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Comment by sago | Hacker News Reader

It is not incorrect. To make everything positive (and use the subtraction as you have) you need to have two different types of 'positivity' Credit and debit. And then you have to remember which things are subtracted and added so it gets back to balancing. That's why it gets so complicated.

Money in your bank account is _negative_. It is a _debit_ in your accounts (this is not my invention this is true). Your bank account statement is from the bank's perspective. The money came from you, so it is a credit from their perspective only. Try to submit your statutory accounts with 'bank credit' and you'll get in trouble! Your software or accountant will definitely flip it to become a debit!

Your transaction to start your account:

Equity: $100 (or $100CR)

Bank account: $-100 (or $100DB)

Loan:

Debt: $100 (or $100CR)

Bank account: -$100 (or $100DB)

Accounts:

Assets > Bank account: $-200 (or $200DB)

Liabilities > Debt: $100 (or $100CR)

Equity: $100 (or $100CR)

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> Money in your bank account is _negative_.

Say I have two million dollars and deposit one million in the bank and buy a one million house.

What is the value of my assets? -$2mn? $0mn? Something else?

The "confusing" answer would be that the value of my assets (which is equal to the value of my equity, as I don't owe anything to anyone) is two million dollars.

In a conventional double accounting system:

  Deposit
  Asset>Cash in Hand CR$1m
  Asset>Bank: DB$1m

  House purchase
  Asset>Cash in Hand CR$1m
  Asset>Property: DB$1m

So all I'm suggesting is to use of negative numbers instead of tracking everything in terms of credits and debits.

  Deposit
  Asset>Cash in Hand $1m
  Asset>Bank: $-1m

  House purchase
  Asset>Cash in Hand $1m
  Asset>Property: $-1m

In either case the value of your assets at the end is unchanged, because you're just turning assets into different kinds of assets.

But let's say you started with DB$2m (inheritance say, or you won the lottery). You end with DB$2m assets.

I'm not reinventing anything here. Where do you want to label your $2m as 'debit' every time, or use negative numbers, either way is the same.

People do always struggle when learning accounting to comprehend how money in their assets is debit. Because they are so used to seeing 'credit' on their bank statements. But it is only credit because there was from the banks point of view.

I'm not talking about credits and debits. In the version of accounting I know the balance sheet (edit: I'm not talking about the transactions, I'm talking about the aggregate balance) says simply:

  ASSETS
  ======

  $1mn Cash (in the bank) 
  $1mn House
  ----
  $2mn

What does the balance sheet look like for you? -$1mn plus -$1mn, i.e. total assets -$2mn?

Is that less confusing than total assets being $2mn when you have two assets worth $1mn each?

If the things you're doing are so simple that you don't have to worry about credit or debit, you are free to show it that way.

But if you are doing accounting, debits and credits and balancing is important.

So yes, if you are happy to ignore debit/credit/balanced books, you are welcome to view asset as $2m. And lots of the simple accounting software will show it that way.

But by the time you are having to understand different types of accounts and different types of money in it, I think it is easier to use negative numbers are rather than CR/DB.

Yes, balancing is important. That’s why I’d prefer to end with assets that make sense in the balance sheet (or maybe you're happy to ignore balance sheets and don't want meaningful numbers?). I don’t see what do you gain by making the assets negative.

Believe it or not, I’ve seen financial accounts quite more complex than two lines (and they never included those CR/DB annotations in the balance sheets or income statements).

This has been an interesting conversation with several people. I am really surprised how much negative numbers are confusing or interpreted as my idiosyncrasy.

> I’ve seen financial accounts quite more complex than two lines

Definitely.

For hundreds of years the convention has been columns. Credit values in the right-hand column, debit values in a left-hand column. The column is the label of which type of money it is. Most accountancy software (other than very simple personal tracking apps) use this when displaying.

Your printed bank statement probably does (and it may label the columns credit and debit as well, though never line by line, iirc). Mine did back when paper was the thing.

Digital bank statements usually do use negative numbers (DB being negative, as I've been saying). You are used to seeing this, but not used to thinking in your own accounting terms rather than theres. Which is fine. But there is a reason that accountancy education has to undo that assumption.

I have no problem with negative numbers.

But most people would find your idea of using negative numbers for assets rather idiosyncratic.

It's more natural to say that the assets of Goldman Sachs are $1trn than to say that they are -$1trn, for example.

It's definitely not my idea! It wasn't Goldman Sachs, but I did a consultancy 15 Years ago for a large bank (my little job was a long way from programming the core, but used it extensively). Their system stored debit as negative numbers. That's when I learned it and had the aha moment when everything instantly simplified. Since then all the accounting software I've seen the inside of do.

