In this post, we look at the answers to – What is the fundamental equation? How to expand an equation? And what are some expanded basic accounting example problems?

Expanded accounting equation

We derive the expanded accounting equation from the basic accounting equation. The equation provides more details about an owner’s equity. Accounting equations expanded are different for sole proprietorships and stock holder’s equity. The expanded accounting equation divides equity into four elements – owner’s capital, withdrawals, revenue, and expenses.

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Two accounting equation formula

Accounting is an essential part of the business. It involves tracking and recording financial transactions in the company. We use accounting formulas to describe the financial health of a company. We use them to produce financial statements like the balance sheet and profit and loss statement. The two accounting equations are:- the basic accounting equation and the expanded accounting equation.

1. Basic accounting equation

The basic accounting equation is also known as the balance sheet equation. The equation is the foundation of double-entry bookkeeping. The basic accounting equation is

Assets = Equity + Liability

Assets are company resources or things the company owns. These assets can be short-term or long-term. 

Liabilities are assets owed to the creditors. Creditors are entities (vendors, government, bank, employees) that the company owes money to. We can subdivide liabilities into short-term liabilities and long-term liabilities.

Equity is the value of assets that belong to the owners. Equity is the amount left for the owner once assets and liabilities are paid. The owner’s equity increases, when the owner’s investments and revenue increase.

The owner’s equity decreases if there are cash withdrawals, business expenses, or losses.

2. Expanded accounting equation

The expanded account equation uses the basic accounting equation and adds equity items to show how it affects the company. We split the equity account into four or five categories. This split depends on the ownership patterns. The expanded accounting equation is 

Assets=Liabilities+CC+BRE+R−E−D

where:

• Liabilities are all current and long-term debts and obligations
• CC – contributed capital (paid-in-capital) or the capital provided by the original stockholders
• BRE or Beginning retained earnings are earnings that are not distributed from the previous period.
• R or revenue is the income generated by the company from the ongoing operations.
• E or expenses are the costs incurred for business operations.
• D or dividends are earnings distributed to the stockholders.

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Difference between basic and expand equation

The expanded equation is the expanded form of the basic equation. We subdivide the equity components into four elements. The four elements are the owner’s capital, owner’s withdrawals, revenues, and expenses. The section in the basic equation dealing with assets and liabilities remains unchanged. The two equations are as follows:-

Basic equation

Assets = Equity + Liability.

Accounting equation formula

Assets=Liabilities+ Contributed Capital +Beginning retained earning +Revenue –Expenses −Dividend

The expand equation shows the various units of stockholder equity in greater detail. We change the terminology depending on the type of company. We use the term member’s capital in partnerships and owner’s capital to describe sole proprietorships. We substitute dividends by distribution and withdrawals.

The expanded equation gives analysts more information about the health of the company. The expanded accounting equation allows the analyst to scrutinize –

• The effect of net income (due to increase in revenue and decreased expenses) has on equity.
• The effect of transitions with owners (draws, dividends, sale, or purchase of ownership interest).

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Importance of expanded accounting equation

The expanded accounting equation considers the different components of equity. Equity is important because it represents the amount of the investor’s stake in the company and represents the proportion of their shares in the company. The expanded account equation shows the debit and credit entries in the double-entry form.

The equation helps businesses to calculate the assets, liability, and owner’s equity in a period. The investor can track the profitability and finances of the company.

Analysts use the equation to understand the breakdown of equity. The revenue and expenses show the change in net income over the period. They can understand stockholder transactions through contributed capital and dividend.

The equations help determine the effect of change on owners. It helps to save time.

We can rearrange the expanded accounting equation for different purposes

• Assets – Liabilities = Shareholder’s Equity
• Assets – Liabilities = Share Capital + Retained Earnings
• Assets – Liabilities = CC + BRE + R + E + D

These rearrangements are useful when companies are studying bankruptcy. Stockholders can use the equation to understand their compensation. Owners need to pay the liability made up of short-term and long-term debt needs. They can use the remaining liquidated assets to pay off parts of shareholder’s equity.

It is important to remember to balance the equations.

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How does the full accounting equation work?

Analysts want to understand the breakup of the company’s shareholder’s equity. The general accounting equation contains assets and liabilities. We can expand shareholder’s equity into:-

• Contributed capital is the capital provided by the original stockholder.
• Beginning retained earnings or BRE is the carryover retained earnings that were not distributed to stockholders before.
• Revenue comes from the sales and operations of the business.
• Expenses are the costs associated with running the operation.
• Dividends are the earnings distributed between the stockholders of the company.

Analysts examine contributed capital and dividends to understand stockholder’s transactions. The net income earned by the company is the difference between revenue and profit generated and expenses and loss incurred.

The net income earned by the company influences the equity.

The analyst uses the full accounting equation to understand the breakdown of shareholder equity. They can analyze how the equity changes over a period.

The terminology used in expanded accounting equations varies depending on the ownership patterns of the company.

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Real-life examples of the extended accounting equation

The extended accounting equation and used in the balance sheet. We call the extended equation the balance sheet equation. Any changes to the equation will result in the same changes with the balance sheet. Some real-life examples will help understand the accounting equation.

