Accounting and Mathematics

If you ever find yourself having to analyze the financial statements, you will need to learn how to read it.

There is a lot of mumbo-jumbo in the accounting world (for historical and legal reasons,) but there is a very powerful way of thinking about it.

If you have even a slighly mathematical bent, there is great advantage to looking at it from the viewpoint of calculus. (In fact, I am ashamed to admit how many years it took me to grasp this basic point.)

There are two components to the financial statement:

Firstly, the balance sheet which is the snapshot about the financial entity (say, a company) at a particular moment of time.

Secondly, there is the income statement which is about the flow of money through time.

On the balance sheet, there are two things -- assets and liabilities.

assets - liabilities = equity (net worth)

Traditionally, this is always written as:

assets = liabilities + equity

Similarly, on the income statement, you have two things: income and expenses. Traditionally, this is always written as (similar to above):

income = expenses + earnings (net income)

Here's the key point:

The income statement is the derivative of the balance sheet with respect to time.

Or equivalently, the balance sheet is the integral over time of all the income statements from the beginning to the instance of the balance sheet.

If you integrate the second equation:

∑ income = ∑ expenses + ∑ earnings

you will end up at the balance sheet:

assets = liabilities + equity

After this, the big bad bold world of accounting will hold no horrors for you!

Depreciation? Pah! nothing but a delta of writedown, etc. etc.

Now, both of these are complicated (for a real company) but if you think in the language of calculus, you will grasp the mumbo-jumbo far faster than if you think in strictly accounting notation (which uses the language of law not mathematics!)

In fact, the mumbo-jumbo originates because accounting is a subject far older than calculus.

The elegant part about all of this is that because we're talking about money (M), there are only two things: M and ∂M (although the second derivative (∂²M) does show up from time to time -- earnings growth, for example.)

So you can use the old physics trick of using dimensional analysis to see if both sides of the equation match.

Nifty, eh?

(In fact, you can use all the calculus tricks you learnt, and the results are powerful and amazing!)

I just use calculus notation but nobody understands me so I have had to learn to translate it back into "accountant speak", and "trader speak", and ...