If you want to find high-yield stocks trading on the cheap, there's no better place to look than the energy market today. Much to the chagrin of investors who thought that oil and gas prices would finally start to rise again, a barrel of oil has stubbornly remained in the $45-$55 per barrel range for most of the year and tested many investors' patience. For those of us who want to invest over the long term, these oil-price-chasing traders are providing an excellent opportunity to load up on energy stocks again.

Today, three companies that look particularly compelling with fat dividends are Royal Dutch Shell (NYSE:RDS-A) (NYSE:RDS-B), Helmerich & Payne (NYSE:HP), and Terra Nitrogen Company (NYSE:TNH). Here's why investors should consider taking a look at these stocks today.

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An old dog that learned a new trick

Investing in Shell just a couple of years ago looked like a dubious proposition. The company's portfolio was heavily dependent on deepwater and liquefied natural gas (LNG) investments that had rather high breakeven prices compared to most of its peers. Also, the company was in the middle of a major asset sale related to the acquisition of BG Group that made the picture of what exactly an investor was buying a little fuzzy.

Since that time, though, Shell's management has brought the investment picture into focus, and it's looking rather good for a stock that yields 6.6%. The company is generating a lot of free cash flow it can use to lower its debt levels or boost shareholder returns. Also, the company has been able to use the downturn to lower the breakeven costs on several of its growth projects.

Looking at Shell's stock, it isn't selling at a substantial discount to its historical average, but there are two things to consider when you look at stock valuation. First, you have to consider the valuation and where we are in the oil cycle. Earnings should start to rise as oil prices increase modestly and Shell wrings out costs, and cyclical stocks like this will typically trade at a higher valuation when the market is bad and look pretty cheap when times are good.  

Also, Shell has historically not been known as a company that generates high margins and returns, so it has typically traded at a lower valuation than its peers. If the company can hit CEO Ben Van Beurden's target returns on invested capital of 11% across the entire portfolio, then this stock could start to be valued for a much higher premium than it commands today.

Improving business, deteriorating valuation

The shale industry has been a fascinating market to follow over the past couple years. Sometimes it's hard to fathom how much better producers and oil services companies have become at drilling for oil. To give you an example, the active rig count in the U.S. today is about half what it was before prices started to crash -- 900 versus 1,800. With only half the assets deployed in the field, U.S. oil production is up 600,000 barrels per day over the past nine months to near pre-cash levels and growing.

For rig owners like Helmerich & Payne, this isn't good news, because it means the industry needs fewer rigs to achieve the same results. As of the most recent quarter, H&P had about half of its rigs deployed, and it's looking like the appetite for new rigs is drying up fast. This has sent shares plummeting so far in 2017 to the point that Helmerich & Payne's dividend yield is at 6%.

This particular thesis -- that a flattening rig count means this is as good as it gets for rig companies -- overlooks some of H&P's strengths. The land rig market is still in a state of considerable fleet turnover, Helmerich & Payne is in a position to take market share, and its management team has been great stewards of shareholder capital for more than four decades.

As management said on its most recent conference call, it is possible that it could revisit its dividend payout policy if the market were to take another turn downwards. However, the chances of that happening seem less likely than the market staying flat or modestly increasing over the next few years. With shares trading at prices close to what we saw when oil prices were less than $30 a barrel in 2016, Helmerich & Payne could be both a good dividend investment and an opportunity for some sizable gains over the next several quarters.

The market continues to worsen, but the thesis remains intact

Anyone invested in Terra Nitrogen company has to be extremely frustrated with the results over the past few years. I know I am, because I'm a shareholder. While the company isn't necessarily an energy investment, its stock has been significantly affected by the energy markets. The nitrogen fertilizer industry has been in thrown on its head over the past several years thanks to cheap natural gas in the United States, which is a feedstock for producing fertilizer. Gas-based fertilizer production in the U.S. went from one of the most expensive sources in the world to one of the least expensive sources in a matter of a few years, and companies have flocked to build out new domestic facilities to benefit from the cheap feedstock. 

Here's the problem: All of that new, cheap production needs to be absorbed by higher demand, or higher cost supplies of product need to go away. Neither of these two factors have materialized enough to support prices, and it has hit the bottom line of Terra Nitrogen Partners. What's worse for income investors is that since Terra Nitrogen is a variable rate master limited partnership that pays out all available cash at the end of each quarter, its payout has declined with the price of fertilizer. 

 TNH Dividend Chart

TNH Dividend data by YCharts.

This fall has been hard to swallow as an investor, but investors shouldn't be too quick to give up on this stock. The original investment thesis for this business is still intact. Terra Nitrogen remains the lowest cost producer (its net income margin last quarter was 41%); its facility is in the heart of a major U.S. shale basin to provide it with ample, cheap gas supplies; and it is completely debt-free, so all of the cash the company produces flows directly into investors' pockets. 

When cyclical commodity markets like this one get completely up-ended, it takes a long time for them to find equilibrium. When it does, Terra Nitrogen is going to reap the rewards, and investors will likely find themselves with an extremely high-yielding stock.

Tyler Crowe owns shares of Terra Nitrogen. The Motley Fool has no position in any of the stocks mentioned. The Motley Fool has a disclosure policy.