Sweet Accounting

by Tom Veatch

Finally everything clicked so I want to share this with you.

If you are like me and you ever tried, or are now trying, to learn Accounting, please read this if you want to Understand.

I've never been able to get a CPA, Accountant or Bookkeeper, Consultant, Investor, or Teacher to admit what I'm saying is true. They seem to say, teach, and apparently think, that you just have to memorize all these account categories and a bunch of made up terms that have nothing to do with anything, and there's no such thing as actually understanding it.


So I'm going to tell you how it really works, and why. And you are going to really understand it, or tell me why not! Okay?

Okay. Sweet.

TL;DR Summary

(1)   Equity = Assets - Liabilities

The figure of interest in the Actual Accounting Equation (1) is owner's position or Equity, defined as Assets minus Liabilities, viewed at an instant in time (statically). To view a position's changes over a period of time (dynamically), we also separately track and summarize Income minus Expense events or transactions within the period, then apply those also to the position.

(2)   Equity = (Assets - Liabilities) + (Income - Expenses)
Balance is made evident, and signs are specified, by setting one side of the equation to zero and giving Equity a positive sign on the other side. Rearranging (2), then, we have:

(3)   0 = Equity - Assets + Liabilities - Income + Expenses

Thus arranged, to reveal Balance and assert positive Equity, the profession defines "Dr" or "debits" as amounts applied to any account which increase the right hand side of (3), while "Cr" or "credits" are defined as amounts which decrease the RHS of (3).
Thus debits result in expansions in equity, liabilities, or expenses, and contractions in assets or income, while credits are the opposite.
For example, for an increase in Assets balanced by an increase in Equity, the Asset change is in the Cr column which by expanding the (negative) Asset column decreases the sum in the RHS of (3), while an equal Equity change is recorded in the Dr column, increasing the sum, so that Dr balances Cr, and (3) remains zero. Conveniently, symmetric reasoning solves every such accounting puzzle.

Happily, almost all subtraction is eliminated from such a system -- excepting only at the highest level in summarizing using (3) or (2) or (1). Hence for all categories Equity, Asset, etc., T-accounts that show debits on the left and credits on the right will only have positive numbers in them, and for any transaction it can be locally seen by examining only the affected accounts, whether balance is obtained, by seeing that the Dr's equal the Cr's.

The idea of Double Entry Accounting is this balance requirement, that any transaction or transaction summary if it increases the RHS of (3) must at the same time and in equal amount decrease the RHS of (3), so that the total sum remains zero. If even the smallest transaction is written down in a balanced form, meaning its sum view through equation (3) is zero, then any summary sum of such transactions, each individually being zero, will also jointly sum to zero. Thus balance in all transactions automatically yields balance within any summary no matter how encompassing.

"Accountant" may be defined as a person who keeps (3) in their head, including all its positive and negative components. Then, mapping to Dr and Cr accordingly -- and hiding this mystery of their simple meaning -- is both efficient work practice and a high barrier to entry, providing excellent job security.

The Math

Accounting is WAY simpler than what is universally presented and taught. Let me bring you down the sweet and easy path to understanding the mysteries of Accounting. Ready to start? Here we go!

  • A) Everything is for the Owner. You, right? It is indeed all about you. Yes!

  • B) So you, the Owner, basically only want to know one thing, how much do you own here, what is your position, what is your Equity.

    Sometimes it's obvious, but really it's only very obvious if you own all your Assets outright and you have no Liabilities, no debt. Then add up your assets, and that's it. Yes, that would be right, if you could do it, and it's a good idea to go with a strong simple idea sometimes (Dave Ramsey made his career on this) but we want to actually cover everybody here. So we have to deal with Liabilities, too. Even with Liabilities in the picture, the idea is still obvious, if you look at it the right way. Not the Standard way that is taught and doesn't make sense nor the Normalized way that I'll get to later, but the Actual way, in which it actually makes sense.

  • C) The Actual Accounting Equation:
    Equity = Assets - Liabilities

    The actual point of all accounting is, the Owner gets the leftovers.

    Imagine it this way: Sell all your assets (A), use that to pay all your liabilities (L), and then the rest is how much is really yours, we call that owner's Equity. The leftovers. We are honorable and honest here, and you do actually owe what you owe, so first pay off what you owe, and then whatever's left is what you keep, which might be nothing. Because if you have liabilities, then other people have first dibs. You get the leftovers.