Most lay-people find double entry in accounting idiosyncratic. It has this bad reputation for being full of special case rules.

It is interesting that the one comment I got from an accountant on here it seemed fine with debit as negative numbers.

Goldman Sachs absolutely know that they have DB$1tn! Anyone who thinks it is either a credit account or just a bare number is not going to be dealing with that!

Thanks for carrying on the chat.

> It stored debit as negative numbers.

Did it display assets in the balance sheet as negative numbers?

> the one comment I got from an accountant on here it seemed fine with debit as negative numbers

Was that accountant fine with assets as negative numbers?

> Goldman Sachs absolutely know that they have DB$1tn!

The did have $1tn in their balance sheet. No DB, no CR. Just $1tn.

> Did it displayed assets

It's an API. There are many tools built on top of it, many with UIs. I'm sure they display things in many different ways for people internally and externally. The system I was working was back-end. It used negative numbers for debits. And it was really important you didn't confuse credit and debit numbers.

> Was that accountant fine with assets as negative numbers?

I find it hard to believe they didn't understand that's what Using negative numbers for debits means. They would be pretty aware that assets are debit accounts.

> The did have $1tn in their balance sheet. No DB, no CR. Just $1tn.

Did they have a complex balance sheet (I.e. beyond that just a couple of lines summary) with no columns? How do they represent a balance if you couldn't tell which were credits and debits?

For the record, this is what the consolidated balance sheet looks like: https://imgur.com/a/i8q0Fa2

Neat. Thank you. I get what you're saying now.

And that makes sense. You can see the balance. Because it will balance. Or you'd know which of the things were debit accounts and which went credit accounts.

Yep.

But I definitely bet it's not raw unsigned/untyped numbers behind that document! I suspect we've just been mismatching on different levels: I began this discussion about developers understanding double entry bookkeeping. I would be surprised if you could get very far if you didn't understand the difference between debit and credit. But your pushback makes sense. Thank you.

I do understand the difference between debit and credit. The point is not whether you can balance the books looking at them when they fit in a single page. The point is that in a balance sheet assets appear as $x (where x is rarely negative, an asset with negative value would become a liability).

People want assets to be positive in the balance sheet. This may be a convention but it's a reasonable convention. I don't think you're helping developers who try to understand accounting by telling them that assets are negative quantities (it may make sense as an implementation detail, but not so much as an accounting concept).

If you are using a negative numbers you can do it in three ways.

1. positive numbers represent the default for an account (A positive number in a debit account is a debit, but a positive number in a liability say, is a credit). This is done a lot. But he causes a lot of rules about when to add and went to subtract what the balance with what. I think this is why they lot of double entry bookkeeping and has a hard reputation. Certainly if you coded it you would have to code all those rules manually.

2. The approach I'm used to of having negative numbers in the debits and positive credits. This makes all the double accounting balancing much simpler. But I can see it may confuse some people when assets are negative.

3. Make credits at the beauty of an debits positive (incidentally I only today learned that beancount does it this way). Again balancing and double-entry accounting becomes simpler. Now money in the bank would be positive, like your bank statement. But sales income would be negative (it is a credit). I wonder if that would confuse people.

So maybe that's why UI should make everything positive and undifferentiated. But given the amount of time the Accounting 101 has to drill in all the rules of what

> 2. The approach I'm used to of having negative numbers in the debits and positive credits. This makes all the double accounting balancing much simpler. But I can see it may confuse some people when assets are negative.

So, if people were able to overcome their confusion, would you have balance sheets written like this?

   $ in millions
   
   ASSETS                                        LIABILITIES AND SHAREHOLDERS' EQUITY
   
   Cash and Short Term Investments   -133546     Deposits                      117756
   Other Assets                      -859422     Other liabilities             784947
   ------------                      -------     -----------------             ------
   Total Assets                      -992968     Total liabilities             902703

                                                 Shareholders' equity           90265
                                                 ====================          ======
                                                 Total liabilities
                                                 and shareholders' equity      992968

If you really want to change the signs in one of the sides, so instead of getting the same totals they sum to zero, it would make much more sense to do it the other way: keep assets positive and let liabilities be negative (as other commenters have suggested).

   $ in millions
   
   ASSETS                                        LIABILITIES AND SHAREHOLDERS' EQUITY
   
   Cash and Short Term Investments    133546     Deposits                     -117756
   Other Assets                       859422     Other liabilities            -784947
   ------------                       ------     -----------------            -------
   Total Assets                       992968     Total liabilities            -902703

                                                 Shareholders' equity          -90265
                                                 ====================         =======
                                                 Total liabilities
                                                 and shareholders' equity     -992968

But one property of the usual presentation is lost: equity is no longer equal to net assets (which are $90265mn). You would need to change the sign of equity when considering it as an asset.

