The accounting equation

Before you start

You will be able to

State the accounting equation and explain why it must balance after every transaction.
Analyse a business transaction into its effects on assets, liabilities and equity.
Use the expanded accounting equation to show how revenue, expenses and dividends change equity.
Distinguish contributed capital from retained earnings.
Calculate a missing element of the equation, including net income, from beginning and ending balances.

Review first

Accounts, terminology and classifications — You need the five kinds of account (assets, liabilities, equity, revenue and expenses) and what belongs in each.
Adding and subtracting positive and negative numbers.

Fictional case A fictional coffee business founded by Ana Lim. It starts as a catering and barista-training service, opens its own cafés and an online shop for beans, and plans a canned cold brew.

The idea

Fictional case

On 1 March 2026 Ana Lim opens a bank account for her new company, Lantern Coffee Co., and pays in $20,000 of her own savings. In exchange the company issues her shares of common stock. The same day the company borrows $10,000 from Coastline Bank. Lantern now holds $30,000 of cash. Ask where that cash came from and there are only two answers: $10,000 came from a lender, who expects to be repaid, and $20,000 came from the owner, who expects nothing back except a share of whatever the business becomes.

That is the whole idea of this lesson. A business has resources, and every one of those resources was supplied by someone with a claim on it. Accounting records both sides of that fact: what the business has and who has a claim on it.

Three words, one equation

The resources are assets: things the business controls that are expected to bring it economic benefits, such as cash, equipment, supplies and amounts customers owe it. The claims come in two kinds. Liabilities are what the business owes to outsiders: a bank loan, a supplier’s unpaid bill, a deposit for a service not yet delivered. Equity is the owners’ claim, and it is a residual claim: the owners are entitled to whatever is left of the assets after every liability has been settled.

Because the claims account for every dollar of resources, the two must be equal. This is the accounting equation:

\text{Assets} = \text{Liabilities} + \text{Equity}

It holds for a coffee cart, a hospital and a multinational, and it holds at every moment, not just at the end of the year. It is not a rule that accountants enforce by adjusting numbers; it is true by construction, because equity is defined as what is left after liabilities. Rearranged, the equation says exactly that:

\text{Equity} = \text{Assets} - \text{Liabilities}

For this reason equity is often called net assets. After its first day, Lantern has assets of $30,000, liabilities of $10,000 and equity of $20,000, and $30{,}000 = 10{,}000 + 20{,}000$ .

Every transaction has two sides

A transaction is an exchange or event that changes the business’s resources or the claims on them. Because the equation must stay true, no transaction can change just one number. If assets go up, something else must also change: another asset goes down, a liability goes up, or equity goes up. This is the dual aspect of every transaction, and it is why the system you will learn in the next module is called double-entry bookkeeping.

Look at Lantern’s first week, transaction by transaction. For each one, ask two questions: which items changed, and in which direction?

Lantern’s first six transactions and their effect on the equation (fictional)
Transaction	Assets	Liabilities	Equity
1 Mar: Ana invests $20,000 for common stock	+20,000 Cash		+20,000 Common Stock
1 Mar: borrows $10,000 from the bank	+10,000 Cash	+10,000 Notes Payable
3 Mar: buys $12,000 of equipment, $4,000 in cash, $8,000 owed	+12,000 Equipment −4,000 Cash	+8,000 Accounts Payable
4 Mar: pays $1,800 for a year of insurance	+1,800 Prepaid Insurance −1,800 Cash
5 Mar: buys $1,500 of supplies on account	+1,500 Supplies	+1,500 Accounts Payable
8 Mar: receives a $2,400 deposit for three future events	+2,400 Cash	+2,400 Unearned Revenue
Totals after 8 March	41,900	21,900	20,000

Check: 21,900 + 20,000 = 41,900. The equation balances after every row, not just at the end.

Three things in that table are worth slowing down for. First, buying equipment partly for cash (3 March) changes three items, and the equation still balances because the asset gained ($12,000) equals the cash given up ($4,000) plus the new debt ($8,000). Second, paying for insurance in advance (4 March) changes no totals at all: one asset, cash, turns into another, the right to a year of insurance cover. Third, the deposit from Harbor Tech (8 March) brings in cash but is not income yet. Until Lantern caters the events, it owes Harbor Tech either the service or the money back, so the deposit is a liability called unearned revenue.

