Trading oranges as money - new conventions
The first time through I tried using the conventional accounting conventions but the overall result was unsatisfactory so that here I have reverted to something that makes more sense and show how the accounting conventions are built from it.
So we rework the previous example and treat the oranges as a money equivalent stock item. This allows complete accounts to be done. In order to make clear the sign difference between a node in graph terminology and an account in accounting terminology I will refer to nodes in a graph sense (with positive and negative balances) and accounts in a conventional accounting sense (credits and debits).
Converting stock purchase as money
The conversion of amounts of things to their monetary value is a key element of accounting records. This makes it much possible to create accounts. So we are going to represent the stock as money and at the cost price. This is not present in the original stock taking accounting of the Sumerians where each type of item eg barley or malt was shown on the transaction.
Trading
So to recap the scenario is:
- invest in your business.
- buy oranges from an orange farmer
- sell them at a profit at market
Investment
We start from nothing. The first step is an injection of cash from an external investor. We are going to separate out boundary modes/accounts from those inside the business.
Figure 1
Investment
Buying stock / inventory
For each stage there is only the entries of that stage although the balances of any nodes are also shown. I have used the term stock as it is a British English term Wikipedia has inventory as the American synonym see this comparison.
Having got investment in the business lets buy 25 oranges from a farmer for one pound for each orange. The exchange of cash for oranges is denoted by a single accounting entry.
Figure 2
Buying stock
Selling the stock at market
So now we go to market and sell the oranges:
Figure 3
Selling the stock
So when you make a sale you transfer money from the Sales revenue node to the cash node.
Overall nodes
So now looking at the overall picture using money values you have:
Figure 4
Summary
From this you can see that no money is owed to the Farmer nor is there any stock. There is also a nice flow of capital from left to right. The total value of the business is the sum of all the nodes (1) inside the internal box. Since this is a directed graph this is necessarily the opposite of the sum of the nodes on the outside. On the outside you have the negative equity that was put in originally and the sum of the trading (sales and purchases).
To make this double entry and to have meaning the inflows must be kept separate from the outflows. This allows the tracking of profitability. In this case it is easy but with different stock items you could separate out profitable and unprofitable lines.
From now on we will leave the external boundary and look only what happens in the firm. We will keep the internal box as this nicely delineates the boundary nodes and the internal ones.
Figure 5
Summary for the business
Adding an example liability
If we modify the story a bit we can add a liability. If instead of giving cash to the farmer at the time of the purchase of the oranges you promise to pay on the way back from the market. Then when you get back you will owe the farmer for the oranges (and might not need an investor).
Figure 6
Unfinished business with a liability
Looking at the business we have inputs and outputs in external nodes (in bold edges) and internal nodes such as assets and liabilities (in thin edges). The total value in the business is the sum of those internal nodes assets + liabilities, as the liabilities are negative. It is important to note that both figures 5 and figure 6 have the same overall value. This is because in figure 6 we have not yet paid the farmer.
Balance sheet interpretation
In fact the definition of an asset is an internal node with a positive balance and a liability as an internal node with a negative liability. Typically but not always nodes are either assets or liabilities. For instance a pile of cash will always be positive. However if you store your money in a bank it can seamlessly switch from positive to negative and back again. So summarising the value in the entity is called the total net assets (net as we have combined the assets and liabilities).
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} totalNetAssets=\colorbox{asset}{internalNodes}=\colorbox{asset}{assetNodes}+\colorbox{liability}{liabilityNodes}=£37.50 $$
We have promised to pay the farmer and have the cash to do so. The value of the totalNetAssets will not change when we pay the farmer. Because this is a graph all the external nodes equals the negative of all the internal nodes.
Looking at the position of the entrepreneur, they have invested £25 in the business and so the rest of the balances will add up to £25. This says nothing about the health of the business (Balance sheet) or its trading position (Profit and Loss).
Full balance sheet
We know that all the nodes must add up to zero:
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} \definecolor{equity}{RGB}{238,238,187} \definecolor{income}{RGB}{187,204,238} \definecolor{expense}{RGB}{255,204,204} 0=\colorbox{asset}{assetNodes}+\colorbox{liability}{liabilityNodes} +\colorbox{equity}{equityNodes}+\colorbox{income}{incomeNodes}+\colorbox{expense}{expenseNodes} $$
So the full equation becomes:
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} \definecolor{equity}{RGB}{238,238,187} \definecolor{income}{RGB}{187,204,238} \definecolor{expense}{RGB}{255,204,204} totalNetAssets=\colorbox{asset}{assetNodes}+\colorbox{liability}{liabilityNodes} =-(\colorbox{equity}{equityNodes}+\colorbox{income}{incomeNodes}+\colorbox{expense}{expenseNodes}) $$
with liabilities, equity and income being typically negative.
To an accountants balance sheet
As we have touched on accountants avoid negative numbers so we do the following transformations in a report stage to create accountant friendly reports. This is much the same ways as formatting cells in Excel:
| Node Account | Usual value | Accountant term | transform |
|---|---|---|---|
| Asset | +ve | Debit Normal | +1 |
| Liability | -ve | Credit Normal | -1 |
| Equity | -ve | Credit Normal | -1 |
| Income | -ve | Credit Normal | -1 |
| Expense | +ve | Debit Normal | +1 |
Accountants like to start with the accounting equation rather than the outcome of treating transactions as movements within a single entity. I am going to present it for a point in time as:
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} \definecolor{equity}{RGB}{238,238,187} \colorbox{equity}{Equity}=\colorbox{asset}{Assets}-\colorbox{liability}{Liabilities} $$
I like this arrangement as it says from an equity holders point of view how much is a business worth. So using the table above to translate the raw balances to this we get:
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} \definecolor{equity}{RGB}{238,238,187} \definecolor{income}{RGB}{187,204,238} \definecolor{expense}{RGB}{255,204,204} (-\colorbox{equity}{equityNodes})=\colorbox{asset}{assetNodes} - (-\colorbox{liability}{liabilityNodes}) $$
and repeating for the full equations you get:
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} \definecolor{equity}{RGB}{238,238,187} \definecolor{income}{RGB}{187,204,238} \definecolor{expense}{RGB}{255,204,204} \colorbox{equity}{Equity}=\colorbox{asset}{Assets}-\colorbox{liability}{Liabilities} +\colorbox{income}{Income} -\colorbox{expense}{Expenses} $$
and using node balances:
$$ \definecolor{asset}{RGB}{204,221,170} \definecolor{liability}{RGB}{221,221,221} \definecolor{equity}{RGB}{238,238,187} \definecolor{income}{RGB}{187,204,238} \definecolor{expense}{RGB}{255,204,204} (-\colorbox{equity}{equityNodes})=\colorbox{asset}{assetNodes} - (-\colorbox{liability}{liabilityNodes}) +\colorbox{income}{incomeNodes} -(-\colorbox{expense}{expenseNodes}) $$
Note on income and expenses
These are both boundary nodes. You could combine them in a single input and output node. However you would then lose the ability to track the total volume of sales. So a low profit business with a large turnover would look the same as a high profit business with a small turnover.
Inside a business if you have multiple sales lines, a single trading account loses the ability to track the profitability of say of two lines, eg in this case oranges and lemons.