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# Fundamental Accounting Equation: Problems and Solutions

An accounting equation builds the foundation for all accounting system. The double entry accounting system is based on basic accounting equation only. A simple accounting equation illustrates two simple facts about a company: what it owns and what it owes.

Let us first understand the elements of an accounting equation. The financial position of a company is measured in the following terms:

• Assets (what it owns) (for example, cash, accounts receivable, inventory, prepaid insurance, and investments)
• Liabilities (what it owes to others) (notes or loans payable, account payable, salaries and wages payable and interest payable)
• Capital (the difference between assets and liabilities)

The general accounting equation states the relationship among the above in the follow manner,

 Asset = Liabilities + Capital

## How to solve a basic accounting equation?

Here is one example using the above formula.

• Problem: Find out how accounting equation is satisfied after taking into consideration each of the following transactions in the books of Mr. A
1. Started business with capital \$100,000

Solution

Capital (100,000) + Liabilities (0) = Assets (cash = 100,000)

1. Bought furniture \$25, 000

Solution

Capital (100,000) + Liabilities (0) = Assets (Cash = 75,000 + Furniture = 25,000)

1. Bought goods for cash \$20, 000

Solution

Capital (100, 000) + Liabilities (0) = Assets (Cash = 55,000 + Furniture = 25,000 + Goods = 20,000)

1. Brought goods from Mr. Nelson on credit \$5,000

Solution

Capital (100, 000) + Liabilities (Nelson = 5,000) = Assets (Cash = 55,000 + Furniture = 25,000 + Goods = 25,000)

1. Sold goods for cash for \$15, 000

Capital (100,000) + Liabilities (Nelson = 5,000) = Assets (Cash = 70,000 + Furniture = 25,000 + Goods = 10,000)

1. Sold goods to Mr. William on credit \$8,000

Solution,

Capital (100,000) + Liabilities (Nelson = 5,000) = Assets (Cash = 70,000 + Furniture = 25,000 + Goods = 2,000 + William = 8,000)

1. Paid cash to Nelson \$4,000

Solution,

Capital (100,000) + Liabilities (Nelson = 1,000) = Assets (Cash = 66,000 + Furniture = 25,000 + Goods = 2,000 + William = 8,000)

1. Received cash from William \$5,000

Solution

Capital (100,000) + Liabilities (Nelson = 1,000) = Assets (Cash = 71,000 + Furniture = 25,000 + Goods = 2,000 + William = 3,000)

### Types of accounting problems

• Accounting equation for a corporate
• Accounting equation for a sole proprietorship
• Calculating a missing amount within owner’s equity
• Expanded accounting equation for a sole proprietorship
• Expanded accounting Equation for a corporation

### Solving accounting equation for a corporate

The accounting equation for corporation is,

 Assets = Liabilities + Stockholder’s Equity

With the help of examples, you can see how a given transaction affects the accounting equation for a corporation and how the same transaction will be recorded in the company’s general ledger accounts,

Example:

Let’s assume that member of Bill family form a corporation called Accounting Software, Inc. (ASI). On December 1, 2013, several member of Bill family invest a total of \$10, 000 to start ASI. In exchange, the corporation issues a total of 1, 000 shares of common stock. The effect on the corporation’s accounting,

 Asset (+ \$10,000) = Liabilities (no effect) + Stockholder’s Equity (+ \$10,000)

The above equation says that, ASI increases its assets and stockholder’s equity by the same amount (\$10,000), the sources of these assets was the stockholders. In other words, it states that the corporation has the assets of \$10,000, and only stockholders can claim them.

Let us have a look on how the accounting equation for a corporation can affect the balance sheet,

The balance sheet of ASI’s financial position at the end of the December 1, 2013,

Accounting Software Inc.

Balance Sheet

December 1, 2013

 Assets Liabilities Cash =                                                          \$ 10,000 Stockholder’s equity =                                 \$10,000 (Common Stock) Total Assets =                                             \$ 10,000 Total Liabilities and Stockholder’s Equity =                         \$ 10,000

## Solving accounting equation for a sole proprietorship

A sole proprietor is a kind of business that is owned by one person.

Example:

Let’s assume, Mr. Bill is the sole proprietor of XYZ Co. (ASC). On December 1, 2013, Mr. Bill invests personal funds of \$10,000 to start XYZ Co. So after this transaction, the accounting equation will be,

Assets (+ \$10,000) = Liabilities (No effect) + Owner’s equity (+ \$10,000)

As you can see, the assets and owner’s equity increase by same amount (\$10,000), so the accounting equation says that, XYZ Co. possesses assets of \$10,000 and the source of those assets was the owner, Mr. Bill. In other words, XYZ Co. has assets of \$10,000 and the owner has a claim for the remainder.