In depth

What the definitions say

The equation rests on precise definitions, set by the bodies that write accounting standards. In the United States the Financial Accounting Standards Board (FASB) defines an asset as “a present right of an entity to an economic benefit”, a liability as a present obligation to transfer an economic benefit, and equity as the residual interest in the assets after deducting liabilities (Concepts Statement No. 8, Chapter 4, issued December 2021). The International Accounting Standards Board (IASB), whose IFRS Accounting Standards are required in more than 140 jurisdictions, words it differently but builds the same structure: an asset is a present economic resource controlled by the entity as a result of past events, a liability is a present obligation to transfer an economic resource as a result of past events, and equity is the residual interest (Conceptual Framework, March 2018).

Two consequences of these definitions matter from the start. An item belongs on the asset side only if the business controls it and expects a benefit from it, so a loyal customer base or a talented barista, however valuable, is not recorded as an asset: the business neither owns nor controls them in the accounting sense. And a liability needs a present obligation, so a plan to buy a van next month is not a liability; nor is a signed order for one, until the van is delivered.

The expanded accounting equation

Equity changes for four reasons, and separating them tells a much richer story than one equity total. Owners can put money in, and they receive stock for it: that is contributed capital, recorded in Common Stock. The business can earn revenue by delivering goods or services, which increases equity. It incurs expenses in doing so, which decrease equity. And it can pay some of its profits back to the owners as dividends, which also decrease equity. Profit kept in the business accumulates in retained earnings. Putting the pieces into the equation gives the expanded accounting equation:

\text{Assets} = \text{Liabilities} + \text{Common Stock} + \text{Retained Earnings}_{\text{beginning}} + \text{Revenue} - \text{Expenses} - \text{Dividends}

Revenue minus expenses is net income for the period (a net loss if expenses are larger). At the end of the period, net income minus dividends is added to retained earnings, so the expanded equation collapses back into the basic one. Common stock is contributed capital; retained earnings are earned capital.

Here is the rest of Lantern’s March, from 10 to 31 March, in the expanded form. Revenue, expenses and dividends now have their own columns inside equity.

Lantern’s remaining March transactions in the expanded equation (fictional)
Transaction	Assets	Liabilities	Equity
10 Mar: pays $350 for March advertising	−350 Cash		−350 Expense
12 Mar: invoices $4,200 for a conference	+4,200 Accounts Receivable		+4,200 Revenue
15 Mar: runs a workshop for $1,500 in cash	+1,500 Cash		+1,500 Revenue
18 Mar: pays $1,000 owed for supplies	−1,000 Cash	−1,000 Accounts Payable
20 Mar: pays $1,600 of wages	−1,600 Cash		−1,600 Expense
25 Mar: collects $3,000 from the conference client	+3,000 Cash −3,000 Accounts Receivable
28 Mar: pays $1,200 kitchen rent for March	−1,200 Cash		−1,200 Expense
30 Mar: pays a $300 dividend	−300 Cash		−300 Dividends
31 Mar: receives a $260 utilities bill, due in April		+260 Accounts Payable	−260 Expense
Totals at 31 March	43,150	21,160	21,990

Equity of 21,990 = common stock 20,000 + revenue 5,700 − expenses 3,410 − dividends 300. These are the balances before the month-end adjustments you will make in lesson 9.

At 31 March the expanded equation reads $43{,}150 = 21{,}160 + 20{,}000 + 0 + 5{,}700 - 3{,}410 - 300$ . Lantern began with no retained earnings, so the beginning balance is zero; net income for March, before adjustments, is $5{,}700 - 3{,}410 = 2{,}290$ .

The nine patterns

Since a change in assets must equal the change in liabilities plus the change in equity, a transaction that touches two items can only follow one of nine patterns. Recognising the pattern is the fastest way to check your analysis. Some transactions combine several patterns, as Lantern’s equipment purchase did.

Every two-sided transaction follows one of these patterns
Pattern	Example	Total assets
Asset up, asset down	Buy equipment for cash; collect a receivable	Unchanged
Asset up, liability up	Borrow from a bank; buy supplies on account	Up
Asset up, equity up	Issue stock for cash; earn revenue	Up
Asset down, liability down	Pay a supplier; repay a loan	Down
Asset down, equity down	Pay wages or rent; pay a dividend	Down
Liability up, liability down	Replace a supplier’s bill with a bank note	Unchanged
Liability up, equity down	Receive a bill for an expense, to pay later	Unchanged
Liability down, equity up	Deliver a service the customer paid for in advance	Unchanged
Equity up, equity down	Move a period’s profit into retained earnings	Unchanged

When does something enter the equation?

