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Mathematical basis

For the user of Banana's Double-entry accounting, it may seem strange that the revenue/income (sales) and the liabilities (start-up capital) appear in negative, while normally one expects that the sales appear in positive and the expenses in negative.

The double-entry accounting is based on the debit and credit principle that usually appear in two seperate columns. If the amounts in debit and in credit appear in one column, the mathematics of the Double-entry accounting anticipates the use of the minus sign (-), so that the amounts in debit can be easily distinguished from the amounts in credit.

Banana goes completely with the mathematical logic of the Double-entry accounting and thus indicates the amounts with the minus sign (and in red print to let the user distinguish even better the amounts in debit and in credit). In the Double-entry accounting the amounts in negative (credit) don't have the same meaning as in the accounting that is based on income and expenses.

The indication of the credit amounts in negative is a much more efficient system than other ones that add codes to amounts, such CR, DEB, CR or brackets.

This system is based on simple mathematical equations which assure that the accounting is correct. It is not by accident that the Double-entry accounting method has in fact been encoded by Luca Pacioli in 1494, one of the most illustrious mathematicians of the Italian Renaissance (he taught mathematics to Leonardo da Vinci). In his "Summa de arithmetica, geometria, proportioni et proportionalita", Luca Pacioli didn't just deal with the Double-entry accounting, but also with other mathematical questions.

In the Renaissance there were no electronic calculators, and so they used to indicate the amounts in debit and in credit in separate columns. The result was that it became easier to totalize the amounts. Today, with the computers, no calculations need to be made and the principal issue is to use a user-friendly system which is at the same time easy and correct.

For those interested in accounting mathematics and the equations on which Banana accounting is based, the following explanation can be interesting. 

Debit/Credit

The Double-entry accounting leans on the principle that each movement is noted in debit as well as in credit and the amounts have to match.

Debit = Credit

The balance (the total difference between debit and credit) has to always be equal to zero

Debit - Credit = 0

In order to easily distinguish (very useful while working on the screen), the amounts in credit are indicated in red, preceded by the minus sign 

Debit + (-Credit) = 0

 

Two transaction examples

Debit

Credit

 

Debit + (- Credit)

Cash income

200

 

 

200

for product sales

 

200

 

-200

 

 

 

 

 

Several cash payments

 

170

 

-170

for purchase of merchandise

100

 

 

100

for office supplies

50

 

 

50

small expenses

20

 

 

20

Total

370

370

 

0

Balance (Debit - Credit)

0

 

0


Balance Sheet and Profit/Loss Statement

The mathematics of the Double-entry accounting anticipates the use of two "accounts".

  • Balance Sheet Account (Balance Sheet) keeps note of the financial state at a certain moment.
    • Debit represents the Assets
    • Credit represents the Liabilities (here will always means including the Equity)
  • Profit/Loss Account (Profit and Loss) keeps note of the progress.
    • Debit represents the Expenses
    • Credit represents the Revenue

The transactions are entered in debit and in credit in the appropriate accounts of the Balance Sheet and the Profit/Loss statement.

 

Balance Sheet 

 

Profit/Loss Statement 

Registrazioni

Assets

Liabilities 

 

Expenses

Revenue

Cash income

200

 

 

 

 

for product sales 

 

 

 

 

200

 

 

 

 

 

 

Several cash payments 

 

170

 

 

 

for purchase of merchandise

 

 

 

100

 

for office supplies 

 

 

 

50

 

small expenses 

 

 

 

20

 

Total

200

170

 

170

200

Balance (difference debit - credit)

30

 

30

 

 

Equations with two columns

Debit = Credit

370 = 370

Assets + Expenses = Liabilities + Revenue

200 + 170 = 170 + 200

Assets - Liabilities = Revenue - Expenses

200 - 170 = 200 - 170

Balance = Balance

30 = 30

 

 

 

The same transactions can be represented in a single column (credit in negative)

The result is, of course, the same.

