The Balance Check: Why the Balance Sheet Balances

Introduction

When Luca Pacioli published his *Summa de Arithmetica* in Venice in 1494, he included a short treatise describing how Venetian merchants kept their books, recording every transaction in two places so that the totals always agreed. A first edition sold at Christie's in 2019 for $1.2 million, as FM magazine, published by the Association of International Certified Professional Accountants, reported in its story on the Pacioli sale. More than five centuries later, the same idea sits at the heart of every financial model a banker builds: if the balance sheet does not balance, something has been recorded in one place but not the other.

The balance check is the test of that idea. In a set of historical statements, the balance sheet balances by construction. In a projection, where each statement is forecast separately and linked to the others, as in a three-statement financial model, the check confirms that every link is in place. A model that balances is not necessarily right, but a model that does not balance is certainly wrong, and the size of the difference is usually the best clue to the error.

The accounting equation, explained in the accounting equation, says assets equal liabilities plus equity. It holds at every date, so it must also hold for the change between two dates: the change in assets must equal the change in liabilities plus the change in equity. Every flow recorded on the income statement or the cash flow statement has to respect that, and each one does, because each has two ends:

Balance check

The test that total assets equal total liabilities plus shareholders' equity at every balance sheet date. In a financial model it is usually shown as the difference between the two totals, which must be zero in every period; any non-zero figure means a flow has not been linked correctly.

The Cash Flow Statement Is the Equation Rearranged

The cash flow statement is what closes the loop. Split assets into cash and everything else, and the equation can be rearranged to show that the change in cash equals the change in liabilities and equity, less the change in non-cash assets:

That is exactly what an indirect-method cash flow statement computes. It starts from net income, the main change in equity; adds increases in liabilities and subtracts increases in non-cash assets, line by line; and arrives at the change in cash. If every non-cash balance sheet movement appears somewhere on the cash flow statement, the resulting cash figure is precisely the one that makes the balance sheet balance. The full map of those links is in how the three statements link.

Accrued interest, interest that has been incurred but not yet paid, is a good test, because it touches all three statements without moving the cash for interest at all. Suppose a company accrues $40 of interest at year end, to be paid next year, and pays tax at 25%:

Assets rise by $10, the tax the company no longer pays. Liabilities rise by $40 and equity falls by $30, a net $10. The balance sheet balances because each of the three movements was recorded with both of its ends: the expense reduced equity and created a liability, the tax saving raised cash and reduced tax expense, and the cash flow statement added back the unpaid interest so that cash rose only by the tax saving. Leave out the accrued interest line on the cash flow statement and cash falls by $30 instead, assets fall by $30, and the balance sheet is out by $40, exactly the amount of the missing link. The step-by-step method for any transaction is set out in tracing a transaction through the statements.

Bookkeepers have long used the size of a difference to find errors in a trial balance: they divide an unexplained difference by 2, to look for a balance entered on the wrong side, and by 9, to look for transposed digits. The same reasoning works on a model's balance check, translated into the language of links:

Links That Are Easy to Miss

Most imbalances come from a small set of links. Non-cash transactions, such as equipment acquired under a lease or debt converted into shares, change the balance sheet without passing through the cash flow statement, so a model must link them directly; they are listed in the supplemental disclosures. Dividends must reduce both cash and retained earnings, and the retained earnings roll-forward is the place to confirm it. Stock-based compensation is added back on the cash flow statement and must also increase paid-in capital. Deferred taxes need both a cash flow line and a balance sheet balance. And every new balance sheet line added to a model needs a matching line on the cash flow statement, or the equation breaks.

Circularity causes a different kind of problem. When interest is calculated on average debt or cash, and cash depends on interest, the model loops; if the loop fails to settle on a single interest figure, or an error spreads around it, the balance check can fail even though every link is in place. How models handle that loop is explained in the blog's guide to circular references in financial models.

A balance sheet that balances proves the links are consistent, not that the numbers are sensible. A model can balance perfectly while projecting implausible margins, working capital that grows faster than revenue, or capex below depreciation for a decade. It can also balance while classifying items wrongly, for example recording an acquisition as capex, because both are investing outflows that land on long-lived assets. The check is a test of the wiring, not of the judgment.

That is why bankers run it first and then move on to sense checks: does cash flow from operations track net income over time, do PP&E and debt roll forward cleanly, does the cash balance stay positive without unexplained revolver draws. The Valuation guide's article on building the three-statement model covers how those checks fit into a full model. The balance check is the floor beneath all of them: it does not make a model right, but no model is right without it.