The accounting equation
Everything a business owns (its assets) was paid for either by borrowing (liabilities) or by its owners (equity). So the two sides always balance. The balance sheet is this equation laid out line by line, and every transaction in double-entry bookkeeping keeps it true.
Rearranged, it solves for any one piece: Liabilities = Assets − Equity, and Equity = Assets − Liabilities.
The expanded accounting equation
The expanded form splits equity into what owners put in and what the business has earned and kept.
Retained earnings = Beginning retained earnings + Revenues − Expenses − Dividends
Assets = Liabilities + Contributed capital + Beginning RE + Revenues − Expenses − Dividends
For a corporation, contributed capital is common stock and payouts are dividends. For a sole proprietorship, it's the owner's capital and payouts are owner draws (withdrawals). The arithmetic is the same.
Worked example
A new company raises $30,000 from its owners and borrows $40,000. In its first period it earns $25,000 of revenue, has $15,000 of expenses and pays $2,000 in dividends.
- Net income = 25,000 − 15,000 = $10,000.
- Retained earnings = 0 + 10,000 − 2,000 = $8,000.
- Equity = 30,000 + 8,000 = $38,000.
- Assets = 40,000 + 38,000 = $78,000.
| Transaction | Assets | Liabilities | Equity |
|---|---|---|---|
| Owners invest $30,000 cash | +30,000 | +30,000 | |
| Borrow $40,000 from a bank | +40,000 | +40,000 | |
| Earn $25,000 revenue in cash | +25,000 | +25,000 | |
| Pay $15,000 of expenses | −15,000 | −15,000 | |
| Pay $2,000 dividends | −2,000 | −2,000 | |
| Total | 78,000 | 40,000 | 38,000 |
Limitations
- This checks the arithmetic of the equation, not whether your figures are recorded correctly. A balanced equation can still hide offsetting errors.
- The expanded form here covers one period with simple items. Real statements add other comprehensive income, treasury stock and more.
- Negative equity is possible (liabilities larger than assets) and is shown as such.