 

Transactions 

Balance 

Sheet 

 

Profit/Loss 

Statement

Cash income 

200

 

 

for product sales 

 

 

-200

 

 

 

 

Several cash payments 

-170

 

 

for purchase of merchandise 

 

 

100

for office supplies 

 

 

50

small expenses 

 

 

20

 

 

 

 

Balence (debit - credit)

30

 

-30

 

 

Equations single column (credit in negative)

Debit - Credit = 0

270 - 270 = 0

Assets + Expenses - Liabilities - Revenue = 0

200 + 170 - 170 - 200 = 0

Assets - Liabilities - Revenue + Expenses

200 - 170 - 200 + 170 = 0

Balance - Balance = 0

30 - 30 = 0

 

 

Equations for the business results

The business result is the balance (Debit - Credit) of the Balance Sheet and the Profit/Loss Statement.

 

Equations double column

Assets - Liabilities = Revenue - Expenses

200 - 170 = 200 - 170

Balance of the Balance Sheet = Balance of Profit/Loss Statement

30

Balance of the Balance Sheet = Assets - Liabilities

30

 

 

Equations for the determination of the result (in two columns)

Profit 

Assets > Liabilities

Expenses < Revenue

Balance

Assets = Liabilities

Expenses = Revenue

Loss

Assets < Liabilities

Expenses > Revenue

 

One has a profit when the assets are higher than the liabilities and the revenue more than the expenses.

One has a loss when the liabilities are higher than the assets and the revenue is lower than the expenses. 

 

Equations single column (credit in negative)

Assets - Liabilities - (Revenue - Expenses) = 0

200 - 170 - (-200 - 170) = 0

Balance of the Balance Sheet - Balance of Profit/Loss Statement = 0

30 - 30 = 0

Balance of the Balance Sheet

30

Balance of Profit/Loss Statement

-30

 

 

Equations for the determination of the result in a single column

Profit 

Assets - Liabilities > 0

Expenses - Revenue < 0

Balance 

Assets - Liabilities = 0

Expenses - Revenue = 0

Loss 

Assets - Liabilities <0

Expenses - Revenue > 0

 

One has a profit, when the balance of the Balance Sheet is positive and the balance of the Profit/Loss Statement negative.  

One has a loss, when the balance of the Balance Sheet is negative and the balance of the Profit/Loss Statement positive.

Use of noting in a single column

Noting the data in double columns is ideal for transactions in paper books. The amounts in debit and in credit are inscribed in separate columns. The totals are being calculated at the end of the page and the totals and calculation of the results are being done at the end of the period.  

Computerized systems offer the possibility to keep the balances of the accounts constantly updated. For the calculations, the software therefore normally use noting in a single column, with the amounts in debit in positive and the amounts in credit in negative. In order to use noting in double columns, the software would have to register the credit amounts in the Balance sheet in negative, and, in the Profit/loss Statement, register the credit amounts in positive and the debit amounts in negative.

For the programmer's point of view, this solution is more complicated, and thus the majority of the software use internally the mathematics of the single column and noting in double columns only for the presentation. 

Banana Accounting instead systematically uses the minus sign to indicate the credit amounts. Initially, the user has to get used to this system, but it has the advantage of being linear and allows for a better understanding of the mathematics on which the Double-entry accounting is based, especially when more complicated operations are being required like write-off's, profit at the end of the year or VAT due/recoverable.  

For the presentation of the Balance Sheet and the Profit/loss Statement, the logic of the double columns is however more adapted. 

Thus the print-outs of the Balance Sheet and the Profit/Loss Statement that are used for the presentation of the results are edited with Assets, Liabilities, Expenses and Revenue always in positive. When the Profit/Loss Statement is presented in a scalar format (Revenue minus Expenses), the Revenue is indicated in positive and the Expenses in negative.

 

 

 

 

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