The balance sheet and the tie

The income statement and the cash flow statement both cover a stretch of time and are meaningless without one. The balance sheet is a single instant. Nothing on it happened during the month; everything on it is what was left standing at the end of it.

That is why the sheet has no subtotal you can call performance. It has a shape instead, and the shape is the whole argument: what the business controls on one side, and who has a claim on it on the other.

Each row the engine returns carries the whole sheet, plus the two totals and the difference between them. There is no separate balance sheet object, because the sheet is the row.

No credentials of any kind are involved. If an example ever needs one, the string is the word placeholder.

Everything a business controls was paid for by somebody: a supplier waiting to be paid, a lender, or the owners, including through profits they left in the business. There is no fourth source. So the total of what it controls is the total of the claims on it, necessarily, not by agreement.

That is what makes the sheet usable as a test. A rule can be waived and a convention can be argued about. An identity cannot fail, so when the two sides differ the failure is in the recording, and the recording is the thing you can go and look at.

Payables and debt are claims for fixed amounts: a supplier is owed what the invoice says. Equity is whatever is left after those are satisfied, which means it absorbs every change that is not itself a claim. Profit raises it, a loss lowers it, and no one negotiates the figure.

In this engine that residual character is literal. Equity is the only balance on the sheet that no assumption drives directly. It opens as a solved number and then moves by net income, once a month, for as long as the model runs.

One balance, two opposing flows. Capex adds to it and never touched the income statement. Depreciation takes off it and never touched the bank. A single netFixed figure therefore tells you nothing about either on its own, which is exactly why both appear separately on the cash flow statement.

Marchmont spent £180,310 and depreciated £102,025 over twelve months, so the line grew. A company whose net fixed assets shrink year after year is depreciating faster than it is investing, which is a fact about the future rather than the past.

Equity is not a measurement of anything. It is a definition: what is left when the claims of everybody else are met. Asking a modeller to supply it as an input is asking them to state a number that, if it disagrees with the other six, is simply wrong, because the other six describe things that physically exist and equity does not.

So the engine computes it once, at month 0, from the six balances that do describe real things.

Session 1 set out the argument against this and it is a real one: a solved opening means month 0 cannot fail, so the tie is testing the forward mechanics rather than the opening data. The useful response is not to argue, it is to know precisely which half of the model the check covers.

A plug is a figure inserted repeatedly to absorb a difference nobody has explained, usually every period, often with a name like other or adjustment. Its signature is that it moves when something unrelated changes and nobody can say why.

Marchmont's opening equity is computed once, from a definition, and never touched again. After month 0 it moves only by net income. If it were a plug, a change in the collection setting would move it; run { dso: 45 } and it does not, because collecting sooner rearranges cash and receivables on the same side of the sheet.

If the tie cannot test the opening position, something else has to. The honest substitute is a reasonableness check on the six given balances, which is a different kind of test and worth running by hand.

Opening receivables of £1,000,000 against month 1 revenue of £400,000 implies two and a half months of sales uncollected, which is the 75 day collection setting and is consistent. Opening inventory of £464,000 against a 60 day stock setting is two months of cost of sales, also consistent. A sheet whose opening receivables implied eight months of sales would tie perfectly and still be wrong, and only this check would catch it.

Each row carries its own tieError, computed as assets - liabsEquity at the moment the row is built. ties walks all of them, keeps the largest absolute value and compares it to a tolerance that defaults to a penny.

Two consequences worth holding onto. The check reads a stored field rather than recomputing, so editing a row's balances without editing its tieError will not be caught. And it reports the worst month only, so a single failing month and a dozen failing months look identical until you inspect the rows.

A computer adding decimal amounts does not land on exact zero, and the residue accumulates slightly with the number of months. Demanding an exact match would make the check fail on correct models, which trains everybody to ignore it.

A penny is the right order of magnitude because it is the smallest amount that could be a real accounting error. The measured worst across all fifty runs is 2.24e-8, which is roughly six orders of magnitude inside that, so the tolerance is not doing any work in practice and would not hide a genuine mistake.

The throw is the load bearing line. A sweep that records failures and keeps going will hand you a summary with a broken run inside it.

In a copy of fin-live.js, stop equity rising in exactly one month and leave every other line alone. This is what recording an invoice against receivables and forgetting the revenue side looks like from the outside.

Run it and the tie error is zero for six months, becomes £38,356 in month 7, and then stays at £38,356 for every month after. It stays flat because later months add their own net income correctly; only the one leg is missing, forever. And £38,356 is month 7's net income, which is the whole point of the check. The failure names the transaction.

Now profit never reaches equity at all. The tie error is non zero from month 1 and grows every month, reaching £445,631 by month 12, which is exactly twelve month net income. A rule has been broken rather than an entry missed, so the damage compounds.

Put the line back and re-run before doing anything else. The discipline that matters here is not the break, it is restoring the file and confirming ties returns ok again, because a broken engine left on disk is the one that gets used next week.

If you would rather not edit the file, you can break a single row in memory. Because ties reads the stored tieError rather than recomputing it, the row's own total has to be updated too, which is itself the lesson.

Change only the first line and the check still passes, which is worth seeing once. A check that reads a stored result can only catch what the recording step recorded.