While computing common measures of business success is often an adventure, it's usually not an overwhelming barrier to understanding public companies. You find the raw numbers on the financial statements, plug them into the formulas, and crank out the results. What is especially difficult for most of us, though, is figuring out which formulas we should rely on in a given business scenario and exactly what the results tell us. (You can find out other user-friendly ways to evaluate businesses in our popular online seminar, Choosing Stocks With The Motley Fool, starting September 13th.)

Our case in point here highlights two similar measures: Return on Equity (ROE) and Return on Assets (ROA). On the surface, both are straightforward ratios of a company's earnings to the amount of upfront investment that went into generating these earnings. This is how ROE and ROA are the same. The tricky -- and interesting -- part is digging deeper and asking how these two are different.

To really grasp the difference between ROE and ROA, you have to become very comfortable with one basic idea  -- debt leverage. Personally, I grappled for a long time with the concept of leverage and, consequently, with the difference between ROE and ROA. The breakthrough took place when I began to think more carefully about something simple -- the fundamental accounting formula.

Back to basics
The fundamental accounting formula looks like this:

• Owner's Equity = Assets - Liabilities

If this relationship isn't already second nature to you, perhaps the most easily understood example is home ownership. Let's say that my house is worth \$100,000 on the open market and that my outstanding mortgage loan balance is \$75,000. Then:

• My Equity = Home Value - Loan Balance
Or
• \$25,000 = \$100,000 - \$75,000

Now, starting with this fundamental accounting relationship, let's do the simplest of algebraic manipulations to get:

• Assets = Owner's Equity + Liabilities

Continuing our home ownership example, this translates into:

• Home Value = My Equity + Loan Balance
Or
• \$100,000 = \$25,000 + \$75,000

Take a good look at this last pair of equations. It may look a little funny at first glance, but if you stare at them long enough you'll see a familiar concept. In everyday language, we often hear:

• My House = My equity + The bank's loan

This explanation glosses over a subtle but important detail that we'll look at later. For now, however, it is all that we need to tackle the root of all differences between ROA and ROE.

Tackling debt leverage
With the basics in hand, let's leave home mortgages behind and delve into a corporate example. Suppose ScootCo (Ticker: OUCH) is a long-time, low-growth manufacturer of slick two-wheel scooters for kids. Its major assets are the plant where its scooters are assembled and its brand name. These two assets combined could be sold for (have a market value of) \$100,000. Finally, let's assume OUCH has no long-term debt outstanding.

Simplistically then, we can sum up its financial situation with our rearranged accounting formula as follows:

• Assets = Equity + Liabilities
Or
• \$100,000 = \$100,000 + 0

In other words, if there is no debt, then owner's equity and the total value of corporate assets are one and the same number. From this observation, it follows that Return on Equity and Return on Assets must also be the same number (since the Return doesn't change and Equity and Assets are equal). If we ignore the vagaries of working capital for the moment, then, we see that the special case of "no debt" implies that ROE = ROA.

So, let's put some debt into our example to make things interesting. Suppose the demand for kids' scooters suddenly explodes, presenting OUCH with a golden opportunity to grow its business. Seizing the moment, the scooter execs decide to increase production capacity by 50% and head to their friendly banker for a loan of \$50,000 to expand the plant. And the moment this \$50,000 check hits their hot, little, scooter-lovin' hands, we can update our rearranged accounting formula as follows:

• Assets = Equity + Liabilities
Or
• \$150,000 = \$100,000 + \$50,000

Compare this formula to the one above it and, again, stare carefully; the comparison leads directly to the key idea behind debt leverage:

• Taking on debt increases assets and liabilities by the same amount, but has no impact on owner's equity

With this example in hand, the derivation of the term "leverage" should be clear. Debt adds to the assets owned by a business without any further investment required by the owners. Sounds great, eh? But is it?

Tying it all together
Continuing with our corporate example, let's use both ROE and ROA to measure the success of OUCH one year after the \$50,000 expansion. We'll assume the increased production boosts OUCH's profits by 50%. To keep things as simple as possible, we'll ignore any tax benefits arising from loan interest payments.

Prior to the expansion

• No debt
• Assume OUCH is producing a reliable annual profit of \$10,000
• Assets = Equity = \$100,000

• ROE = ROA = \$10,000 / \$100,000 = 10%

Post-expansion

• \$50,000 debt (liability)
• Annual interest payment of \$3,000 (6% of \$50,000)
• Scooter profit = \$15,000 (50% boost to \$10,000)
• Net profit = \$15,000 - \$3,000 = \$12,000
• Assets = \$150,000
• Equity = \$100,000

• ROA = \$12,000/\$150,000 = 8%
• ROE = \$12,000/\$100,000 = 12%

What's it all mean? Well according to ROA, our scooter execs blundered in expanding the plant, shaving 2% from their return on investment, from 10% down to 8% (even though profits increased 20%). According to ROE, however, they did the right thing, improving return by 2%, to 12%. So, which is the right interpretation?

Like all answers worth a darn, this one is: "it depends." Think of ROA as the fundamental business engine. ROE is what happens when you leverage this fundamental business engine by taking on debt. If the engine is sound (produces a positive return on assets), taking on debt to expand the engine will improve shareholders' return. As we saw in this example, the debt doesn't even have to improve the fundamental business engine (ROA) to improve shareholders' return (ROE). It just can't degrade the engine too much.

If the engine is not sound, however, taking on debt will exacerbate shareholder losses, since the company will have to continue making debt payments on assets, even as ROA collapses. This vicious cycle can strike even when the ROA engine collapse is only temporary, as is often the case during broad economic slowdowns.

So the answer is: Look at both. If ROA is sound and debt payments are under control, improving ROE is a sign of successful management. On the other hand, if ROA is declining, or the company does not appear financially sound enough to withstand troubled times, improving ROE could be just a temporary illusion -- a harbinger of serious trouble.

Next: Two Key Concepts Made Easy, Part 2 »

Darn the numbers, Paul Commins thinks the execs at OUCH are doing an excellent job. If he offered opinions on any real companies in this article, you could have checked his profile to see if he owned stock in any of them, in line with the Fool's disclosure policy.