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3.2 Define and Describe the Expanded Accounting Equation and Its Relationship to Analyzing Transactions

The Basic Accounting Equation​

We learned in Chapter 2 that the fundamental accounting equation is:

Assets = Liabilities + Equity

This equation must always balance. Every transaction affects this equation, and understanding how is key to analyzing transactions.

The Expanded Accounting Equation​

The expanded accounting equation breaks down equity into its components:

Assets = Liabilities + Equity

Equity = Share Capital + Retained Earnings + Revenue - Expenses - Withdrawals

Therefore:

Assets = Liabilities + Share Capital + Retained Earnings + Revenue - Expenses - Withdrawals

Components of the Expanded Equation​

Assets (Actif)​

Resources owned by the business that have economic value.

Examples:

  • Cash (510000)
  • Accounts Receivable (410000)
  • Inventory (321000)
  • Equipment (223000)

Effect on Equation: Assets increase on the left side (debit), decrease on the right side (credit).

Liabilities (Passif)​

Obligations owed by the business.

Examples:

  • Accounts Payable (400000)
  • VAT Payable (430000)
  • Bank Loans (120000)

Effect on Equation: Liabilities increase on the right side (credit), decrease on the left side (debit).

Share Capital (Capital Social)​

Owner's initial investment in the business.

PCN Account: 101000

Effect on Equation: Increases equity (credit), decreases equity (debit) if capital is returned.

Retained Earnings (Bénéfices Reportés)​

Accumulated profits from previous periods not distributed to owners.

PCN Account: 104000

Effect on Equation: Increases with net income (credit), decreases with net loss or distributions (debit).

Revenue (Produits)​

Increases in equity from business operations.

PCN Accounts: Class 7 (700000-799999)

Effect on Equation: Increases equity (credit), which increases the right side of the equation.

Expenses (Charges)​

Decreases in equity from business operations.

PCN Accounts: Class 6 (600000-699999)

Effect on Equation: Decreases equity (debit), which decreases the right side of the equation (or increases the left side to maintain balance).

Withdrawals/Distributions​

Money or assets taken out of the business by owners.

Effect on Equation: Decreases equity (debit).

Using the Expanded Equation to Analyze Transactions​

Every transaction affects at least two accounts, and the equation must always balance. Let's analyze common transactions:

Transaction 1: Owner Invests Cash​

Transaction: Marie invests €10,000 cash to start her restaurant.

Analysis:

  • Assets (Cash) increase by €10,000
  • Equity (Share Capital) increases by €10,000

Equation Impact:

Before:  Assets = Liabilities + Equity
        €0    = €0        + €0

After:   Assets = Liabilities + Equity
        €10,000 = €0        + €10,000

PCN Accounts:

  • Debit: 510000 Cash (Class 5)
  • Credit: 101000 Share Capital (Class 1)

Transaction 2: Purchase Equipment on Credit​

Transaction: Restaurant purchases €15,000 equipment, paying €5,000 cash and owing €10,000.

Analysis:

  • Assets (Equipment) increase by €15,000
  • Assets (Cash) decrease by €5,000
  • Liabilities (Accounts Payable) increase by €10,000

Equation Impact:

Before:  Assets = Liabilities + Equity
        €10,000 = €0        + €10,000

After:   Assets = Liabilities + Equity
        €20,000 = €10,000   + €10,000
        (€15,000 equipment + €5,000 cash)

PCN Accounts:

  • Debit: 223000 Equipment (Class 2) €15,000
  • Credit: 510000 Cash (Class 5) €5,000
  • Credit: 400000 Accounts Payable (Class 4) €10,000

Transaction 3: Provide Services for Cash​

Transaction: Restaurant earns €1,200 revenue, receiving cash.

Analysis:

  • Assets (Cash) increase by €1,200
  • Revenue increases by €1,200 (which increases equity)

Equation Impact:

Before:  Assets = Liabilities + Equity
        €20,000 = €10,000   + €10,000

After:   Assets = Liabilities + Equity + Revenue
        €21,200 = €10,000   + €10,000 + €1,200

PCN Accounts:

  • Debit: 510000 Cash (Class 5) €1,200
  • Credit: 701000 Sales Revenue (Class 7) €1,200

Transaction 4: Pay Expenses​

Transaction: Restaurant pays €800 rent expense.

Analysis:

  • Assets (Cash) decrease by €800
  • Expenses increase by €800 (which decreases equity)

Equation Impact:

Before:  Assets = Liabilities + Equity + Revenue - Expenses
        €21,200 = €10,000   + €10,000 + €1,200  - €0

After:   Assets = Liabilities + Equity + Revenue - Expenses
        €20,400 = €10,000   + €10,000 + €1,200  - €800

PCN Accounts:

  • Debit: 612000 Rent Expense (Class 6) €800
  • Credit: 510000 Cash (Class 5) €800

Debits and Credits​

Understanding debits and credits is essential for recording transactions:

Debit (DĂ©bit):

  • Left side of an account
  • Increases: Assets, Expenses
  • Decreases: Liabilities, Equity, Revenue

Credit (Crédit):

  • Right side of an account
  • Increases: Liabilities, Equity, Revenue
  • Decreases: Assets, Expenses

Memory Aid: DEAD CLIC

  • DEbit: Expenses, Assets, Drawings
  • CRedit: Liabilities, Income (Revenue), Capital (Equity)

Luxembourg Compliance Note​

In Luxembourg, all transactions must be recorded using double-entry bookkeeping. This is a legal requirement under the Commercial Code. Every transaction must have:

  • At least one debit
  • At least one credit
  • Total debits = Total credits
  • Proper PCN account classification

Think It Through​

A Luxembourg business purchases inventory for €5,000, paying €2,000 cash and owing €3,000. Using the expanded accounting equation, show how this transaction affects assets, liabilities, and equity. Which PCN accounts are involved?