A double-entry transaction is represented as a “T chart”, with debits on left and credits on the right.

            Debits  | Credits
            --------+--------
                    |
                    |
                    |

Rule #3: A credit does not always increase an account’s balance.

Whether the balance goes up or down depends on the type of account.

Account Increased By Decreased By Examples
Assets Debit Credit cash, checking account, real estate
Expenses Debit Credit food, entertainment, interest payments, etc.
Liabilities Credit Debit mortgage principle, credit card balance
Equity Credit Debit your net worth
Revenue Credit Debit paycheck, interest earned, bond dividends

Book of Accounts (more commonly called “the books”)

Let’s walk through an example—on December 1, 2022 your parents loan you $3,000 for first and last month’s rent (which you pay on the 20th) and on December 25, 2022 you get your first weekly paycheck with the following amounts on your paystub:

   1,000      Gross wages
     120      Federal income tax
      60      State income tax
      15      Medicare tax
      62      Social Security tax
      50      401k savings
  ------
     693      Net pay

      50      401k employer matches your 401K contribution

All this stuff is automated with accounting software, but I find it instructive to work through these old-school books.

The General Journal (the “book of original entry”)

Date         Accounts & Description                 Debit      Credit

12/01/2022   Checking account                       3,000
             Liabilities                                        3,000
             Loan from parents for rent

12/20/2022   Rent                                   3,000
             Checking account                                   3,000
             First and last month's rent

12/25/2022   Checking account                         693
             Federal income tax                       120
             State tax                                 60
             Social security tax                       62
             Medicare tax                              15
             401K Savings Account                     100
             Income                                             1,000
             Employer 401K match                                   50
             My first paycheck!

The general journal records transactions in date order. Each journal entry is a T-chart with a date and an optional description.

The general journal is sometimes called the “the book of original entry.”

The other journals that a business would keep are

The General Ledger (the “book of final entry”)

Account: Checking Account
Date          Description          Debit     Credit    Balance
12/01/2022    Loan                 3,000                 3,000
12/20/2022    Rent                            3,000          0
12/25/2022    Paycheck               693                   693

Account: 401K
Date          Description          Debit     Credit    Balance
12/25/2022    Paycheck                50                    50
12/25/2022    Employer match          50                   100

Account: Liabilities
Date          Description          Debit     Credit    Balance
12/20/2022    Loan                            3,000      3,000

Account: Income
Date          Description          Debit     Credit    Balance
12/25/2022    Paycheck                        1,000      1,000
12/25/2022    Employer match (non-taxable)       50      1,050

Account: Expenses
Date          Description          Debit     Credit    Balance
12/20/2022    Rent                 3,000                 3,000
12/25/2022    Federal income tax     120                 3,120
12/25/2022    State tax               60                 3,180
12/25/2022    Social security tax     62                 3,242
12/25/2022    Medicare tax            15                 3,257

The general ledger contains one or more pages per account. It is sometimes called the “book of final entry” because this is the book from which the financial statements are created.

Speaking of financial statements …

The Balance Sheet

Balance Sheet
As of December 31, 2022

Assets
  Checking               693
  401K                   100
                      -------
                         793

Liabilities
  Loan                 3,000
                      -------
                       3,000

Equity                (2,207)
                      =======

The balance sheet is a snapshot at a given point in time.

The Income Statement

Income Statement
For the period from 12/1 through 12/31/2022

Income                 1,050

Expenses               3,257

Net Income            (2,207)
                      =======

The income statement covers a period, in this example, one month.

A basic financial control

Given:

 equity_start    is the equity at a start of a period
 net_income      is the net income over that period
 equity_end      is the equity at the end of a period


 equity_end = equity_start + net_income

If not, someone is cooking the books.

In our example,

 equity_start    = 0
 net_income      = -2,207
 equity_end      = -2,207

Which matches our equity on 12/31.

Closing the year

Income and revenue accounts are reset to zero at the beginning of each year. To reset them, you “close” the year.

We add a transaction to the general journal,

Date         Accounts & Description                 Debit      Credit
12/31/2022   Income                                 1,050
             Equity                                 2,207
             Expenses                                           3,257

update the income and expenses accounts in the general ledger,

Account: Income
Date          Description          Debit     Credit    Balance
12/25/2022    Paycheck                        1,000      1,000
12/25/2022    Employer match (non-taxable)       50      1,050
12/31/2022    Close year           1,050                     0

Account: Expenses
Date          Description          Debit     Credit    Balance
12/20/2022    Rent                 3,000                 3,000
12/25/2022    Federal income tax     120                 3,120
12/25/2022    State tax               60                 3,180
12/25/2022    Social security tax     62                 3,242
12/25/2022    Medicare tax            15                 3,257
12/31/2022    Close year                      3,257          0

and add an Equity account page to the ledger.

Account: Equity
Date          Description          Debit     Credit    Balance
12/31/2022    Close year           2,207                -2,207

History

The earliest written account of double-entry accounting that I could find a reference to was Luca Pacioli’s Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportion and proportionality), published in Venice, Italy in 1494.

This was a summary work of existing knowledge, so this system was in use before this book was published.

An interesting side note is that after Venice, Luca Pacioli went to Milan to publish his second book. The illustrator for his book was none other than Leonardo da Vinci, whom Luca had befriended in Milan!

This taken from the MacTutor History of Mathematics Archive.