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I have searched for profitable companies that pay very rich dividends and that raise their payouts by more than 13% each year. I also looked for companies where the average analysts' recommendation is a buy or better

I have elaborated a screening method, which shows stock candidates following these lines. Nonetheless, the screening method should only serve as a basis for further research.

The screen's formula requires all stocks to comply with all the following demands:

1. The stock is included in the Russell 3000 index. Russell Investment explanation:

The Russell 3000 Index measures the performance of the largest 3000 U.S. companies representing approximately 98% of the investable U.S. equity market. The Russell 3000 Index is constructed to provide a comprehensive, unbiased, and stable barometer of the broad market and is completely reconstituted annually to ensure new and growing equities are reflected.

2. Dividend yield is greater than 7.0%.

3. Annual rate of dividend growth over the past five years is greater than 13%.

4. Average analyst recommendations are bullish (less than 2).

After running this screen on January 9, 2013, before the market open, I discovered the following three stocks:

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Compass Diversified Holdings (NYSE:CODI)

Compass Diversified Holdings is a public investment firm specializing in acquiring controlling stakes in small to middle market companies.

Compass has a very low forward P/E of 9.33 and the PEG ratio is at 1.26. The average annual earnings growth estimates for the next five years is at 7.50%. The forward annual dividend yield is very high at 9.52% and the annual rate of dividend growth over the past six years was very high at 17.1%. CODI is expected to post a profit of $1.59 a share in the current year and $1.62 in 2013 which probably will sustain dividend payments. Analysts recommend the stock; among the five analysts covering the stock, two rate it as a strong buy, two rate it as a buy and only one rates it as a hold. The stock price is 5.01% above its 20-day simple moving average, 6.00% above its 50-day simple moving average and 9.71% above its 200-day simple moving average, which indicates short-term, mid-term and long-term uptrend. There have been in the last six month 11 purchases of the CODI stock by insiders, net shares purchased - 96,127 at a price between $13.50 to $14.73, at a total sum of about 1.4 $million.

The cheap valuation, the very rich dividend, the analysts' recommendation, the fact that the stock is in an uptrend and the insider buying activity are all factors that make CODI stock quite attractive.

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Data: Yahoo Finance

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Chart: finviz.com

CenturyLink, Inc. (NYSE:CTL)

CenturyLink, Inc. operates as an integrated telecommunications company in the United States. The company provides local and long-distance, network access, private line, public access, broadband, data, managed hosting, colocation, wireless, and video services to consumers and businesses.

CenturyLink has a low forward P/E of 14.99 and the PEG ratio is at 1.80. The forward annual dividend yield is very high at 7.30% and the annual rate of dividend growth over the past six years was very high at 45.5%. The strong operating cash flow of $5.41 billion in the last four quarters should be enough to sustain dividend payments. Analysts recommend the stock; among the 21 analysts covering the stock, eight rate it as a strong buy, eight rate it as a buy and five rate it as a hold. The stock price is 1.22% above its 20-day simple moving average, 3.56% above its 50-day simple moving average and 3.55% above its 200-day simple moving average, which indicates short-term, mid-term and long-term uptrend.

All these factors -- the very rich dividend, the analysts' recommendation and the fact that the stock is in an uptrend -- make CTL stock quite attractive.

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Data: Yahoo Finance

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Chart: finviz.com

Linn Energy, LLC (NASDAQ:LINE)

Linn Energy, LLC, an independent oil and natural gas company, engages in the acquisition and development of oil and gas properties. The company's properties are primarily located in the Mid-Continent, the Permian Basin, Michigan, California, and the Williston Basin in the United States. As of December 31, 2011, it had proved reserves of 3,370 billion cubic feet equivalent of oil and gas, and natural gas liquids, as well as operated 7,759 gross productive wells.

Linn Energy is trading 12.95% below its 52-week high and has 21% upside potential based on the consensus mean target price of $44.62. The forward annual dividend yield is very high at 7.86% and the annual rate of dividend growth over the past six years was very high at 13.4%. LINE is expected to post a profit of $1.41 a share in the current year and $1.80 in 2013, it is not clear if it will be enough to sustain such a high dividend payment. Analysts recommend the stock; among the 18 analysts covering the stock, eight rate it as a strong buy, five rate it as a buy and five rate it as a hold.

All these factors -- the very rich dividend, the analysts' recommendation and the 21% upside potential based on the consensus mean target price of $44.62 -- make LINE stock quite attractive.

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Data: Yahoo Finance

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Chart: finviz.com

Source: 3 Rising High-Yield Dividend Stocks That Analysts Recommend