Accounting Equation

Everything a business owns (its assets) must have been financed in one of two ways: by the owner (capital) or by others (liabilities). That gives the accounting equation:

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

It can be rearranged to find any unknown:

• Capital = Assets − Liabilities (the owner's stake, also called net assets).
• Liabilities = Assets − Capital.

Example. A business has assets of $80,000 and liabilities of $30,000.

• Capital = $80,000 − $30,000 = $50,000.

The equation must always balance, because of duality — every transaction has two equal effects.

Every transaction changes the equation while keeping it in balance. Some examples:

Transaction	Effect	Equation stays balanced?
Owner pays in $5,000 capital	Assets (bank) +5,000; Capital +5,000	Yes
Buy machinery $2,000 by cheque	Assets (machinery) +2,000; Assets (bank) −2,000	Yes (asset swap)
Buy goods on credit $800	Assets (inventory) +800; Liabilities (payable) +800	Yes
Pay a payable $300 by cheque	Assets (bank) −300; Liabilities (payable) −300	Yes
Owner takes $400 drawings	Assets (bank) −400; Capital −400	Yes

Notice that a transaction can affect two assets (an asset swap), an asset and a liability, or an asset and capital — but the two sides always move by equal amounts.

The owner's capital at the end of a period is not the same as at the start — it changes during the year:

$\text{Closing capital} = \text{Opening capital} + \text{Capital introduced} + \text{Profit} - \text{Drawings}$

Rearranged, this gives the formula examiners love for incomplete records:

$\text{Profit} = \text{Closing capital} - \text{Opening capital} + \text{Drawings} - \text{Capital introduced}$

Worked example. Opening capital $50,000; closing capital $62,000; drawings $15,000; no extra capital introduced.

• Profit = 62,000 − 50,000 + 15,000 − 0 = $27,000.

This works because capital = net assets, so the increase in net assets, adjusted for drawings and any capital introduced, must be the profit.

The statement of financial position (SOFP) is just the accounting equation written out formally at a point in time:

• The top half lists the assets (non-current + current), giving total net assets (assets − liabilities).
• The bottom half shows how they were financed — the capital (for a sole trader: opening capital + profit − drawings).

Because net assets = capital, the two halves of the SOFP must agree — exactly as the accounting equation must balance. When a SOFP 'doesn't balance', a transaction has been recorded with unequal effects somewhere.

The basic equation hides what happens to capital during the year. Expanding capital makes the drivers of profit visible:

$\text{Assets} = (\text{Opening capital} + \text{Capital introduced} + \text{Profit} - \text{Drawings}) + \text{Liabilities}$

This single line ties together everything in this subtopic:

• Profit increases capital (income > expenses), so it increases net assets.
• Drawings reduce capital, so they reduce net assets.
• Capital introduced increases capital but is not profit.

Why it matters for A Level. It explains why the incomplete-records formula works: rearranging the expanded equation for profit gives

$\text{Profit} = \text{Closing capital} - \text{Opening capital} + \text{Drawings} - \text{Capital introduced}$

because closing capital already contains opening capital + capital introduced + profit − drawings. Seeing the formula as a rearrangement of the equation, not a rule to memorise, is what lets you adapt it to any variation a question throws at you (extra capital mid-year, goods drawings, etc.).

A sole trader's statement of financial position is the accounting equation in vertical form:

	$
Non-current assets	X
Current assets	X
Less current liabilities	(X)
Less non-current liabilities	(X)
NET ASSETS	X
Capital
Opening capital	X
Add profit for the year	X
Less drawings	(X)
Closing capital	X

The net assets (top) must equal the closing capital (bottom) — because Assets − Liabilities = Capital. If they do not agree, an entry has unequal effects, an item is missing, or profit/drawings have been mis-stated.

Exam discipline. When a statement of financial position 'won't balance', check in this order: (1) is profit correct? (2) are drawings included? (3) is every asset and liability listed once, on the right side? (4) has any adjustment (depreciation, accruals) been applied to both the SOPL and the SOFP?