Profit Equation

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The proft equation or fiscalewinstberekening is a formula to check the consistency of an administation: It calculates profit in two different ways, and they should match. Amongst others, it is used by the Dutch Belastingdienst as a check on company financials when submitting Inkomstenbelasting.

One general way of stating the profit equation: Nett profit according to P&L account = increase of equity -/- nett withdrawals - See below for some alternative expressions.

Belastingdienst

I was first involuntarily confronted with this equation, when entering data concerning an annual account at the site of Belastingdienst. The site pointed out that these two methods of calculating profit, didn't match:

Het saldo fiscalewinstberekening is niet gelijk aan het saldo winst-en-verlisrekening of winstaandeel van uw onderneming. Controleer de bedragen.

In this article (actually all articles concerning bookkeeping on this site), an eenmanszaak is assumed.

Formula

The profit equation or fiscalewinstberekening (see elsewhere for different names for this formula) incorporates two ways to calculate profit, and they should match.

The profit equation is an example of an interval entity: It operates on changes of the values of entities. It's typically calculated over a year, but it can be on any other interval

Various expressions

{Nett equity increase} + {nett withdrawals}  = {nett pprofit} <=>

{closing equity} - {Opening equity} + {nett withdrawals}  = {nett profit} <=>
{asset increase} - {liabilities increase} + {withdrawals} - {deposits} = {nett profits (P&L account)} <=>

{closing assets} - {opening assets} +
- {closing liabilities} + {opening liabilites} +
{withdrawals} - {deposits}                   = {nett profit (P&L account)}

{closing assets} - {closing liabilities}
- {opening assets} + {opening liabilites} +
{withdrawals} - {deposits}                = {nett profit (P&L account)}

In Dutch: 

{toename EV} + {saldo onttrekkingen} = {winst (resultatenrekening)} <=>
{EV eind} - {EV begin} + {saldo onttrekkingen}    = {winst (RR)}
{bezittingen eind} - {bezittingen begin} +
- {verplichtingen begin} + {verplichtingen eind}
+ {saldo onttrekkingen}                           = {winst (RR)}

Belastingdienst

Terminology used by the Belastingdienst at the IB process - https://mijn.belastingdienst.nl/onlineaangifte/ib/aangifte/

  • Winstberekening: General term: Profit calculation
  • Ondernemingsvermogen einde boekjaar: Equity at the end of the year
  • Ondernemingsvermogen begin boekjaar: Equity at the beginning of the year
  • Saldo ondernemingsvermogen: Increase in equity
  • Privéonttrekkingen: Private withdrawal
  • Privéstortingen: Private deposits
  • Winstberekening volgens Winst-en-verliesrekening: Profit calculation according to P&L acount.

Formula: 

Winstberekening = Saldo ondernemingsvermogen +
                  Saldo Privéonttrekkingen
                  <=>

Winstberekening = Saldo ondernemingsvermogen +
                  Privéonttrekkingen -
                  Privéstortingen
                  <=>

Winstberekening = Ondernemingsvermogen einde boekjaar -
                  Ondernemingsvermogen begin boekjaar +
                  Privéonttrekkingen -
                  Privéstortingen

The name of the game - Dutch

I'm still not sure how this formula is called, either in Dutch or in English.

At least, I'm quite sure it's not called [balansvergelijking].

Fiscale winstberekening

Seems reasonable. Found it here:

De Belastingdienst controleert het resultaat van je bedrijf met behulp van de fiscale winstberekening.

aka. fiscalewinstberekening.

I'm quite sure (2024.10) that this is the actual name of it.

Fiscalewinstvergelijking

I think this is even better, as it ends in vergelijking.

Verandering Eigen Vermogen

Deze site doesn't give it a name, but states

De verandering van het eigen vermogen is als volgt

Vermogensvergelijking

For a while, I settled on this name, aka. kapitaalsvergelijking, and I have the sources to back it up:

However, I think fiscale winstvergelijking or just winstvergelijking better describes what this formula is about.

The name of the game - English

Profit equation

In 2024, I somehow seem to have settled on this name, and I like it: The formula incorporates two different ways to calculate profit, and they have to match. Hence profit equation seems a really good name.

Balance Sheet Equation?

Maybe it's just an application of the familiar balance sheet equation? 

{Equity increase} + {nett withdrawals}  = {Profit according to income statement}

I doubt this.

Equity Reconciliation Formula

Sounds nice, but an online search doesn't confirm this name

Owner's Equity Reconciliation

Reconciliation of net worth

This seems a statement or document and not so much just a formula [1]

Statement of changes in equity

Again, a statement, rather than a formula, but it's getting close: [2], [3]

→ Statement of owner's equity

Statement of changes in owner's equity

→ Statement of owner's equity

Statement of Owner's Equity

Accountingtools.com calls this Statement of Owner's Equity, also called statement of changes in owner's equity. It looks promising:

  • Although it's called a statement, the example that they show is really just one formula
  • It's mentioned that this specifically applies to sole proprietorship
  • It comes close to the formula at the beginning of this articele, but not entirely.
beginning capital balance + income - withdrawal = ending capital balance

Sources

Equity equation

The rather common Dutch name vermogensvergelijking translates to equity equation. However:

  • The formula is rather about profit, not equity
  • This name is too close to balance sheet equation, at least in description.

