Are you a beginning investor? Congratulations! You're venturing into a world where riches come to those who possess some basic math knowledge and the patience to study businesses.

Well, that's actually not quite right. Learning accounting and valuation techniques can be difficult, especially when you first start sifting through financial reports. That's when concepts such as return on invested capital and cash conversion cycle will invite themselves over for dinner and stay for a movie, leaving you frustrated and short on pocket change.

But it doesn't have to be that way, Fool. Everything you need to know about successful investing can be boiled down to two ideas. First, that there's a direct link between earnings growth and stock returns. And second, that earnings growth often comes from improving margins.

What are margins? There are three that matter when studying an income statement. Let's run though each, one at a time.

First, there's the gross margin. Gross margin -- also sometimes referred to as the "top line" -- is what's left after the cost of goods sold is subtracted from sales. So, for example, if it costs Sneezy Handkerchiefs \$100 to produce 100 handkerchiefs that it sells for \$200, its gross margin is \$100 (\$200 - \$100 = \$100).

Margins can also be expressed as a percentage. For Sneezy Handkerchiefs, its gross margin percentage is gross margin divided by total sales, or 50% (100 / 200 = .50, or 50%). Still with me? Great, let's move on to operating margin.

Operating margin is what's left after the cost of goods sold and other costs for running the business day-to-day. Research and development and administrative expenses are common operating costs. What are administrative expenses? Salaries, office supplies, rent, and the like are typically grouped under the "general and administrative" line item on the income statement.

Calculating operating margin is no different than the math for gross margin. So, if Sneezy Handkerchiefs generates \$20 in operating expenses in a quarter when it sells \$200 worth of hankies that cost \$100 to produce, its operating margin will be \$80 (\$200 - \$100 - \$20 = \$80).

And what about the percentage? That's easy: 40% (80 / 200 = .40, or 40%).

Now, let's move on to net margin. Net margin -- also sometimes referred to as the "bottom line," "earnings," or "net income" -- is what's left after all costs are subtracted, including interest payments and taxes.

Calculating net margin is just as easy as it is for the others. So, assuming Sneezy Handkerchiefs pays \$20 in taxes and \$10 in interest in addition to its cost of goods sold and operating costs, its net margin is \$50 (\$200 - \$100 - \$20 - \$20 - \$10 = \$50).

Its net margin percentage will be 25% (50 / 200 = .25, or 25%).

Why margins matter
Here's why this math lesson matters: Firms that boost margins are generating more with less. So, for example, if Sneezy Handkerchiefs invents a new space-age polymer that allows it to produce each hankie for \$0.50 instead of \$1, its gross margin will rise as long as it doesn't lower prices.

Such efficiency often leads to higher earnings. How do I know? I checked with screening tool Capital IQ. It says there are 101 firms worth at least \$1 billion that improved gross margin and earnings by more than 50% annually over the past three years. Of those, 45 have more than doubled. Here are seven of the most interesting:

Company

% Change

NutriSystem (NASDAQ:NTRI)

4,856%

Hansen Natural (NASDAQ:HANS)

3,894%

Frontier Oil (NYSE:FTO)

585%

Valero Energy (NYSE:VLO)

421%

aQuantive (NASDAQ:AQNT)

130%

FormFactor (NASDAQ:FORM)

123%

Halliburton (NYSE:HAL)

116%

Source: Capital IQ

What can we learn from this list? Efficient firms can make for wonderful investments. Some of them, such as chip equipment maker FormFactor, have even made the ranks of our stock-picking newsletters.