When things get challenging on Wall Street, smart investors turn their attention to dividend stocks. Companies that pay a regular dividend are almost always profitable on a recurring basis and have transparent long-term growth outlooks.

What's more, income stocks have mopped the floor with non-paying stocks over long periods. According to a report by J.P. Morgan Asset Management, a division of money-center bank JPMorgan Chase, companies that initiated and grew their payouts between 1972 and 2012 produced an annualized return of 9.5%. By comparison, publicly traded companies not offering a dividend scraped and clawed their way to an annualized return of just 1.6% over the same four-decade time frame.

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Ideally, income investors want the highest yield possible with little or no risk. In reality, risk and yield tend to correlate once a stock hits high-yield status (4% yields and above). What this suggests is that high-yield stocks can sometimes be more trouble than they're worth. Since yields are determined by dividing a company's payout into its share price, a struggling business with a falling share price can lure unsuspecting income seekers into a yield trap.

But not all high-yield dividend stocks are bad news. In fact, the energy sector is packed high-quality companies that can pad your pocketbook and offer the potential for long-term share-price appreciation.

For example, if you want to receive $500 in quarterly dividend income, there's an ultra-high-yield energy stock trio -- "ultra-high-yield" is an arbitrary term I'm using to describe stocks with yields of at least 7% -- that can make it happen. If you were to invest $23,600 (split equally three ways) in the following ultra-high-yield energy stock trio, which is averaging an 8.51% yield, you'd net $500 in quarterly dividend income.

Enterprise Products Partners: 7.45% yield

The first supercharged dividend stock in the energy sector that can help you bring home the Benjamin's is oil and gas stock Enterprise Products Partners (EPD 0.10%). Enterprise has the "lowest" yield of this trio at about 7.5%. However, the company has increased its base annual distribution every year for a quarter of a century

The biggest fear oil and natural gas investors likely have is getting caught up in a situation similar to what happened in 2020. The initial stages of COVID-19 lockdowns led to a historic demand drawdown for oil and natural gas. During a brief period in April 2020, West Texas Intermediate (WTI) crude oil futures traded below $0 and reached negative $40 per barrel. The solace I can offer income investors is that Enterprise Products Partners is shielded from this volatility.

Enterprise is a midstream energy company. It's effectively a middleman that transports energy commodities and stores oil, natural gas, natural gas liquids, and refined product. It has more than 50,000 miles of pipeline, two dozen natural gas processing facilities, and can store 14 billion cubic feet of natural gas. 

The reason some midstream energy companies, like Enterprise Products Partners, can dole out jaw-dropping distributions is because they sign long-term, fixed-fee contracts with drilling companies. No matter how volatile the spot prices are for WTI crude and natural gas, Enterprise can accurately forecast what it'll generate in operating cash flow for a given year.

Knowing how much cash flow will be generated annually is incredibly important for energy companies. In Enterprise's case, the transparency of its annual outlook is what allows it to set aside capital for new infrastructure projects, acquisitions, and its distribution, without adversely impacting the company's profitability. Enterprise Products Partners has roughly a dozen major projects under construction at a total expense of $5.5 billion that should all be online by mid-decade. 

And make no mistake about this payout -- it's as solid as it gets in the energy space. The company's distribution coverage ratio (DCR) never fell below 1.6 during the worst of the COVID-19 pandemic. The DCR is ratio of distributable cash flow from operations relative to what was paid to investors. A figure of 1 or below would imply an unsustainable payout. As noted, Enterprise's DCR never dropped below 1.6.

Alliance Resource Partners: 9.75% yield

A second ultra-high-yield energy stock that can help you generate $500 in quarterly dividend income from an initial investment of $23,600 (split three ways) is coal producer Alliance Resource Partners (ARLP -0.17%). Alliance Resource has the highest yield of this trio at nearly 9.8%.

For those of you who were on the fence when I said "oil and gas stock," I can only imagine your expression reading "coal producer." With most developed countries pledging to reduce their carbon emissions, the idea of investing in a coal producer might sound silly. But thanks to certain macroeconomic shifts, it's a smarter investment than you might realize.

Nearly one year ago, Russia invaded Ukraine. This action cast doubt on the energy supply needs of Europe. But even more pressing is the fact that global energy companies had to reduce capital investments for years during the pandemic due to demand uncertainty. Following years of underinvestment, ramping up oil and gas production won't happen overnight. In other words, it's rolled out the red carpet for coal to regain its luster.

Appalachia-focused producer Alliance Resource Partners has certainly benefited from higher coal prices. Perhaps more important has been management's consistent efforts to lock in volume and price commitments up to three years in advance. As of the end of September, all 35.9 tons of coal production was committed and priced for 2022. However, 32.9 million tons and 22.8 million tons were also locked in for 2023 and 2024, respectively.  Just like Enterprise, Alliance Resource Partners' success is dependent on cash-flow transparency.

Another reason Alliance Resource Partners can outperform is the conservative approach management has taken with regard to expanding production. Taking measured steps to increase output based on macroeconomic cues has kept net debt at a very manageable $146.6 million, as of the end of September. This is a company with superior financial flexibility, compared to other coal stocks.

Lastly, Alliance Resource Partners holds oil and natural gas royalties. If the price of energy commodities remains elevated, this royalty segment should enjoy a bump in adjusted earnings before interest, taxes, depreciation, and amortization (EBITDA).

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Antero Midstream: 8.32% yield

The third ultra-high-yield energy stock that can assist you in pocketing $500 in quarterly dividend income with an initial investment of $23,600 is midstream energy company Antero Midstream (AM -1.13%).

Antero Midstream is an energy middleman that specializes in natural gas gathering, storage, and processing. Further, most of its contracts are with its parent company, Antero Resources (AR -3.21%). Antero Resources is the nation's fifth-largest natural gas producer and the second-biggest natural gas liquids producer. 

Keeping with the theme of this list, Antero Midstream enjoys the benefit of exceptionally predictable operating cash flow. Every single contract it signs is fixed-fee. This means inflation and wild swings in the price of natural gas have no impact on the contracts it's locked in with its parent company and other upstream drillers. The cash-flow transparency has allowed Antero Midstream to make acquisitions and undertake new infrastructure projects.

But over the next couple of years, it's the broken global energy supply chain that could be one of its biggest catalysts. The aforementioned invasion of Ukraine by Russia, coupled with reduced capital investments from global energy majors due to COVID, may be able to provide a relatively safe floor beneath energy commodities. If natural gas prices were to bounce off of their recent lows, it could entice additional domestic production and the need for more energy infrastructure.

Antero Midstream will also be benefiting from Antero Resource's decision to increase drilling on the former's owned acreage. Antero Midstream actually reduced its distribution by 27% in 2021 so it would have plenty of capital to cover the expense of new infrastructure as its parent company increased production. Not only is Antero Midstream's existing dividend sustainable, but these new projects should add $200 million in incremental free cash flow through 2025. This adds a tailwind to the company's share price, as well as buoys its already delectable payout.