    Now the Standard Accounting Equation is usually written E + L = A, with all the numbers positive (as if a Liability is positive), but since you know arithmetic, you know that's the same thing as E = A - L, just subtract L from both sides. Standard and Actual are the same, 100% equivalent to each other, but I say start with E = A - L in the first place, because that is intuitive to me, and it answers the Owner's question, which is the whole point.

    The thing is, it involves subtracting. A lot goes into being organized about subtracting in accounting, because people have a Hard Time with subtraction.

    That's why we add everything up inside each of the different categories, like Liabilities for example, all the liabilities are positive numbers, we add them all up as positive numbers, but then in the Actual Accounting Equation we subtract the (added up) Liabilities from the Assets to get Equity, one subtraction, one time, only at the top level.

    We are going to try to avoid, or at least minimize, the subtracting bit. I have a hard time with it, too, and unless you're an accountant, so do you, and that is the whole driver of the mystery we are going to unpack here. We will see more about it in a second. But for now, it's all about Equity: E. And as the owner, your central question is E, What is E?

  • D) Yes, Equity: this curious beast, this fascinating, most desireable and least fathomable number. It is what wildly fluctuates around as assets and liabilities come and go. It is the invisible number. Equity is the derivative value, what is left over, and what you actually want to know about, as the owner. You have to add and subtract everything else that's actually real, the debts and purchases and inventory and everything and it's the unobservable left over amount that's what we actually care about. It added up differently? You Lost! Or Won! It's all about keeping track of Equity. (Just my opinion. Okay if I'm the Owner then my opinion is the only one that matters. Hah! Right?)

  • E) I'm sure you noticed that things are always in balance, right? Balance is a basic principle in accounting. Things are in balance, things happen in equal amounts in different places: balanced. More Assets: more Equity. More Liability: less Equity. Even transactions that cancel without an effect on equity, like when you buy some job material, then cash goes out and inventory comes in, the out and the in have to be in balance according to their value, which needs to be the same. And remember Equity: we want to know their effect on Equity, which in this case is well defined as a zero effect. Thus we see the different effects, money goes out, product comes in, we see they have the same value, they cancel out, we know nothing else is affected, great, that's satisfying. Balance.

    Balance says: ....

    Did you guess it yet? I know you are close!

    Balance says: Double entry. If you have a number here, it also needs to be over there, so it can be in balance. Sounds like double entry to me. This is what lets you keep track of Equity as you account for all the activity. Stuff sells, cash comes in, the stuff goes out, the stuff didn't cost that much as what came in, so poof some profit appears in Equity. Actually that's triple entry: cash, inventory, and equity. The number, "two" (or is it "duo"), as in duoble entry, is not the point, there could probably be quadruple entry transactions or more. (Wow, then which ones would have to add up, that would be a mess. Soon this will all suddenly become clear; patience!) The point we start from, and stay on, is: balance.

  • F) Okay, now: Observing this balance of effects everywhere, keeping track of positive and negative is the core organizing problem. Nobody wants to use negative numbers. -1 is way too complicated for most people. Seriously, me too, that's why we are walking slowly up behind this one. Sneaking up on it! So okay, let us resolve to make a system where everything we write down is positive in its particular column, and where we can add them all up safely, using a sum of positive numbers for everything in a column or category, and then after almost all is done, at the end, we can do just one or two summary subtractions at the very end, when we can think about it properly, and only do it once. This way we avoid negative numbers (though you might still need to be able to subtract, in the end, or at least compare two numbers to see if they are the same, which just like a way of subtracting and getting zero as the result).

  • G) Finally we come to the big technical idea, which is going to be to write the accounting equation in Normalized Form, that is, as a sum starting with Zero Equals, and with Equity as a *positive* number, and everything else lands however Arithmetic decides.

    Why Zero? Zero is a way to talk about the balance. Zero means any change anywhere has to immediately cancel out with a balancing opposite change elsewhere, otherwise the total won't add up to zero. Zero emphasizes the balance aspect here.

