Accounting Principles and the Mathematics behind them

In the last week or so, I have posted a few articles relating to a mathematical challenge and how to get the correct answer. One of the concepts needed for the challenge was a number line. Number lines help explain what happens when adding to or subtracting from a negative number. They also make Accounting simple.

If you want to read the original articles, here they are:

• Trending: Only for genius ?? 3 – 3 x 6 + 2 = ??
• Answer: Only for genius ?? 3 – 3 x 6 + 2 = ??
• Conclusion: Only for genius ?? 3 – 3 x 6 + 2 = ??

Disclaimer: I am not an Accountant and have never had any formal Accounting training.

I need to take you back to before I worked with Microsoft Dynamics GP, to my first commercial role as an employee. I was still studying engineering and had had my own software development business for a number of years. My maths knowledge was good but I had never done any Accounting.

The company I was working for purchased an open source accounting system called SBT, which was written in dBase and could be customised. Part of my role involved customising the system as well as making sure the accounting data was correct. I needed to learn accounting fast and so my brother, who was a Chartered Accountant at the time, gave me a quick lesson which has helped me to the present day.

Below is the summary of how to understand accounting principles from a purely mathematical perspective:

The main two reports for running a business are the Balance Sheet (which is a permanent record) and the Profit and Loss Statement (which resets each financial year). Those two reports in their simplest forms are governed by the following formulas:

• Balance Sheet: A = E + L : Assets = Equity + Liabilities
• Profit and Loss: P = I – X : Profit = Income – eXpenses

Debits and Credits are from the bank’s point of view and so are the opposite of what you expect when it comes to the maths involved. Yeah, I know it is backwards, but that is just the way it is, deal with it. 🙂

• Debits are positive
• Credits are negative

The different types of accounts on the reports have a usual balance that is either a Debit or Credit balance:

• Assets and Expenses are Debit Accounts and have a positive balance
• Liabilities and Income are Credit Accounts and have a negative balance

Now I can explain how number lines make accounting easy, just treat debits and credits as positive and negative numbers, respectively.

Debit balance accounts are positive.

• If I Debit (add to) a Debit account it gets more positive and has a larger value
• If I Credit (subtract from) a Debit account, it gets less positive and has a smaller value

Credit balance accounts are negative.

• If I Debit (add to) a Credit account, it gets less negative and has a smaller value
• If I Credit (subtract from) a Credit account, it gets more negative and has a larger value

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Let’s try a Practical Example:

I have $100 cash in the bank and I purchase a consumable item (Expense) for $10 from a supplier on account. Here are the values of the accounts before any transactions.

Account Name	Account Type	Account Value
Bank Account	Asset	$100
Accounts Payable	Liability	$0
Expense	Expense	$0

There are two transactions (journals) that will occur. The first when I pick up the item and using my account with the supplier to pay for it.

Account Name	Debit	Credit
Bank Account
Accounts Payable		$10
Expense	$10

Then the second transaction occurs when I pay the account with cash from the bank.

Account Name	Debit	Credit
Bank Account		$10
Accounts Payable	$10
Expense

So now what’s the maths involved (with mathematical terms and values shown in red):

Here are the values of the accounts before any transactions.

Account Name	Account Type	Account Value
Bank Account	Asset (Debit/Positive)	$100  +$100
Accounts Payable	Liability (Credit/Negative)	$0      -$0
Expense	Expense (Debit/Positive)	$0      +$0

The first transaction in mathematical terms.

Account Name	Debit (Positive)	Credit (Negative)
Bank Account
Accounts Payable		$10    -$10
Expense	$10    +$10

Here are the Account Values after the first transaction.

[Edit] Note that Accounts Payable is a Credit Balance account so it is normally negative, so the negative Maths value is shown as positive on the reports.

Account Name	Maths Value	Accounting Value
Bank Account	+$100	$100
Accounts Payable	-$0 -$10 = -$10	$10
Expense	+$0 +$10 = +$10	$10

The second transaction in mathematical terms.

Account Name	Debit (Positive)	Credit (Negative)
Bank Account		$10    -$10
Accounts Payable	$10    +$10
Expense

Here are the Account Values after the second transaction.

Account Name	Maths Value	Accounting Value
Bank Account	+$100 -$10 = +$90	$90
Accounts Payable	-$10 +$10 = -$0	$0
Expense	+$10	$10

So the final account values back in accounting terms are below:

Account Name	Account Type	Account Value
Bank Account	Asset	$90
Accounts Payable	Liability	$0
Expense	Expense	$10

I know that the accountants reading this article will hate the way I have simplified everything, but this helped the engineer/mathematician in me understand the terminology and calculations involved.

What do you think?

David

PS: Stay tuned for another poll on a new mathematical puzzle.

This article was originally posted on http://www.winthropdc.com/blog.

18-Feb-2016: Fixed Typos and added comment about Accounts Payable being a Credit Account.