Not every business event is a transaction. On 20 March a hotel signs a contract with Lantern to cater its June conference for $5,000, payable after the event. Nothing has changed hands: Lantern hasn’t delivered any coffee and the hotel hasn’t paid anything. Each side has only promised to perform later, so Lantern records nothing yet. A contract like this, where neither party has performed, is called an executory contract, and it stays out of the equation until one side acts. If the hotel paid a deposit, Lantern would record cash and unearned revenue; when Lantern caters the conference, it records revenue.

The same test explains other non-events. Hiring a barista who starts next week creates no asset or liability today: wages become an expense, and a liability if unpaid, as the barista works. Placing an order for supplies that haven’t arrived and haven’t been paid for is a promise, not a transaction. What enters the equation is a change in resources or in obligations that already exist, measured reliably in money. This is why some important facts about a business, such as a large contract just signed or a key employee leaving, appear in the notes to the financial statements or not at all, rather than in the equation.

What a balanced equation does and doesn’t prove

A balanced equation proves that every recorded transaction affected both sides consistently. It does not prove the records are right. If Lantern recorded its espresso machine as supplies, or forgot a transaction entirely, or recorded a $1,500 purchase as $150 on both sides, the equation would still balance. You will meet the same limitation again when you prepare a trial balance in lesson 7.

Nor does equity tell you what the business is worth. The amounts are mostly historical costs, what Lantern paid for things, and some valuable resources are not recorded at all. A buyer might pay far more, or far less, than Lantern’s $21,990 of equity (before the month-end adjustments). Equity is the owners’ accounting claim, not a market price and not a pile of cash: Lantern’s equity is spread across cash, equipment, supplies and what customers owe.

Formulas

\text{Assets} = \text{Liabilities} + \text{Equity}

$\text{Assets}$: Resources the business controls that are expected to bring economic benefits$
$\text{Liabilities}$: Present obligations to transfer resources to outsiders$
$\text{Equity}$: The owners’ residual claim on the assets$

Assumes. All three are measured at the same moment, in the same currency.

True after every transaction, because equity is defined as assets minus liabilities.

Equity as net assets

\text{Equity} = \text{Assets} - \text{Liabilities}

$\text{Equity}$: The residual claim: what would be left for owners after every liability is settled at book amounts$

Use it to find any one element when the other two are known.

The expanded accounting equation

A = L + CS + RE_{\text{beg}} + R - E - D

$A,\ L$: Assets and liabilities at the end of the period$
$CS$: Common stock: capital contributed by owners$
$RE_{\text{beg}}$: Retained earnings at the start of the period$
$R,\ E$: Revenue and expenses for the period$
$D$: Dividends declared in the period$

Assumes. Revenue, expenses and dividends are the period’s totals, not yet moved into retained earnings.

Net income

\text{Net income} = \text{Revenue} - \text{Expenses}

$\text{Net income}$: Profit for the period; negative means a net loss$

Dividends are not expenses and are not subtracted here.

Retained earnings at the end of a period

RE_{\text{end}} = RE_{\text{beg}} + \text{Net income} - \text{Dividends}

$RE_{\text{end}}$: Profit kept in the business since it began, at the end of the period$

Worked examples

A first example: Lantern after its first three transactions

Fictional figures

Lantern issues $20,000 of common stock for cash, borrows $10,000 from the bank, then buys $12,000 of equipment, paying $4,000 in cash and owing the supplier $8,000. What are total assets, liabilities and equity, and does the equation balance?

Stock issue: cash (an asset) rises by $20,000 and common stock (equity) rises by $20,000. Pattern: asset up, equity up.
Bank loan: cash rises by $10,000 and notes payable (a liability) rises by $10,000. Pattern: asset up, liability up.
Equipment purchase: equipment rises by $12,000 and cash falls by $4,000, so assets rise by a net $8,000; accounts payable rises by $8,000. Change in assets 8,000 = change in liabilities 8,000 + change in equity 0.
Add up. Assets: cash 20,000 + 10,000 − 4,000 = 26,000, plus equipment 12,000, makes 38,000. Liabilities: 10,000 + 8,000 = 18,000. Equity: 20,000.

Answer. Assets $38,000 = liabilities $18,000 + equity $20,000.