Example - Start easy

Let's run a simple example to see this in action:

  • Company A is started in 2022
  • It provides services, has no direct or indirect costs.

Booking facts

All booking facts (if that's the correct name) during this year:

  • An invoice of € 1.000 (ex. 21% VAT) has been send to customer B
  • Payment has been received on A's business account
  • Half the amount has been retained and half withdrawn
  • VAT has been disbursed to Belastingdienst.

Balance beginning of the year

Balance at the beginning of this year: 0 - 0 at both sides

Balance at the end of the year

  • Balance business account: € 500
  • No debt/foreign capital (vreemd vermogen)
  • Equity formula: Equity = Assets - Liabilities [4] <=> Eigen vermogen = Bezittingen - Schulden
  • In this case: Equity = € 500 - € 0 = € 500.

Resulting balance: 

Debit                               Credit
------------------------------------------
Business account: € 500 | Equity: € 500
                        |
Total             € 500 | Total   € 500

Income statement

Easy: 

Revenue (omzet):                           € 1.000
Direct costs (directe kosten):             €     0
--------------------------------------------------
Gross profit (brutowinst):                 € 1.000
Indirect costs (indirecte kosten):         €     0
--------------------------------------------------
Operational profit (operationale winst):   € 1.000
Interest (rente)                           €     0
--------------------------------------------------
Profit (winst)                             € 1.000

I believe that withdrawals (onttrekking) shouldn't be incorporated in the income statement. Otherwise you could always depress profit by simply siphoning it off.

Profit calculations

Finally, we can apply the formula from the start of this article: 

{Equity increase} + {nett withdrawals}  = {Profit according to income statement} <=>
{Toename EV}      + {Saldo onttrekking} = {Winst volgens resultatenrekening}

with

  • Equity increase = € 500
  • Nett withdrawals = € 500
  • Profit according to income statement = € 1.000
{Equity increase} + {nett withdrawals}  = {Profit according to income statement} <=>
€ 500 + € 500 = € 1.000

Notes:

  • The calculation above confirms that the income statement should not include withdrawals
  • Strange to see that withdrawals are not included in either balance or income statement
  • Maybe this is why you need three documents to get a complete picture of a business' finance: Balance, Income statement and Cashflow statement: In the latter, withdrawals will be visible
  • A balance is a snapshot of certain aspects of a business at a specific time, whereas a income statement is a statement over a time period. There's a analogy with electricity: current is at any one point where voltage is the difference over an interval. In physics, there are actually many such analogies and this isn't too remarkable
  • Note that in this equation, all entities are of the interval-kind: The equity- and withdrawal-related entities are converted to interval-like. The income profit number is already interval-like
  • Could all three entities be converted to point-like entities? I'm not sure: What would profit be as a point-like entity? - It doens't seem to make sense.

Example - Non-disbursed VAT

Now let's extend the example above with VAT not being disbursed to the Belastingdienst during this year

Booking facts

  • An invoice of € 1.000 (ex. 21% VAT) has been send to customer B
  • Payment has been received on A's business account
  • Half the amount has been retained and half withdrawn
  • VAT (€ 210) has been retained this year, and only disbursed in January of the next year

Balance beginning of the year

Balance at the beginning of this year is the same as before: 0 - 0 at both sides

Balance at the end of the year

  • Balance business account: € 710
  • There is debt to the Belastingdienst of € 210
  • Equity formula: Equity = Assets - Liabilities [5] <=> Eigen vermogen = Bezittingen - Schulden
  • In this case: Equity = € 710 - € 210 = € 500.

Resulting balance: 

Debit                               Credit
------------------------------------------
Business account: € 710 | Debt:   € 210
                        | Equity: € 500
------------------------| ----------------
Total             € 710 | Total   € 710

Income statement

The income statement is the same as before: VAT doesn't have anything to do with income statements.

Profit calculations

{Equity increase} + {nett withdrawals}  = {Profit according to income statement} <=>
{Toename EV}      + {Saldo onttrekking} = {Winst volgens resultatenrekening}

with

  • Equity increase = € 500
  • Nett withdrawals = € 500
  • Profit according to income statement = € 1.000
{Equity increase} + {nett withdrawals}  = {Profit according to income statement} <=>
€ 500 + € 500 = € 1.000

Notes:

  • The profit calculation doesn't change
  • Maybe because all entities are converted to interval-like entities, which is like the domain of the income statement, and VAT doesn't play here a role.

