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You can gain valuable insights into companies by making sense of their financial statements. Let's review the income statement, sometimes called the statement of operations.

The income statement summarizes sales and profits over a period of time, such as three months or a year. It usually offers information for the year-ago period, too, so you can compare numbers and spot trends.

Consider Motley Fool Hidden Gems and Motley Fool Rule Breakers recommendation Blue Nile's (NASDAQ:NILE) income statement for the period ended July 2. At the top, as with every income statement, you'll find net sales, sometimes called revenues. For Blue Nile, they're $56.9 million.

Working our way down the income statement, we see that various costs will be subtracted from the revenues, leaving different levels of profit. The item you'll find just under revenues is "cost of goods sold" (abbreviated as COGS, and sometimes called "cost of sales"). It represents the cost of producing the products or services sold. At Blue Nile, it's $45.6 million. Subtract the COGS from revenues, and you'll get a gross profit of $11.4 million.

To find the gross margin, which reflects the costs of production compared with sales proceeds, simply divide the gross profit by revenues. Dividing $11.4 million by $56.9 million yields a gross margin of 0.20, or 20%. It's often illuminating to compare the results with those of industry peers and competitors -- Tiffany (NYSE:TIF) had a gross margin of 56% for its quarter ended in April 2006.

Next, the remaining costs involved in operating the business, such as support staff salaries, utility bills, and advertising expenses, are subtracted, leaving the operating profit (also known as operating income). Blue Nile's operating profit is $3.6 million. Dividing this figure by revenues yields an operating margin of 6%, revealing the profitability of the company's principal business. Looking at trends in the company's operating margin can tell us how the company is doing compared with previous years.

Finally, after items such as taxes and interest payments are accounted for, we come to net profit (more commonly known as net income), near the bottom of the statement. Blue Nile's is $3.1 million. Dividing that figure by revenues yields a net profit margin of 5%. This number reflects how much of every dollar of sales a company keeps as profit.

Compare all these margins with those from previous years. Increasing margins indicate increasing efficiency and profitability. Check out the margins of the company's competitors. Is the company more efficient than its peers? Look for significant changes in revenues, SG&A (selling, general, and administrative) expenses, and costs of goods sold.

And, finally, note that margins vary widely by industry. Software companies such as Motley Fool Inside Value recommendation Microsoft (NASDAQ:MSFT), for example, tend to have high margins, while retailers tend to have low ones. Fellow Inside Value pick Wal-Mart (NYSE:WMT) is proof that a company can do phenomenally well for itself and its investors despite low margins. It just makes up for them with high volume.

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Shruti Basavaraj, Adrian Rush, and LouAnn DiCosmo updated this article, which was originally written by Selena Maranjian. Adrian does not own shares of any company mentioned. LouAnn owns shares of Microsoft, while Shruti owns shares of Blue Nile. The Motley Fool has a disclosure policy.