    Why is Equity positive? We could instead decide to subtract it from both sides, so it could be negative on the other side instead; why do we make the arbitrary choice for Equity to be positive? Because as I have been saying, Equity is what it's all about, Equity drives the whole picture. How so? By being positive in this equation. Everything else gets whatever sign happens to fall on it, plus or minus, just so long as Equity is positive.

    From E = A - L we can get E - A + L = 0, or 0 = E - A + L.

  • H) The Normalized Accounting Equation:
    0 = Equity + Liabilities - Assets - Income + Expenses

    (Now, just try to keep track of positive and negative with that mess of signs! That's what we are about to do!) A dollar profit coming in as Income is balanced by a dollar Equity increase. How? By having increases in Income be negative to balance the corresponding increase in Equity. Because it balances. Because they add together to make zero. That's why income is negative in (H). If you get some positive income, okay add that to Income so Income is bigger, now that makes the "- Income" in (H) a bigger negative number, which cancels out a bigger positive number in Equity, because you have to put some over there too, to balance. Perfect. Ditto for everything else. For example, assets up: equity up. Why? Because in (H), an increase in E balanced with an increase in A cancels each other out because of the minus sign in (H) on A, so the total still equals zero. Balance.

On The Classification of Numbers

Now, can you remember all the signs for those categories in (H)? That's your whole entire job, that's what separates the accounting department from sales or production. Once you get that, you can put the price on the whole enterprise and sell it or buy it to make money, and everybody swings from your little finger. So now go memorize (H).

Memorize what is positive, and what is negative in the equation which adds everything to Zero and in which Equity is Positive!)

I'll make it easier for you. Hint, hint! Suppose the things that pull out of the company are positive, and the things that the company has in hand to be pulled from, are negative. So the Owner can pull out their Equity, and Liabilities to lenders are just their right to pull money out of the company in the future, and Expenses are pulling money out of the company immediately, and those are all positive. Pull is Positive. Whereas the negatives are the solid basis, the held-in-hand resources from which there is something to be pulled, those are the Assets and in the current period also the Income. So this equation sets the positive direction to mean in the direction of pulling stuff up and out of the company, and negative being back down towards balance at zero. You can think of it that way if you want, and everything falls out consistently.
Should I cheat and skip ahead to the next secret? Only when you're ready and if you want to, go ahead. Did you remember the positives and negatives in (H) yet? Quiz yourself and then come back here. Now quiz yourself again and then come back here. Don't cheat! It only cheats yourself.

Sorry, this is about to get a little bit uglier. Can you hold on for another complication? Well maybe you were already wondering. See it turns out, of course, that every one of those categories in H can be made larger or smaller (by adding to it or subtracting from it). Even the negatives like assets and income can be made larger (farther from zero) or smaller (closer to zero). And of course, the positives like equity, liability, and expenses can also be made smaller or larger. So plus and minus are no longer a simple matter because there is adding to a negative category and subtracting from a positive category, and we have to be sure the right things go up and down in the end, especially Equity.

But there's really only two directions here, up and down, ultimately.

So what we really need is a concept of what we might call ultimate plusses and ultimate minuses, which we can label every balancing number with, whether within a single transaction, or summed across a whole period of lots of transactions. Because if all the ultimate plusses and all the ultimate minusses each add up to the same number, then they will cancel each other when they are summed up ultimately in (H).

How can we do this? For every category in equation (H) we might find increases as well as decreases in that category, so we'll need two columns for each one, to collect them together separately. It's a holy mess. How do we classify all of them? Answer: Methodically. Let's look at the different combinations, starting from the obvious cases.

  • One thing is really obvious: We could add all the plusses in the plus columns (like additions to or increases in Equity, Liabilities, or Expenses) and put them together. Those obviously pull the sum in the same (positive) direction in (H), right? + + = +.

  • But we could use the double negative concept too, and put the minusses in the minus columns (such as reductions on Income (e.g., discounts), or reductions of Assets (e.g., "shrinkage")) also over here with these ultimate positives. Because − − = +. Together with the previous + + group, that would be everything that contributes an ultimate increase to the result in (H). (Of course it will need, on the other side, to be balanced by a pile of decreases.)

  • Now that we have put together all the increases, the next step would be to find all the decreases in (H) to balance them out, and if the sum of these decreases put together comes out the same as that sum of increases, then they are in balance.

