Question

During 2012, Gibson Company's assets decreased $\mathrm{\$}50,000$ and its liabilities decreased $\mathrm{\$}90,000$. Its owner's equity therefore: a. increased $\mathrm{\$}40,000$. c. decreased $\mathrm{\$}40,000$. b. decreased $\mathrm{\$}140,000$. d. increased $\mathrm{\$}140,000$.

Short answer

Owner's equity increased by $\mathrm{\$}40,000$.

Step-by-step solution

Understanding the Basic Accounting Equation

The basic accounting equation is: $\text{Assets}=\text{Liabilities}+\text{Owner's Equity}$. This equation must always hold true.

Assessing the Changes in Assets and Liabilities

We are told that the assets decreased by $(50,000$ and liabilities decreased by $)90,000$. We need to determine the effect on owner's equity while keeping the accounting equation balanced.

Mathematical Setup of Change

Let the initial asset, liability, and equity values be $A_0$, $L_0$, and $E_0$ respectively. Then the equation $A_0-50,000=L_0-90,000+E$ must hold for new equity $E$.

Solving for Change in Owner's Equity

To keep the equation balanced, if liabilities decrease by more than the decrease in assets, owner's equity must increase by the difference. So: $A_0-50,000=L_0-90,000+E$ simplifies to $E=E_0+(90,000-50,000)=E_0+40,000$.

Conclusion from Analysis

Owner's equity has increased by $\mathrm{\$}40,000$ to balance the overall decrease in liabilities and the smaller decrease in assets, which is consistent with choice (a).

Key concepts

Assets and Liabilities

In accounting, understanding assets and liabilities is crucial as they form the backbone of the financial position of any business. Assets are resources owned by a company that are expected to bring future economic benefits. They can include tangible items like cash, inventory, and equipment, or intangible items like patents and trademarks. On the other hand, liabilities represent the company's obligations or debts, such as loans, accounts payable, and mortgages.
The basic accounting equation, which is:$$\text{Assets}=\text{Liabilities}+\text{Owner's Equity}$$ensures that the assets owned by the business are balanced out by its liabilities and the owner's equity. It is crucial to continually assess how changes in assets and liabilities affect the overall financial health of a company. For example, in any given period, an increase in assets or a decrease in liabilities can have a significant positive impact, tuning up the company's financial condition.

Owner's Equity

Owner's equity refers to the ownership interest of the business owner in the company. It represents the residual interest in the assets of the entity after deducting liabilities. Essentially, it is what the owner effectively owns outright, once all debts and obligations have been cleared.
Owner's equity can be affected by changes in both assets and liabilities. For instance, when liabilities decrease more than assets, as seen in the provided exercise, owner’s equity increases. This occurs because the overall obligations of the company have lessened without an equivalent reduction in assets, thereby boosting the owner's stake. Common components that might impact owner's equity include:

• Retained Earnings: Profits that are reinvested in the business instead of being distributed to the owner.
• Owner’s Withdrawals: Amounts taken out by the owner for personal use.
• Capital Contributions: Additional funds injected into the business by the owner.

These components directly modify owner's equity and reflect the dynamic nature of a business's net value.

Financial Analysis

Financial analysis is a fundamental process used to evaluate and understand the financial health and performance of a business. It involves examining various financial statements and metrics to make informed decisions.
A core aspect of financial analysis includes the assessment of changes in the accounting equation over time, which helps in:

• Identifying trends in asset growth or depletion, indicating how effectively a company is managing its resources.
• Monitoring changes in liabilities to ensure that a company is maintaining healthy levels of debt.
• Evaluating shifts in owner’s equity, which might suggest business expansion or other strategic initiatives.

By understanding the relationship between assets, liabilities, and owner's equity, stakeholders can gauge a company's solvency, liquidity, and overall financial stability. This analysis is not just useful for accountants but is essential for managers, investors, and anyone with a vested interest in the business's success. It helps ensure that decisions are based on solid financial data and insights.