Sole Proprietary expanded basic accounting equation

Here are expanded basic accounting example problems for a sole proprietorship. Alicia Jones runs a wholesale clothing shop Adorables. During the fortnight of operations, she engages in the following transactions:

• Mar. 01: Alicia invests $60,000 in the business.
• Mar. 05: She purchases clothing items costing $20,000.
• Mar. 12: She sells clothing items to a retailer for $8,000 cash, the cost of goods sold is $5,000.
• Mar. 14: Alicia takes $200 cash for her personal use.

	Assets	Liabilities	+Owners Capital	+Revenue	-Expenses	-Drawing
March 01	+60,000		60,000
March 05	-20,000 +20,000
March 12	+60,000 +8,000 -5,000		60,000	8,000	5,000
March 14	+63,000 -200		60,000	8,000	5,000	200
	62,800		60,000	+8,000	-5000	-200

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Journal entry for expanded accounting equation examples

1. Mr. Alex invested $20,000 to start a printing business
2. The company obtained a loan from a bank, $30,000
3. The company purchased printers and paid a total of $1,000
4. Rendered services and received cash, $500
5. Rendered services on account, $750
6. Purchased office supplies on account, $200
7. Had its equipment repaired for $400, to be paid after 15 days
8. Mr. Alex, the owner, withdrew $5,000 cash for personal use
9. Paid one-third of the loan obtained in transaction #2
10. Received customer payment from services in transaction #5.

Assets = Liabilities + (Capital at beginning + Additional Contributions – Withdrawals + Income – Expenses)

	A	L	Con	With	Inc	Exp
1	20,000		+20,000
2	30,000	30,000
3	1,000 (1,000)
4	500				+500
5	750				+750
6	200	200
7		400
8	(5000)			5000
9	(10,000)	(10,000)
10	750 (750)
Balance	36,450	20,600	+20,000	-5000	+1250	-400

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Corporation expanded accounting equation example

Foods & Drugs Inc. The Company was incorporated on 1 June 2019 with a paid-up capital consisting of 1000 shares having a value of $50. During the first month of its operations, the company has entered into the following transactions:

• 1-Jun Capital introduced – $ 50,000
• 6-Jun Paid $10,000 for purchase of furniture and computers.
• 15-Jun Paid $ 5,000 towards purchase of machinery and equipment.
  Paid $ 1,000 towards purchase of raw materials
• 22-Jun Incurred expenditure towards advertising and marketing amounting to $200
• 25 June Earned revenue of +10,000
• 26 June Earned revenue of +15,000
• 30-Jun Paid salaries to its employees – $13,000
• 30-Jun Paid Rent and telephone bills – $15,000
• 30-June Paid dividend of -500

Date	Nature	Asset	Paid up Capital	Liabilities	Income	Expenses	Dividend
June 1	Capital and Assets	50000	50000
6 June	Expenses and Assets (Fixed Assets)	-10,000				10,000
15 June	Expenses and Assets (Fixed Assets)	-5000				5000
15 June	Expenses and Assets (Inventory)					1000
22 June	Expenses and Assets (cash)					200
25-June	Revenue and Assets (cash)				10,000
26-June	Revenue and Assets (cash)				15,000
30 June	Expenses and Assets (cash)					13000
30 June	Expenses and Assets (cash)					15000
30 June	Dividend						50

Assets = Paid-up Capital – Treasury Stock (if any) + Liabilities + Income – Expenses – Dividends

Assets = 50000 – 0 + 0 + 25000 – (-44200) – (-50) = 30,750

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What is the expanded accounting equation for a sole proprietorship?

The expanded accounting equation for sole proprietorship shows accounts for the components that make up the owner’s equity. These components are –

• Owner’s Capital
• Revenues
• Expenses
• Withdraws

The elements of the accounting equation are represented by

Assets =Liabilities + owner’s capitals+ Revenues – Expenses – owners draw

Where,

The owner’s capital or owner’s equity is the equity account that shows the owner’s stake in the business.

The owner draws is the amount of the money taken from the sole proprietorship, partnership, or LLC or corporation by the owner for their personal use. It is a way owner pays themselves instead of a salary.

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What is the expanded accounting equation for corporations?

The expanded accounting equation gives us a break-up of the shareholder’s equity amount. 

The expanded accounting equation for corporations is as follows –

Assets = Liabilities + Paid-in Capital + Revenues – Expenses – Dividends – 

Treasury Stock.

Where,

Liabilities are obligations made by the corporation. These may be financial, account-related, or legal. Accounting liabilities appear on the balance sheet.

Paid-in capital is cash or asset that a shareholder gives to the company in exchange for stock. 

Revenue is the value earned from the sale of goods and services.

Treasure Stock or reacquired stock is the stock. 

The dividend is the distribution of profit to shareholders. 

Expenses are the cost incurred running the company.

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What is the expanded accounting equation for corporations?

The expanded accounting equation for corporations 

What is the meaning of an l/c r e and d in an expanded accounting equation?

The expanded accounting equation is   

Assets = Liabilities + CC+ BRE+R-E-D

Where,

CC – Contributed Capital i.e. capital provided by the original stockholder (paid-in capital)

BRE – Beginning retained earning. The BRE is earnings that have not been distributed to the stockholder previously.

R = Revenue is the amount a company receives in exchange for its good and services or conversely. It is the income generated from the ongoing operations of the company.

E = Expenses are the cost incurred to run operations of the business

D = Dividends, earnings distributed to the stockholders of the company. Dividends can be in the form of cash payment, stock, or other forms. Dividends are a part of the profit that a company shares with its stockholder.