3M (MMM 0.46%), Walgreens Alliance Boots (WBA 0.57%), and Verizon (VZ 1.17%) currently offer big-time dividends that yield more than 6%. That's several times higher than the market's average (the S&P 500's dividend yield is 1.6%). 

There are good reasons for their high dividend yields. While they're all well-known and successful companies, they're currently facing some stiff headwinds. These issues have weighed on their earnings and share prices, pushing up their dividend yields.

Despite their issues, however, their big-time dividends seem safe. Because of that, yield-hungry income investors should consider holding their noses and buying these big-time dividend stocks.

The legal troubles are starting to fade

Iconic industrial-giant 3M currently yields 6.1%, following a 35% plunge in the share price from its 52-week high. Driving that downdraft is a myriad of issues facing the company, including supply chain challenges and legal problems.

The company recently agreed to settle one of its legal issues, pledging to pay more than $10 billion over the next 13 years. While that's a lot of money, the company has the cash flow and balance-sheet strength to cover this liability.

3M is also working to address a separate legal issue and improve its margins as it battles supply chain issues. Earlier this year, the company unveiled a $700 million to $900 million restructuring to cut costs.

That restructuring should help drive further improvement in its operating cash flow, which was up 26% during the first quarter to $1.3 billion. After covering capital spending, 3M produced about $900 million in adjusted free cash flow. It returned nearly all that money to shareholders via its dividend ($827 million).

While cash flow is tight these days, 3M does have an elite balance sheet, enhancing its financial flexibility. Despite a recent credit-rating downgrade, it has a strong A bond rating, backed by a low leverage ratio and a cash-rich balance sheet (nearly $4 billion in cash at the end of the first quarter and $12 billion of net debt). Even though 3M isn't out of the woods just yet, its strong balance sheet, improving cash flow, and waning legal issues should allow it to maintain its dividend.

Working hard to get healthy again

Walgreen's stock has fallen more than 30% over the past year, including dropping big this week following its lackluster quarterly results. The pharmacy, retail, and healthcare company recently cut its earnings guidance on concerns about a slowing economy. This sell-off pushed its dividend yield up to 6.8%.

While Walgreens is facing some near-term pressures, the company is working hard to reaccelerate growth. It recently launched an incremental $600 million cost-saving program to improve profitability.

The company is also investing heavily to expand its consumer-centric healthcare platform, which it expects will be a major long-term growth driver. It closed its acquisition of CareCentrix and increased its investment in the rapidly expanding VillageMD to support its acquisitions of Summit Health and Starling Physicians.

The company has also been simplifying its portfolio by selling non-core investments to reduce debt and fund its growth initiatives. It recently sold its remaining shares of Option Care Health for $330 million and $644 million of its shares in AmerisourceBergen. While the company's headwinds and heavy investments have weighed on its shares, Walgreen's strategy to reignite growth should pay dividends over the longer term. 

Free cash flow is about to get a big boost

Verizon's stock has also lost about 30% of its value over the past year. That has driven its dividend yield up to 7.2%. Weighing on the telecom giant has been declining free cash flow as it invests heavily to build out its next-generation 5G network.

The company funded the final payment of a major multiyear investment related to 5G in the first quarter. Because of that, its free cash flow will improve by $5 billion over the next year from 2022's spending level.

That will further improve the company's free cash flow, which was a strong $14.1 billion last year (more than enough to cover its $10.8 billion in dividend payments). The growing excess cash will enable Verizon to strengthen its already solid investment-grade balance sheet.

Free cash flow should get additional boosts from the company's investments to grow its business and its cost-saving initiatives. Verizon's investments are paying dividends. Wireless subscribers grew 5.3% in the first quarter, while it also saw the most broadband additions in over a decade.

Meanwhile, last fall, the company launched a plan to cut another $2 billion to $3 billion in costs by 2025. These drivers will help further increase the company's cash flow, giving it more money to pay dividends and strengthen its balance sheet.

Better days are ahead

3M, Walgreens, and Verizon are all facing a barrage of headwinds that have weighed on their cash flow and stock prices. Despite those issues, they still generate solid cash flow and have strong balance sheets, which should preserve their high-yielding dividends.

Meanwhile, they should see improvements in the coming year with turnaround plans well underway. While they're higher risk than other dividend stocks, they offer income investors the prospect of a higher reward through their attractive dividends and upside potential as their shares recover.