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If you're a mathy person, you might find this brief explanation is enough to get going. Where I say 'you', I mean 'your company', not you personally. * Assets:

If you're a mathy person, you might find this brief explanation is enough to get going. Where I say 'you', I mean 'your company', not you personally. * Assets: things you own (e.g. tractor, money in bank, money owed by customers) * Liabilities: things you owe (e.g. unpaid supplier bills, loan owed to bank) * Assets and liabilities are both measured in a single currency (e.g. $). * Equity (aka 'book value'): A measure of the value of the company. Calculated as Assets minus Liabilities. Two ways to write the equation above: * Equity = Assets - Liabilities * Equity + Liabilities = Assets Equity changes in response to (i) company operations, and (ii) financing activities. Financing activities are things like: - selling new shares - buying back shares (or paying dividends) - borrowing money (bank loans, or issuing bonds) If there were no financing activities in the period, then profit is the derivative of equity with respect to time. It's a measure of the change in (book) value over a period. If book value went up, you made a profit. If book value went down, you made a loss. (Of course, book value would also go up if you just sold some shares, and profit doesn't count those changes, as they're just financing activities.)

antaviana 5y ago
AFAIK, borrowing money does not change Equity, because it increases Assets (more money in the bank) and Liabilities (more debt) by the same amount so Equity stays the same.
- xbryanx 5y ago
  Where are you borrowing this money without any interest? "Money you borrow" and "cost to borrow that money" are rarely the same value.
  - dragonwriter 5y ago
    Normal interest that will be charged if the debt is not paid off is initially neither an asset or liability, it is an expense as it is charged.
  - rahimnathwani 5y ago
    If you take a $1MM loan from a bank: - Your bank account (an asset) goes up by $1MM - Your loan account (a liability) goes up by $1MM So equity is unchanged at that point. But every month after that, you'll be charged interest: - Loan account (liability) increases (CR) - P+L account (equity) decreases (DR)
    - ALittleLight 5y ago
      Presumably you'd have to pay back more than you get in the loan, right? Wouldn't your liability increase by more than a million dollars?
      - brewdad 5y ago
        Not until the interest accrues. You could (no idea why you would) borrow $1MM and immediately pay it back before owing any interest. You would need to reflect this on your books but nothing material has changed.
        thaumasiotes 5y ago
        > You could (no idea why you would) borrow $1MM and immediately pay it back before owing any interest. Can you in fact do that? It's possible with a residential mortgage in the US, because there are laws prohibiting prepayment penalties. And I think even those don't apply to refinanced mortgages?
        avianlyric 5y ago
        Yes, just because it’s hard to find a lender that will except those terms doesn’t mean it’s not possible.
  - djbebs 5y ago
    Interest is not reflected in the balance sheet, but in the income and cashflow statements.
- rahimnathwani 5y ago
  Sorry, yes, I should have been more clear! 1. Profit/loss measures changes in equity resulting from operating activity, as opposed to financing activities (which just rearrange how the company is financed). 2. Examples of financing activities are taking out (or paying back) loans, issuing (or buying back) shares, and issuing dividends. 3. Some (not all, as you point out!) of those financing activities will increase or decrease equity. So, when thinking about profit as the rate of change of book value, you should be careful add back any changes that are the result of financing activities. (specifically: ignore changes in equity due to money going to, or coming from, shareholders)
- riccardomc 5y ago
  This is true in a perfect market, based on Modigliani-Miller theory of capital structure. In reality, increasing debt to a certain point also increases risk, which in turn increases return on equity.
  - mcguire 5y ago
    * should increase return on equity. :-)
  - rahimnathwani 5y ago
    A change in return on equity isn't the same as a change in equity. When a company takes a loan, even if that loan is so large as to make insolvency almost inevitable, there is no impact on equity (book value).
deleted 5y ago
[deleted]
haberman 5y ago
This blog entry taught me a mathy way of understanding double-entry accounting: https://martin.kleppmann.com/2011/03/07/accounting-for-computer-scientists.html https://martin.kleppmann.com/2011/03/07/accounting-for-compu... Summarized: a ledger is a directed graph of accounts, where edges are transactions, and each transaction is recorded twice: in the "from" node and the "to" node.
- rahimnathwani 5y ago
  The article is mostly correct[0], and is very good if the explanation clicks for you. I suspect some people (even some HN readers) would find it easier to think of ledgers as lists of transactions with running totals. [0] e.g. it's not strictly true that book value is a lower bound on company value
- wutangson1 5y ago
  But “a ledger” is not a directed graph of accounts, is it? There is no ‘from - to’ in a ledger. A ledger simply reorganizes the transactions from chronological order (aka journal entries) into subject/account headings. Not the same, but similar to clicking ‘subject’ column tab on your email client to reorganize your emails from descending date to subject attribute.
  - rahimnathwani 5y ago
    That explanation didn't click with me, either. But I guess you could model each transaction as an edge, with the direction specifying which account is debited and which credited, and the weight determining the amount. I don't find that particularly helpful myself, but I put that down to my unfamiliarity with graph data structures and the associated algorithms. Maybe there's something you can do more easily with a graph database, than you can if you have the same info in a table?
    - wutangson1 5y ago
      Sure. Just like blockchain- or any other decentralized ledger- may be a tremendously disruptive technology for property recording, sale/transfer, and financing in the future (compared to the current archaic system of deeds/titles for real property or UCC financing recording for secured transactions); so to, a graph database may clearly illustrate the point of bookkeeping along with the share of assets creditors and investors are entitled to realtime.

