The accounting equation

$\text{Assets} = \text{Liabilities} + \text{Equity}$

This is not a law discovered about businesses. It is true by definition, and understanding why is worth more than memorising it.

Why it cannot fail

Assets are everything the business controls. Liabilities and equity are a complete answer to where it came from — either somebody lent it or the owners supplied it.

Every rupee of resource has exactly one source. So the left side lists the resources and the right side lists the claims on them, and they describe the same pile from two directions. A balance sheet that does not balance has an arithmetic error, not a business problem.

What each term actually means

Assets — resources the entity controls, from past events, expected to produce future economic benefit. Three conditions, and all three matter:

• Controls, not owns. A leased machine can be an asset (chapter 10).
• Past events. A contract signed for next year's purchase is not yet an asset.
• Future benefit. Something that will generate nothing is not an asset, however much was paid for it.

Liabilities — present obligations from past events whose settlement is expected to transfer resources out. Again present and past: an intention to spend is not a liability.

Equity — the residual. This is the term people misunderstand most:

$\text{Equity} = \text{Assets} - \text{Liabilities}$

Equity is defined as what is left over, not measured independently. It is not the company's value, not its market capitalisation, and not cash available to owners. It is a subtraction. Chapter 19 of the Company analysis subject's caution about price-to-book is this fact arriving at a valuation.

The equation expanded

Equity has parts, and separating them is what makes the income statement connect to the balance sheet:

$\text{Assets} = \text{Liabilities} + \text{Share capital} + \text{Retained earnings}$

Share capital is what owners put in. Retained earnings is accumulated profit that was not paid out — every year's profit adds to it and every dividend subtracts.

So the income statement is not a separate document. It is an explanation of the change in one line of the balance sheet, and chapter 3 of the Company analysis subject's "three statements that connect" is this link.

Working the problem

Step	Assets	=	Liabilities	+	Equity
Invest ₹10L	Cash 10		0		Capital 10
Borrow ₹5L	Cash 15		Loan 5		Capital 10
Buy equipment ₹8L	Cash 7, Equipment 8		Loan 5		Capital 10
Sell services ₹2L	Cash 9, Equipment 8		Loan 5		Capital 10, Retained 2

Three observations worth more than the arithmetic:

Borrowing did not make you richer. Assets rose by ₹5 lakh and so did liabilities. Equity is unchanged. Debt changes the size of the balance sheet, not the owner's stake — which is chapter 11 of the Corporate finance subject's starting point.

Buying equipment changed nothing on the right. One asset became another. Spending cash is not an expense; it is a swap, until the asset is consumed.

Only the sale touched equity. Earning does. Financing and swapping do not. That is the distinction the whole system is built to preserve.

Why it still balances after everything

Every transaction does one of four things:

1. Increases an asset and an equal liability or equity
2. Decreases an asset and an equal liability or equity
3. Swaps one asset for another
4. Swaps one claim for another

There is no fifth option, because there is nowhere else for a rupee to go. That constraint is what chapter 3 turns into a mechanical bookkeeping rule.

The point

Assets equal liabilities plus equity by construction: the left side lists resources, the right side lists where they came from, and both describe the same pile. Equity is a residual — a subtraction, not a measurement — and retained earnings is the line through which the income statement connects to the balance sheet. Borrowing changes the size of the balance sheet without changing the owner's stake, and spending cash on an asset is a swap rather than an expense.