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Expanded Accounting Equation

Introduction

Like the basic accounting equation, the expanded accounting equation shows the relationships among the accounting elements. In this version, "capital" is expanded.

In a Nutshell

In the expanded accounting equation, the "capital" portion is broken down into several components: contributions, withdrawals, income, and expenses.

Basic Accounting Equation:
Assets = Liabilities + Capital

Expanded Accounting Equation:
Assets = Liabilities + (Beginning Capital + Additional Contributions - Withdrawals + Income - Expenses)

Components Affecting Capital

We know that capital is affected by contributions, withdrawals, income, and expenses.

Contributions and income increase capital. Withdrawals and expenses decrease it.

Hence, the accounting equation for a sole proprietorship can be rewritten by expanding the capital element:

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

Example

Let's take a look at how it works. Assume the following transactions:

  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.

The effects to the expanded accounting equation of the transactions are as follows. (Capital at the beginning is zero since the business has just started so we'll just leave it out for now.)

  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 +   -   +   - 400
8 (5,000) =   +   - 5,000 +   -  
9 (10,000) = (10,000) +   -   +   -  
10 750
(750)
=   +   -   +   -  
Bal 36,450 = 20,600 + 20,000 - 5,000 + 1,250 - 400

Notice that the equation stays in balance. If you take the total of the right side of the equation (i.e. liabilities, capital contribution, income, expense, and withdrawals) you will get $36,450, which is equal to the total assets in the left side.

For a bit of challenge, study the examples above and try to determine what specific items were affected under each element and why they increased or decreased. Do that for each transaction. If you find it difficult, you may refer back to the explanation in the previous lesson.

Conclusion

The accounting equation, whether in its basic form or its expanded version, shows the relationship between the left side (assets) and the right side (liabilities plus capital). It also shows that resources held by the company are coupled with claims against them.

There is a two-fold effect in every transaction. This results in the movement of at least two accounts in the accounting equation. The amount of change in the left side is always equal to the amount of change in the right side, thus, keeping the accounting equation in balance.

The accounting equation is very important. It will guide you in understanding related accounting principles and provides a foundation that will help you solve many accounting problems.

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