Triple-Entry Accounting

Triple-Entry Accounting Briefly Explained

Of all the wonderful things that Italy has brought to this world, two of them have really stood the test of time – musical staff notation by Guido d’Arezzo, a Medieval musical theorist whose invention set the foundation for music; and double-entry bookkeeping by Luca Paccioli, a Renaissance mathematician whose book Summa de Arithmetica, Geometria, Proportioni et Proportionalità set the foundation for accounting, the language of modern capitalism. Like the best of the Italian recipes, these two incredible Italian inventions have been frozen from the moment they were invented and have never been changed to this date.

As I do not purport to be an expert in music or culinary art, I would simply focus on double-entry bookkeeping, a subject that I have spent the last seven years trying to break the secret code of its longevity – why the capital market and its participants, namely, investors, issuers, intermediaries and regulators, have maintained such as a blind faith in double-entry and its accounting equation of Equity = Asset – Liability for so long and never once doubted the validity of an ancient concept in a highly evolved modern capital market with accounting as uncertain as fair value and products as complex as derivatives, not during the 2008 financial crisis, not even today.

The consequence of the blind faith in double-entry bookkeeping has been catastrophic since 1970’s when commercial uses of personal computers and the mathematization of finance in the economy gave rise to discounted cash flow (“DCF”) valuation and contingent revenue, which is a unilateral economic activity based on assumption makings that most fiscal models and asset valuation models are premised on. What has made DCF valuation and contingent revenue truly catastrophic is that as they are not subject to any economic disciplines such as accounting principles or legal constraints such as covenants. They are the wild, lawless frontier of finance. For example, Donald Trump proclaimed that the annual economic growth rate in his budget would be 5% or even 6% because the actual annual economic growth rates of 1% during the last eight years had been too low. Since he alone can make America great again, why cannot he alone make the economy grow at 6%?

Given the economic gravity defying assumption of the 6% economic growth rate, the contingent tax revenue would pay for his proposed massive tax cut, the trillion-dollar infrastructure programs, reductions of national debts and fiscal deficits as well as many of his electoral promises. However, the simple question that nobody has asked is “what would happen if the economy grows at actual 1% instead of the assumed 6%?”

Accrual accounting dictate that whenever revenue is recognized, there must be matched expenses recognized as well – they are called the revenue recognition principle and the matching principle, a cornerstone of GAAP. In accounting for goods sold and services rendered, revenue and costs must be accrued in double-entry ledgers first and then posted to financial statements for recognition and matching when realized. Hence, as per the same accounting principles, when contingent tax revenue is realized, there must be contingent economic expenses realized and matched during the same reporting period. Unfortunately, given there is not an accounting journal entry for prospective, contingent expenses, the non-accrual of contingent expenses of contingent revenue based on assumption making has rendered recognition of contingent revenue a practice of cash accounting instead of accrual accounting.

What would happen if Donald Trump fails to deliver his promise for 6% economic growth that his economic gravity defying budget is premised on but delivers an actual 1% economic growth? How would the contingent expenses of the 5% shortfall in growth rate be accounted for? Sadly, they are neither accrued nor posted for recognition and matching with the recognized contingent revenue. As a matter of fact, Donald Trump’s electoral promise for the 6% economic growth is a free political gamble – if he did achieve the 6% target rate, the contingent tax revenue would be recognized (free of any matching expenses) as his accomplishment, whereas if he failed to deliver by achieving only 1% actual growth rate, the contingent expenses (the unrealized contingent revenue of the 5% growth rate shortfall) of an egregiously irresponsible political gamble would be accrued as actual tax revenue shortfall to his unfortunate successor during the next electoral cycle. What a master for the art of the deal!

To be fair to Donald Trump, he did not invent this electoral shenanigan. The use of cash accounting for recognition of top line contingent revenue in public budgeting and the use of accrual accounting for recognition of the bottom line fiscal performance was a long-established fiscal practice. The political consequences of the double accounting mismatching (the mismatching between cash accounting recognition of top line contingent tax revenue and accrual accounting recognition of bottom line, actual fiscal performance, and the mismatched revenue and expenses reporting periods) was discussed in my recent article The Failure of Public Governance.

Double-entry bookkeeping was designed to accrue historically incurred costs in bilateral transactions that are easily recognizable, but was not designed to accrue prospective, contingent expenses that are probabilistic and evolving (dynamic). Unfortunately, unaccrued contingent expenses of contingent revenue based on assumption making are historically cumulative and will post themselves when realized suddenly on the day of reckoning, i.e. when actual performance is less assumed.

Triple-entry bookkeeping, the first level of cognitive discovery of GC economics, is designed to accrue contingent expenses of contingent revenue with a third entry called probit. Each probit entry is for accruing an assumption with a portfolio of likely contingent expenses. When one of the contingent expenses is either realized (100% probability) or is above a certain probabilistic threshold (say 80% probability) for being realized, it would be posted to financial statements for recognition and matching with the contingent revenue. In GC rating, this is called discharges of fiscal or valuation uncertainties.

If the assumption proves to be realistic during a reporting period, there would be zero contingent expenses realized to be recognized during the same reporting period. However, if market conditions changed to prove the assumption unrealistic during the next reporting period, a certain contingent expense from the probit portfolio would be realized to be posted in financial statements to be recognized and matched with the contingent revenue (GC rating discharged) during the same reporting period.

Triple-entry bookkeeping can effectively deter irresponsible electoral promises that politicians often make during elections as well as reckless corporate assumption making for generating excessive valuation gains by matching contingent expenses with contingent revenue during the same reporting period – this would reduce the urge for making excessively aggressive assumptions. It also provides traceable audit trails so that audit of contingent revenue, assumption making and contingent expenses would be possible.

Mr. Paccioli made a significant contribution to fraud detection and prevention in financial reporting (via the accounting equation of Equity = Asset – Liability) that made modern institutional capitalism (focusing on the rights and profits of nonproprietary, institutional shareholders) possible, whereas triple-entry bookkeeping expands the fraud detection/prevention to unilateral economic activities (via the Valuation Solvency Test – please see its conceptual page for more detail) so that civil capitalism (focusing on the civil and economic rights of all stakeholders, including individuals) would become possible.

I wonder how Mr. Guido d’Arezzo’s musical notation invention can be further improved to allow music compositions convey more sentimentalities. This may require the imagination of a musical genius bigger than Bach and Mozart.