# 3.2. Accounting Equations

The five financial statement elements noted previously serve as the inputs for equations that underlie the financial statements. This section describes the equations for three of the financial statements: balance sheet, income statement, and statement of retained earnings. A statement of retained earnings can be viewed as a component of the statement of stockholders’ equity, which shows all changes to owners’ equity, both changes resulting from retained earnings and changes resulting from share issuance or repurchase. The fourth basic financial statement, the statement of cash flows, will be discussed in a later section.

The balance sheet presents a company’s financial position at a particular point in time. It provides a listing of a company’s assets and the claims on those assets (liabilities and equity claims). The equation that underlies the balance sheet is also known as the “basic accounting equation.” A company’s financial position is reflected using the following equation:

Equation (1a)

Assets = Liabilities + Owners’ equity

Presented in this form, it is clear that claims on assets are from two sources: liabilities or owners’ equity. Owners’ equity is the residual claim of the owners (i.e., the owners’ remaining claim on the company’s assets after the liabilities are deducted). The concept of the owners’ residual claim is well illustrated by the slightly rearranged balance sheet equation, roughly equivalent to the structure commonly seen in the balance sheets of UK companies:

Equation (1b)

Assets – Liabilities = Owners’ equity

Other terms are used to denote owners’ equity, including shareholders’ equity, stockholders’ equity, net assets, equity, net worth, net book value, and partners’ capital. The exact titles depend upon the type of entity, but the equation remains the same. Owners’ equity at a given date can be further classified by its origin: capital contributed by owners, and earnings retained in the business up to that date:4

Equation (2)

Owners’ equity = Contributed capital + Retained earnings

The income statement presents the performance of a business for a specific period of time. The equation reflected in the income statement is the following:

Equation (3)

Revenue – Expenses = Net income (loss)

Note that net income (loss) is the difference between two of the elements: revenue and expenses. When a company’s revenue exceeds its expenses, it reports net income; when a company’s revenues are less than its expenses, it reports a net loss. Other terms are used synonymously with revenue, including sales and turnover (in the United Kingdom). Other terms used synonymously with net income include net profit and net earnings.

Also, as noted earlier, revenue and expenses generally relate to providing goods or services in a company’s primary business activities. In contrast, gains (losses) relate to increases (decreases) in resources that are not part of a company’s primary business activities. Distinguishing a company’s primary business activities from other business activities is important in financial analysis; however, for purposes of the accounting equation, gains are included in revenue and losses are included in expenses.

The balance sheet and income statement are two of the primary financial statements. Although these are the common terms for these statements, some variations in the names occur. A balance sheet can be referred to as a “statement of financial position” or some similar term that indicates it contains balances at a point in time. Income statements can be titled “statement of operations,” “statement of income,” “statement of profit and loss,” or some other similar term showing that it reflects the company’s operating activity for a period of time. A simplified balance sheet and income statement are shown in Exhibit 3.

Exhibit 3. Simplified Balance Sheet and Income Statement
ABC Company, Inc.
Balance Sheet
As of 31 December 20X1
ABC Company, Inc.
Income Statement
For the Year Ended 31 December 20X1
Assets2,000 Revenue250
Liabilities500 Expense50
Owners’ equity1,500 Net income200
2,000

The balance sheet represents a company’s financial position at a point in time, and the income statement represents a company’s activity over a period of time. The two statements are linked together through the retained earnings component of owners’ equity. Beginning retained earnings is the balance in this account at the beginning of the accounting period, and ending retained earnings is the balance at the end of the period. A company’s ending retained earnings is composed of the beginning balance (if any), plus net income, less any distributions to owners (dividends). Accordingly, the equation underlying retained earnings is:

Equation (4a)

Endingretainedearnings=Beginningretainedearnings+Netincome−DividendsEndingretainedearnings=Beginningretainedearnings+  Netincome−Dividends

Or, substituting Equation 3 for Net income, equivalently:

Equation (4b)

Endingretainedearnings=Beginningretainedearnings+Revenues−Expenses−DividendsEndingretainedearnings=Beginningretainedearnings+Revenues−  Expenses−Dividends

As its name suggests, retained earnings represent the earnings (i.e., net income) that are retained by the company—in other words, the amount not distributed as dividends to owners. Retained earnings is a component of owners’ equity and links the “as of” balance sheet equation with the “activity” equation of the income statement. To provide a combined representation of the balance sheet and income statement, we can substitute Equation 2 into Equation 1a. This becomes the expanded accounting equation:

Equation (5a)

Assets = Liabilities + Contributed capital + Ending retained earnings

Or equivalently, substituting Equation 4b into Equation 5a, we can write:

Equation (5b)

Assets=Liabilities+Contributedcapital+Beginningretainedearnings+Revenue−Expenses−DividendsAssets=Liabilities+Contributedcapital+Beginningretainedearnings+  Revenue−Expenses−Dividends

The last five items, beginning with contributed capital, are components of owners’ equity.

The statement of retained earnings shows the linkage between the balance sheet and income statement. Exhibit 4 shows a simplified example of financial statements for a company that began the year with retained earnings of $250 and recognized$200 of net income during the period. The example assumes the company paid no dividends and, therefore, had ending retained earnings of \$450.

Exhibit 4. Simplified Balance Sheet, Income Statement, and Statement of Retained Earnings
Point in Time: Beginning of Period Balance Sheet Change over Time: Income Statement and Changes in Retained Earnings Point in Time: End of Period Balance Sheet
ABC Company, Inc.
(Beginning) Balance Sheet
As of 31 December 20X0
ABC Company, Inc.
Income Statement
Year Ended 31 December 20X1
ABC Company, Inc.
(Ending) Balance Sheet
As of 31 December 20X1
Assets2,000 Revenue250 Assets2,200
Expense50
Liabilities500 Net income200 Liabilities500
Contributed equity1,250 Combined equity1,250
Retained earnings250 Retained earnings450
Owners’ equity1,500 Owners’ equity1,700
2,000 2,200
ABC Company, Inc.
Statement of Retained Earnings Year Ended 31 December 20X1
Beginning retained earnings250
Plus net income200
Minus dividends0
Ending retained earnings450

The basic accounting equation reflected in the balance sheet (Assets = Liabilities + Owners’ equity) implies that every recorded transaction affects at least two accounts in order to keep the equation in balance, hence the term double-entry accounting that is sometimes used to describe the accounting process. For example, the use of cash to purchase equipment affects two accounts (both asset accounts): cash decreases and equipment increases. As another example, the use of cash to pay off a liability also affects two accounts (one asset account and one liability account): cash decreases and the liability decreases. With each transaction, the accounting equation remains in balance, which is a fundamental accounting concept. Example 1 presents a partial balance sheet for an actual company and an application of the accounting equation. Examples 2 and 3 provide further practice for applying the accounting equations.