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A calculator will come in handy. Image source: iStock/Thinkstock.

How should an investor who's interested in learning about Bank of America (NYSE:BAC) measure its profitability?

This seems like a straightforward question that should have a straightforward answer. However, because of the idiosyncratic way banks report certain financial figures, it's more convoluted than one might assume.

Defining profitability

On one level, profitability refers simply to the amount of money a bank earns. In the most recent quarter, Bank of America made $4.5 billion after deducting dividend payments on preferred stock.

That's a lot of money. It ranks Bank of America seventh in terms of third-quarter earnings on the S&P 500.

But the problem with looking at profitability in this way is that it doesn't account for size. One reason Bank of America generates more profit than, say, U.S. Bancorp (NYSE:USB), which earned $1.4 billion last quarter, is because Bank of America has $2.2 trillion worth of assets on its balance sheet compared to U.S. Bancorp's $454 billion.

This means that for every $100 billion in assets on Bank of America's balance sheet, it earned $203 million. The same figure for U.S. Bancorp was $316 million. Viewed in this light, U.S. Bancorp is obviously much more profitable.

To normalize for size in this way, analysts rank banks according to return on assets, a ratio that's calculated by dividing a bank's annualized net income by its total assets.

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Factoring leverage into the equation

There's nothing wrong with using Bank of America's return on assets to gauge its profitability. That said, by using it alone, you miss a critical piece of the puzzle: Leverage.

Let's say that a group of people start a bank with $10 million worth of their own money. This is known as capital, or shareholder's equity. The bank will then leverage that up by borrowing $100 million from depositors and institutions.

The borrowed money is used to buy assets, in this case $100 million worth. The bank's profit thus comes from the difference between what the funds cost to borrow (interest expense) and how much income it generates from the assets it invests the funds in (interest income). This is known as interest rate arbitrage.

One consequence of this business model is that a bank's profit depends on the amount of leverage it uses. Excluding rules and regulations, the hypothetical bank above could have earned twice as much net interest income (interest income minus interest expense) by borrowing $200 million and thereby owning $200 million worth of assets. The downside to doing so, of course, is that it exposes the bank to more risk.

The way to capture this in the context of bank profitability is by calculating a bank's return on equity. This is derived in a similar way to a bank's return on assets, you just substitute shareholders' equity in the place of assets.

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Measuring Bank of America's profitability

If you've gotten this far, you should have a good idea how to calculate Bank of America's profitability using, as most analysts do, its return on equity. But there's still one last piece of the puzzle that's important to understand -- namely, there are different ways to calculate shareholders' equity.

One way is to just look at the total amount of shareholders' equity, which can be found at the bottom of a bank's balance sheet. Another way is to subtract a bank's intangible assets from the total amount, seeing as though they don't generate income in the say way as a loan does. And a third way is to subtract both intangible assets and preferred stock, as the latter is more akin to debt anyway.

Measures of Shareholders' Equity

Calculation

Total Shareholders' Equity

Total Shareholders' Equity

Average Tangible Shareholders' Equity

Total Shareholders' Equity minus Intangible Assets

Average Tangible Common Shareholders' Equity

Total Shareholders' Equity minus Intangible Assets minus Preferred Stock

Banks generally prefer to use the third measure of profitability when calculating return on equity -- in which case, it's formally known as a bank's return on tangible common equity.

Here's how that works out for Bank of America: As I've already noted, it earned $4.5 billion in its latest quarter. If you annualize that (i.e., multiply it by four to reflect the four quarters in a year) you get $18 billion worth of annualized earnings. By dividing that by Bank of America's $173 billion in average tangible common shareholders' equity, you get 10.4%.

This isn't bad compared to Bank of America's performance through much of the past decade when it was weighed down by costs related to the financial crisis. But it's nevertheless below many of its peers -- the same figure at U.S. Bancorp last quarter was 13.5% -- and is also below Bank of America's own 12% target.

John Maxfield owns shares of Bank of America and US Bancorp. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.