I agree with what Michael or Penny wrote, but I'm going to post anyway
because seeing it described in slightly different ways may be helpful
for the original questioner.
On 2022-08-28 15:38, W. Neal Lewis wrote:
However, although (A+L)=Eq, (A+L)≠Eq+(I+Ex). I have added a term to the
right side that is most decidedly not on the left ∴ they cannot be equal.
∴ A and L must be terms that include other factors.
First off, it's assets MINUS Liabilities, not plus, and the same for
Expenses. If you have a $500,000 house and a mortgage balance of
$150,000, with no other assets or liabilities. your net worth (Equity)
is not $500,000+150,000 = $650,000; it's $500,000-150,000 = $350,000.
Secondly, your two equations assume different conditions. The more
general equation
Assets - Liabilities = Equity + Income - Expenses
is always valid, so that's probably the one to think about until it's
second nature.
But what happens if(*) you "close the books"? This means to total up the
year's or month's income and expenses, post the total net income or net
loss into an Equity account such as Retained Earnings, and zero out all
the income and expense accounts. GnuCash has a menu item to perform this
closing for you. Since all income accounts and all expense accounts have
zero balances right after closing the books, the general equation
reduces to
Assets - Liabilities = Equity
(*) I say _if_ you close them, because there's no requirement to do so
in GnuCash. Some people including me like a fresh start each year;
others don't.
But that shorter equation is always valid, even when there are nonzero
income and expense account balances, if you interpret "Equity" in a more
general way. GnuCash actually does this for you when you run a balance
sheet.
It adds up all income account balances and subtracts all expense
account balances, obtaining your net income or net loss to date. That
total is shown in the Equity section of the balance sheet as Retained
Earnings.
GnuCash doesn't change any account balances, and the computed
Retained Earnings don't get posted to any actual account in your
database; it's purely a rollup of the income and expense balances rather
than showing them individually on the balance sheet. If we interpret
Equity as "all equity accounts plus the net income (or minus the next
expense) since the books were last closed",(**) then once again you have
Assets - Liabilities = Equity
(**) This might seem like cheating, but it's not. All income and expense
amounts are logically part of your net worth, as the following example
will show.
Suppose you have earned $90K salary so far this year and spent $76 K of
it in food, clothes, and so forth. You still have a $500 K house with
$150 K mortgage.
Assets: $514 K ($500 K house, plus the $14K part of your salary that's
still in your in a bank account)
Liabilities: $150 K (mortgage balance)
Equity: $365 K (The $350 equity in your house, plus your $90 K in salary
income, minus your $76 K in expenses)
Once again, Assets - Liabilities = Equity: $514 K - $150 K = $364 K.
Suppose you want a balance sheet that doesn't roll net income or expense
into Retained Earnings, but shows the individual account balances? That
is called a Trial Balance, and GnuCash can create such a report for you.
Or of course you can run a Balance Sheet for the desired date and an
Income Statement (Profit and Loss statement) for the period starting the
day after the books were closed and ending the date of the Balance Sheet.
Stan Brown
Tehachapi, CA, USA
https://BrownMath.com
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