> But sales income would be negative (it is a credit). I wonder if that would confuse people.

It does tend to cause some confusion, but IMHO less than you would get with negative asset balances, much less the traditional version where "credits" and "debits" have different signs depending on the type of account and nothing ever just sums to zero.

The less confusing way to think of it is that an income account represents not "how much income have I received" but rather the source of the income, e.g. your employer or customer. They paid you, so they have less than they started with.

⋄ Money moves from employer to me: decrease "Income:Employment" and increase "Assets:Cash".

⋄ Money moves from me to my landlord: decrease "Assets:Cash" and increase "Expenses:Rent".

⋄ Deposit money at the bank: decrease "Assets:Cash" and increase "Assets:Bank:Checking".

⋄ Take out a loan: decrease "Liabilities:Loan" (negative since I owe them money) and increase "Assets:Cash".

Note that Income and Expense account balances are relative—which is why it makes sense for Income balances to sometimes be negative, and why these accounts are zeroed out at the end of the reporting period with transfers to or from equity—in contrast to most other accounts which have absolute balances.

Assets + Liabilities + Equity = 0 is incorrect.

It's just simple basic maths formula, A = L + E so it's either 0 = L + E - A or A - L - E = 0, or A - L = E or A - E = L all stands true.

A=L+E

is true because L and E are Credit dollars and A is Debit dollars. And the total Debit is equal to the total Credit.

But instead of using debit and credit unsigned dollars, you can use negative numbers: Credit is Positive, Debit negative.

In that case

(-Assets) = Liabilities + Equity, so A+L+E=0

-Assets because you've made those debit dollars negative.

In fact you don't even have to remember which. Sum(Everything)=0. 'Balancing' means summing to 0.

The software I am aware of that does large-scale double entry calculations for large banks works this way (I did some consulting 15 years ago on data laundering for that system). And all those accounting rules about what accounts are debit or credit accounts, whether a credit increases the debit account, etc, it all isn't needed at a low-level. The confusing bits are only in the UI. Where a number stored as -10 is displayed as 10DB, while +10 becomes 10CR.

So it's definitely not 'just simple maths'. It is the convention you use to express numbers: turning debit numbers into positive, and having rules to keep the math consistent in other places. And since the original article was aimed 'at developers', I think that the widespread negative number format is much stronger.

Equity is similar to a liability. Ít is owed to the owners of the entity.

Making assets positive in code is conventional.

> Equity is similar to a liability. Ít is owed to the owners of the entity.

You can kind of see the easy rationale there. I'm not sure it's very deep though. Revenue is in the same group (Credit). And the assets are like expenses (Debit). That is a bit more of a just-so-story in my mind.

> Making assets positive in code is conventional.

Are you sure? What code are you talking about?

Making everything positive in the UI is certainly common. And not showing whether a value is credit or debit. But I really hope my accountancy software isn't coded that way! It needs to track whether a number is a credit or a debit. It could do it with an unsigned value in a struct with a 'is_cr' Boolean and some custom operations to combine the money structs. But I've only ever seen code using signed values, because it is so much faster and less errorprone. Doing it manually is just reinventing the math of negative numbers. And then, the overwhelming convention is the former is positive, the latter negative, not the other way round.

For one example, read the docs for Beancount, which is mentioned above.

Signed values are the way to go!

> Signed values are the way to go!

100% agree!

> For one example, read the docs for Beancount, which is mentioned above.

Do you have other examples too?

You are dead right with this one. It is the opposite way to the way the systems I'm familiar with did it. Debit is positive, And credit negative.

Thanks so much for the link.

I'm still not sure what I would concede that it is conventional ;) But my assumption it was nothing but the other way is definitely incorrect!

I wonder if they did it this way because they felt people would understand negative income being a good thing better than a negative bank accounts being a good thing. The bank account is usually the big problem with understanding debit and credit.

As usual, the world is more complex and interesting then I assume!

When you first open a business, you put in capital - owner's equity. So the cash account (an asset) increases, and the equity account (a liability) also increases.

In a computerized system, one of these accounts carries a negative balance, the other a positive balance. A choice has to be made - but it's not a matter of good or bad.

There are several implementations of the Ledger system. The transaction registers and GL are human-readable. I looked at Ledger, and assets were positive.

I looked in the code for the GNUCash engine, but there are so many features that I didn't manage to get to the bottom of it w/o spending too much time on it :-)

I do recollect working with low level GC transaction data years ago, and I think I would remember if the assets were negative.

There are a couple of Wikipedia pages with links to FOSS accounting systems.

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