Let’s see how balance is affected by the accounting equation for a sole proprietorship,

Here is the balance sheet of ASC at the end of December 1, 2013.

XYZ Co.

Balance Sheet

December 1, 2013

 Assets Liabilities Cash =                                                              \$ 10,000 Liabilities (Owner’s Equity, Mr. Bill Capital)  =           \$ 10,000 Total Assets =                                   \$10,000 Total liabilities and Owner’s equity =        \$ 10,000

### Calculating a missing amount within owner’s equity

Here is an example of how to decide one of the components if it is unknown,

Example:

Let’s assume that the net income for the year 2013 is unknown, but the amount of the draws and the beginning and ending balances of owner’s equity are known, you can calculate the net income. So this is a sample how you should do it taking the same above company as an example,

 Assets as of December 31, 2012 \$100,000 Liabilities as of December 31, 2012 40,000 Assets as December 31, 2013 128,000 Liabilities as of December 31, 2013 34,000 Owner investment in business in 2013 10,000 Owner draws in 2013 40,000

Step 1 The owner’s equity at December 31, 2012 can be computed with the help of the accounting equation

Assets = Liabilities + Owner’s equity

\$ 100,000 = \$40,000 + Owner’s Equity

Owner’s Equity = \$100,000 – \$40,000

Owner’s Equity at Dec 31, 2012 =   \$60,000

Step 2 The owner’s equity at December, 2013,

Assets = Liabilities + Owner’s equity

\$128,000 = \$34,000 + Owner’s equity

Owner’s Equity = \$128,000 – \$34,000

Owner’s Equity at Dec, 31, 2013 = \$94,000

Step 3 The ‘subtotal’ can be calculated by adding (Owner’s equity at Dec 31, 2014 + Owner draws in 2013) (\$94,000 + \$40,000 = \$134,000), and after inserting the result (\$134,000) n the statement of changes, giving us,

 Owner’s Equity at December 31, 2013 \$60,000  (Step 1) Add: Owner’s investment + 10,000 (given) Net income ? ? Subtotal \$134,000 (Step 3) Deduct : Owner’s Draws -40,000 Owner’s equity at December 31, 2013 \$94,000 (step 2)

Step 4 The net income is the difference between the

 {(Owner’s Equity at Dec, 31, 2012 + Owner’s investments) – subtotal}

So you can find the result as adding Owner’s equity at Dec, 2012 and Owner’s investments, (\$60,000 + \$10,000= \$70,000), and after subtracting the result (\$70,000) from subtotal, (\$134,000 – \$70,000 = \$64,000). So the Net income must have been \$64, 000.

 Owner’s Equity at December 31, 2013 \$60,000  (Step 1) Add: Owner’s investment + 10,000 (given) Net income \$64,000 Subtotal \$134,000 (Step 3) Deduct : Owner’s Draws -40,000 Owner’s equity at December 31, 2013 \$94,000 (step 2)

## Solving expanded accounting equation

In the expanded accounting equation, Owner’s equity replaces with the following components which are Owner’s Capital + Revenues – Expenses – Owner’s Draws.

### Expanded accounting equation for a sole proprietorship

The expanded accounting equation for a sole proprietorship is,

 Assets = Liabilities + Owner’s Capital + Revenues – Expenses – Owner’s Draws

The eight transactions that already been listed under the basic accounting equation are demonstrated in the expanded accounting equations,

 Assets = Liabilities + Owner’s Capital + Revenues _ Expenses _ Owner’s Draws 1 +10, 000 = + +10, 000 2 -100 _ +100 3 + 5, 000 -5, 000 = 4 +7, 000 = + 7, 000 5 -600 = – + 600 6 +900 = + +900 7 = + 120 – +120 8 + 500 -500 = T 17, 200 = 7, 120 10, 000 900 720 100

So, you can calculate the Net Income,

 Revenues (\$900) – Expenses (\$720) = Net Income (\$180)

## Solving expanded accounting Equation for a corporation

Here the formula becomes:

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

So, eight transactions are shown in the following expanded accounting equation in order to find Net Income,

 Assets = Liabilities + Paid-in Capital + Revenues _ Expenses _ Dividends and Treasury Stock 1 +10, 000 = + +10, 000 2 -100 _ +100 3 + 5, 000 -5, 000 = 4 +7, 000 = + 7, 000 5 -600 = – + 600 6 +900 = + +900 7 = + 120 – +120 8 + 500 -500 = T 17, 200 = 7, 120 10, 000 900 720 100

So, you can easily find out the Net income of the corporate by calculating,

 Revenues (\$900) – Expenses (\$720) = Net Income (\$180)

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A Complete Guide to Solving an Accounting Question

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