  • So obviously some of the decreases in (H) are the minuses in the plus columns (like decreases in Equity (like when a loss accumulates in the business), or decreases in Liabilities (like when a loan is paid off), or decreases in Expenses (like when a vendor gives a discount)). − + = −.

  • But some of the other decreases in (H) are the plusses in the minus columns (like increases in Assets or Income). + − = −.

  • Both of those piles are single negatives, so they are ultimately negatives in their influence on the sum in (H). So now if you add up this pile of ultimate negatives, it should end up to the same as the other pile, the pile of ultimate positives. So that in the end there is balance.

Now we are really done with the hard part. There's more to talk about, but you know everything now, even if you don't know that you know. So settle in and let me talk a little bit, you'll be surprised and happy.

So, what we want is to be safe and comfortable, I mean, every step we take should keep us safe and comfortable. Not letting things get all out of control and then just hoping and crossing our fingers that it turns out right in the end. No, we want to maintain balance the whole time. We want, in short, a system that works when the whole picture gets put together at the end, and also works for every single transaction taken in isolation. At the micro or transaction level and the macro or summary level: Both.

We could say we just want the "In"s to equal the "Out"s, but as you see income above has opposite sign from equity and both are nice numbers that we want to be positive, so it's a little confusing. "In" to who? Income is "in" to the business, Equity is "in" to the Owner -- therefore "out" from the Business. How can we keep track?

What I personally find confusing is, I want my Equity to grow, and stay in the Company, and keep on getting bigger and bigger so I'm worth more and more, it's not an Out number to me, it's an In number: stay In there and keep on Growing. If I was to liquidate it and have the money, instead, well, money is subject to inflation and it becomes worth less and less, whereas a nice performing Company grows and grows and even changes its prices to follow and outgrow inflation, so thinking of Equity as something I (could) take Out is not the way I like to think about it. Because unfortunately, I identify with my company.

Still, I could take my Equity out, so that's how we account for it.

Anyhow you see we are struggling for some terms here for the Ultimate Plusses and Ultimate Minusses to tag our (temporarily all positive) entries with, so that we can add them up separately and show they are equal. We could say Giver and Reciever like the inventor of double entry said but since he was Italian and doesn't make 100% sense to us we use Italian words, "dare" (to give) and "credere" (to believe), or "Dr" and "Cr" (yes properly trained CPAs do use Dr/Cr for this), or Debit and Credit. That's where it came from. We could use anything so long as they are opposite and we can point them either direction according to (H).

The truth is, these words have no meaning outside of equation (H). But we do need some words like this, like "ultimate positives" (Credits) and "ultimate negatives" (Debits), that will be understandable in the right way if you are following equation (H), and so that the values will cancel in the right way, both with each other within a transaction and across the big equation so that the whole equation stays true at every step as all kinds of transactions go on. So we will invent these two words in order to keep track of the balancing that we require.

So the principle is, we require that debits equal credits in every transaction. This handles the micro level balancing, at the level of each tiny transaction, so we can feel comfortable when the debits equal the credits in any transaction. And when we add and subtract (or compare) the columns at the end using the formula (H), it will also make it work at the macro level, for the whole system altogether after any given period of time.

It works because the ins and the outs, the Gives and Recieves, whatever you want to call them, they are organized to come together following (H). What we say is:

The credits are positive for the positive accounts in equation H. (What follows are negatives and double negatives, based on that.) So: Debits are negative values or reductions that come into the positive accounts in (H). Debits are also positives or increases in the negative accounts in (H). And using the double negative, credits are also those negatives or reductions applying to the negative accounts in (H).

See? That's it.

So yes, sorry, you now have to memorize what accounts are positive credit/negative debit, and which ones are the opposite. Actually you aleady did, with the Normalized Accounting Equation (4) above. And now you know why. It's all because Equity is what we want to calculate and because we use an equation with the sum equal to Zero.

That's really it! Now you understand debits and credits and double entry and balance and owner's equity and every mystery of Accounting.

Go snow 'em!

If you agree that now you do understand it, please will you share it with others? Yes!

Any comments are much appreciated.

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Copyright © 2000-2020, Thomas C. Veatch. All rights reserved.
Modified: January 11, 2018; November 21, 2018, reformatted 6/11/2020