Finding the error

When submitting a jaarrekening at the website of Belastingdienst, the site uses this equation to check for errors. Somehow, I seem never able to preemtively avoid this problem:

2021

In 2021, it took me about a week to fix it, because a lot of this stuff was new to me.

2022

For the 2022 jaarrekening, it only took me a couple of hours to fix it:

  • There were multiple errors at the closing balance sheet
  • The root cause of these: I used explicit numbers at the spreadsheet tab Closing balance, rather than links to figures at the All sheet. These numbers started to deviate from each other and I wasn't aware of this. Suprisingly how often I get errors because formula don't work correctly. Quite an argument against using a spreadsheet for this
  • Partitioning the Proft Equation into separate formulas for eacht month, helped to isolate the errors - See next chapter.

See separate chapter belof for details.

2023

Partitioning

Partitioning the Profit Equation over the year, into 12 equations, each covering a month. This helped in me Aug. 2023 a lot with figuring out some errors in a closing balance sheet: The Profit Equation over December didn't end with the same closing balance as the Profit Equation over the whole year, since they used different figures: The overall Profit Equation used the Closing balance sheet and the December Profit Equation used figures from the All sheet. This section was added to the All sheet, just right of the P&L-account and (in this case) VAT section

Maybe remember from Balance sheet that you cannot partition a year's balance sheet into 12 balance sheets, one for each month, and adding these 12 to get back at the original balance sheet? The reason for this: A balance sheet describes a moment in time, not an interval.

This is not the case for the Profit Equation: It is an 'interval entity'. Eventhough it refers to equity, it doesn't do so as a 'point entity', but as an 'interval entity', since it refers to the change in equity over a certain period - Quite neat, isn't it?

Some more details about the screen shot of the partitioning table here at the side:

  • Figures Equity at end of a period are the same as those at Equity figures at the start of period for the next period. I calculated them each time anyway using a formula, to check that I didn't make any mistakes myself
  • The same counts for the asset and liability figures: They repeat themselves, and I calculated them all through formulas, not through copying
  • Errors in the closing balance sheet would reveal themselves, because the line for December would 'end' at different figures than the separate Closing balance sheet
  • The same would could for errors in the opening balance: The line for the first month would have different figures than the separate Opening balance sheet
  • For a while, I had a small difference of € 0,21 for the 2022 jaarrekening mentioned elsewhere, which was obviously a VAT submission rounding error (when doing submissions, you have to round off to whole euros, and you can decide whether to roung off or up). However, even that turned out to be an error in the Closing Balance Sheet: There was a hardcoded "€ 0" at Accounts payable , while at the All sheet, it was the actual € 0,21.

Case: Fixing errors IB2022

  • Once again, the profit equation didn't work out. The discrepancy wasn't that big: Only € 450
  • The difficulty: I don't know what to look for

Partition the problem

I've added the profit equation lines for each month (file: Bookkeeping-dvb-2022-before-fixing-profit-equation-error.ods. Note that Assets at start at period and Liabilities at start of period have been calculated in different ways, just in case there error was there

As you can see in the screenshot, the € 450 issue is distributed as follows:

  • June: € 100-
  • July: € 50-
  • Sep.: € 200-
  • Oct.: € 100-.

Let's start with troubleshooting September, as the discrepancy is the biggest there.

Some basic checks

Let's start with some basic checks:

  • The usual mutation check columns were working and their nett values was 0 everywhere
  • The field with the summations for mutations, had the correct formulas everywhere.

Let's check for suspicious mutations

  • I actually started with checking all mutations, but I quickly got bored with that, so, let's check for any suspicious mutations. VAT was ok... There was a mutation that involved a purchase of € 200 - The same amount as the discrepancy
  • Quite remarkable: It involved indirect cost, and the column for this account, was the first at the section of domestic indirect costs

Solution

  • The formula in the P&L account that calculated indirect costs, missed the first cell: This column had been added later and the formula hasn't been updated accordingly
  • After fixing this formula, all profit equation issues disappeared.
Problem solved - See all those nice zeros in the last column - Life is good

Recommendations

Include as default features of the bookkeeping system, probably on sheet All, so I can detect errors when entering bookkeeping facts, rather than potentially some years later when filing IB:

  1. Calculation of the profit equation over the whole year
  2. Partition the profit equation

When a discrepancy occurs:

  1. Do the simple checks mentioned above
  2. Check if the formulas in the P&L section are accurate
  3. Search for a transaction with the amount equal to the discrepancy
  4. Check the most suspicious transactions
  5. Check all transactions.

Case: Fixing errors IB2023

Quite similar to the case before:

  • Over July: € 22,95 discrepancy
  • Over December: € 937,78 discrepancy

Fixed the P&L accounts

After reading the case from IB2022 above, I checked the P&L calculation. It turned out, that the calculations of indirect costs over December, somehow missed the last couple of cells → Corrected that, and the € 937,78 problem, disappeared

See also

Sources

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