What it means. Lantern controls $38,000 of resources. Lenders and a supplier have claims on $18,000 of them and Ana, as owner, on the remaining $20,000. Buying the equipment didn’t make her any richer or poorer: it changed what the business holds and whom it owes.

A harder example: Finding net income from the equation

Fictional figures

Kestrel Battery Installers, a fictional company that fits home battery-storage systems, began the year with assets of $480,000 and liabilities of $300,000. During the year it issued $50,000 of new common stock and paid $20,000 of dividends. At the end of the year its assets were $610,000 and its liabilities $370,000. What was its net income for the year?

Equity at the start: $480{,}000 - 300{,}000 = 180{,}000$ .
Equity at the end: $610{,}000 - 370{,}000 = 240{,}000$ . So equity rose by 60,000 during the year.
List what moves equity: new stock adds 50,000, net income adds an unknown $NI$ , dividends subtract 20,000. So $60{,}000 = 50{,}000 + NI - 20{,}000$ .
Solve: $NI = 60{,}000 - 50{,}000 + 20{,}000 = 30{,}000$ .

Answer. Net income was $30,000.

What it means. Assets grew by $130,000, but most of that growth was paid for by new debt ($70,000) and new owners’ money ($50,000). Only $30,000 came from profit, and two-thirds of it was paid out as dividends. Reading the change in equity this way separates growth that was earned from growth that was financed.

Applied: a business decision: Can Lantern borrow for a van?

Fictional figures

After its month-end adjustments, Lantern’s balance sheet at 31 March shows assets of $42,500, liabilities of $21,810 and equity of $20,690. Ana wants to borrow $15,000 to buy a delivery van. The bank lends only if, after the loan, total liabilities are no more than 1.5 times equity. Does the loan fit, and if not, what are her options?

The loan adds $15,000 of cash (soon a van) to assets and $15,000 to liabilities; equity is unchanged. Liabilities become $21{,}810 + 15{,}000 = 36{,}810$ ; assets become $57{,}500$ .
The bank’s limit is $1.5 \times 20{,}690 = 31{,}035$ of liabilities. With 36,810 Lantern would be over the limit; the ratio would be $36{,}810 \div 20{,}690 \approx 1.78$ .
Option A, borrow less: the most Lantern can add is $31{,}035 - 21{,}810 = 9{,}225$ .
Option B, add equity first: Ana buys more stock for cash, raising equity by $x$ . The loan fits if $36{,}810 \le 1.5(20{,}690 + x)$ , so $x \ge 36{,}810 \div 1.5 - 20{,}690 = 3{,}850$ .

Answer. The full $15,000 loan breaks the bank’s condition. Lantern can borrow up to $9,225, or Ana can invest at least $3,850 more in exchange for stock and then borrow the full $15,000.

What it means. Lenders watch the equation because equity is their cushion: the larger it is relative to liabilities, the more the business could lose before creditors go unpaid. The new owner’s money in option B also increases assets, which is why it reassures the bank. You will study ratios like this one properly in F03.

Explore

Common mistakes

“Revenue means cash came in.”
Revenue is earned when the business delivers the service, whether or not it has been paid. Lantern’s $4,200 conference invoice is revenue on 12 March although no cash arrived until later; Harbor Tech’s $2,400 deposit is cash but not revenue, because the events haven’t happened. Ask “has the business done what it was paid for?”, not “has money arrived?”.
“Dividends are an expense.”
Dividends reduce equity, but they are a distribution of profit to owners, not a cost of earning revenue. They are left out of net income and subtracted from retained earnings afterwards. Treating them as an expense would make Lantern’s March profit look $300 smaller than it was.
“Paying a bill is an expense.”
When Lantern pays the $1,000 it owes for supplies, assets and liabilities both fall and equity doesn’t move. The cost was recorded when the supplies were bought (as an asset) and becomes an expense when they are used. Paying the bill only settles the debt.
“Equity is the owner’s money in the bank.”
Equity is a claim on all the assets, not a particular asset. Lantern’s $21,990 of equity at 31 March, before adjustments, is spread across cash, equipment, insurance cover, supplies and receivables. Nor is it a market value: someone buying Lantern would pay what they think its future is worth.
“If the equation balances, the records are correct.”
The equation catches one-sided mistakes only. Recording equipment as supplies, omitting a transaction, or entering the same wrong amount on both sides all leave it balanced. Balancing is necessary, not sufficient.

Guided practice

Work through these with hints when you need them. Every hint and every worked solution is there to be used.