antaviana 5y ago

AFAIK, borrowing money does not change Equity, because it increases Assets (more money in the bank) and Liabilities (more debt) by the same amount so Equity stays the same.

xbryanx 5y ago
Where are you borrowing this money without any interest? "Money you borrow" and "cost to borrow that money" are rarely the same value.
- dragonwriter 5y ago
  Normal interest that will be charged if the debt is not paid off is initially neither an asset or liability, it is an expense as it is charged.
- rahimnathwani 5y ago
  If you take a $1MM loan from a bank: - Your bank account (an asset) goes up by $1MM - Your loan account (a liability) goes up by $1MM So equity is unchanged at that point. But every month after that, you'll be charged interest: - Loan account (liability) increases (CR) - P+L account (equity) decreases (DR)
  - ALittleLight 5y ago
    Presumably you'd have to pay back more than you get in the loan, right? Wouldn't your liability increase by more than a million dollars?
    - brewdad 5y ago
      Not until the interest accrues. You could (no idea why you would) borrow $1MM and immediately pay it back before owing any interest. You would need to reflect this on your books but nothing material has changed.
      - thaumasiotes 5y ago
        > You could (no idea why you would) borrow $1MM and immediately pay it back before owing any interest. Can you in fact do that? It's possible with a residential mortgage in the US, because there are laws prohibiting prepayment penalties. And I think even those don't apply to refinanced mortgages?
        avianlyric 5y ago
        Yes, just because it’s hard to find a lender that will except those terms doesn’t mean it’s not possible.
- djbebs 5y ago
  Interest is not reflected in the balance sheet, but in the income and cashflow statements.
rahimnathwani 5y ago
Sorry, yes, I should have been more clear! 1. Profit/loss measures changes in equity resulting from operating activity, as opposed to financing activities (which just rearrange how the company is financed). 2. Examples of financing activities are taking out (or paying back) loans, issuing (or buying back) shares, and issuing dividends. 3. Some (not all, as you point out!) of those financing activities will increase or decrease equity. So, when thinking about profit as the rate of change of book value, you should be careful add back any changes that are the result of financing activities. (specifically: ignore changes in equity due to money going to, or coming from, shareholders)
riccardomc 5y ago
This is true in a perfect market, based on Modigliani-Miller theory of capital structure. In reality, increasing debt to a certain point also increases risk, which in turn increases return on equity.
- mcguire 5y ago
  * should increase return on equity. :-)
- rahimnathwani 5y ago
  A change in return on equity isn't the same as a change in equity. When a company takes a loan, even if that loan is so large as to make insolvency almost inevitable, there is no impact on equity (book value).

deleted 5y ago

[deleted]

haberman 5y ago

This blog entry taught me a mathy way of understanding double-entry accounting: https://martin.kleppmann.com/2011/03/07/accounting-for-computer-scientists.html https://martin.kleppmann.com/2011/03/07/accounting-for-compu... Summarized: a ledger is a directed graph of accounts, where edges are transactions, and each transaction is recorded twice: in the "from" node and the "to" node.

rahimnathwani 5y ago
The article is mostly correct[0], and is very good if the explanation clicks for you. I suspect some people (even some HN readers) would find it easier to think of ledgers as lists of transactions with running totals. [0] e.g. it's not strictly true that book value is a lower bound on company value
wutangson1 5y ago
But “a ledger” is not a directed graph of accounts, is it? There is no ‘from - to’ in a ledger. A ledger simply reorganizes the transactions from chronological order (aka journal entries) into subject/account headings. Not the same, but similar to clicking ‘subject’ column tab on your email client to reorganize your emails from descending date to subject attribute.
- rahimnathwani 5y ago
  That explanation didn't click with me, either. But I guess you could model each transaction as an edge, with the direction specifying which account is debited and which credited, and the weight determining the amount. I don't find that particularly helpful myself, but I put that down to my unfamiliarity with graph data structures and the associated algorithms. Maybe there's something you can do more easily with a graph database, than you can if you have the same info in a table?
  - wutangson1 5y ago
    Sure. Just like blockchain- or any other decentralized ledger- may be a tremendously disruptive technology for property recording, sale/transfer, and financing in the future (compared to the current archaic system of deeds/titles for real property or UCC financing recording for secured transactions); so to, a graph database may clearly illustrate the point of bookkeeping along with the share of assets creditors and investors are entitled to realtime.