Loading four questions…

On your own

No hints this time. Answer, check, and read the feedback; the solution appears once you have answered or if you ask for it. Your first answers count toward mastery.

Loading six questions…

In practice

Lenders read the equation first. When Ana asks Coastline Bank for more credit, the loan officer looks at how much of Lantern’s assets is financed by owners compared with creditors, because the owners’ equity absorbs losses before the bank does. Loan agreements often turn this into a covenant, a condition such as “total liabilities may not exceed 1.5 times equity”, and checking it means working the equation forward for the planned borrowing, exactly as in the applied example.

Investors and owners read the change in equity, not just its level. Kestrel’s equity grew by $60,000, but only $30,000 of that was earned. A business can grow its assets quickly by borrowing or by raising money from new shareholders; the expanded equation shows how much of the growth came from profitable operations, which is the part that can continue without more outside money.

Managers use the dual aspect as a planning check. Before Lantern commits to a $15,000 van, Ana can write the transaction into the equation and see its consequences: cash rises, then turns into a vehicle; a liability appears that must be repaid with interest; equity is untouched until the van starts earning revenue and costing fuel and depreciation. Financial models built in spreadsheets include a “balance check” row for the same reason: if projected assets ever differ from projected liabilities plus equity, the model has an error, and analysts don’t trust its numbers until it balances.

Knowledge check

Six questions, one attempt each, no hints. Score 80% or more to complete the lesson; you can take it again at any time.

Loading six questions…

Summary

Assets = liabilities + equity, at every moment, because equity is defined as what is left of the assets after liabilities.
Every transaction changes at least two items, and the change in assets always equals the change in liabilities plus the change in equity.
Equity grows when owners invest or the business earns revenue, and shrinks with expenses and dividends: A = L + CS + RE(beginning) + R − E − D.
Net income is revenue minus expenses; dividends are not expenses. Ending retained earnings = beginning retained earnings + net income − dividends.
Cash and revenue are different things: a deposit for future work is a liability, and work invoiced on credit is revenue before any cash arrives.
A balanced equation proves consistency, not correctness, and equity is an accounting claim, not the market value of the business.

Terms introduced

Accounting equation: Assets = liabilities + equity: the business’s resources equal the claims of creditors and owners on them.
Net assets: Assets minus liabilities; another name for equity.
Dual aspect: The principle that every transaction affects at least two items in the accounting equation, so it stays in balance.
Unearned revenue: Cash received for goods or services not yet delivered. It is a liability until the business delivers them.
Contributed capital: Equity supplied by owners in exchange for shares, recorded in Common Stock (share capital under IFRS).
Retained earnings: Cumulative net income kept in the business since it began, after dividends.
Dividends: Distributions of profit to a corporation’s shareholders. They reduce equity but are not an expense.
Net income: Revenue minus expenses for a period. A negative result is a net loss.
Expanded accounting equation: Assets = liabilities + common stock + beginning retained earnings + revenue − expenses − dividends.
Executory contract: A contract in which neither party has yet performed. It is not recorded in the accounts until one side acts, for example by paying or delivering.

Sources

Franklin, M., Graybeal, P. & Cooper, D. (2019). Principles of Accounting, Volume 1: Financial Accounting, section 3.2, “Define and Describe the Expanded Accounting Equation and Its Relationship to Analyzing Transactions”. OpenStax. openstax.org/books/principles-financial-accounting/pages/3-2…
Franklin, M., Graybeal, P. & Cooper, D. (2019). Principles of Accounting, Volume 1: Financial Accounting, section 3.4, “Analyze Business Transactions Using the Accounting Equation and Show the Impact of Business Transactions on Financial Statements”. OpenStax. openstax.org/books/principles-financial-accounting/pages/3-4…
Financial Accounting Standards Board (2021). Statement of Financial Accounting Concepts No. 8, Conceptual Framework for Financial Reporting, Chapter 4: Elements of Financial Statements. Issued 22 December 2021 (copy hosted by PwC Viewpoint). viewpoint.pwc.com/dt/us/en/fasb_financial_accou/statements_o…
IFRS Foundation. Conceptual Framework for Financial Reporting, issued by the IASB in March 2018. ifrs.org/projects/completed-projects/2018/conceptual-framewo…

Before you start

You will be able to

Review first

The idea

Three words, one equation

Every transaction has two sides

In depth

What the definitions say

The expanded accounting equation

The nine patterns

When does something enter the equation?

What a balanced equation does and doesn’t prove

Formulas