The Dow Jones Industrial Average just set a new all-time high, signaling the possible start of a new bull market in the blue-chip index. The Federal Reserve's forecast that interest rates would fall next year gave stocks a boost last week, putting the Dow Jones back to record levels.

The Dow is typically favored by investors looking for safe, reliable blue-chip stocks that pay dividends, and with Treasury yields already falling, investors may turn back to stocks for high yields. Let's take a look at the three highest-yielding dividend stocks on the Dow to see if any are worth buying.

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1. Walgreen Boots Alliance (7.83% dividend yield)

Like some other high-yielding dividend stocks, Walgreen Boots Alliance's (WBA -3.08%) dividend yield of 7.8% is more a result of the stock's underperformance rather than its commitment to paying a high dividend.

The stock has declined over much of the past decade as it's made a number of misguided acquisitions and struggled with broader headwinds in the pharmacy industry, including lawsuits over opioid prescriptions and new competition from e-commerce companies.

However, Walgreens may have gotten cheap enough that it's worth adding to your buy list. The company is currently considering spinning off Boots, unwinding its biggest acquisition of all, and it recently pushed out former CEO Roz Brewer, who seemed to be a poor fit as her background was in retail, rather than healthcare.

On an adjusted basis, the stock trades at a price-to-earnings ratio of less than 8 based on its forecast for the new fiscal year, which is an attractive price for almost any stock. Still, given the company's recent challenges and net losses on the bottom line, investors may want to wait for more signs that a turnaround is underway as well as more clarity from new CEO Tim Wentworth.

2. Verizon (6.96% dividend yield)

In a number of ways, Verizon Communications (VZ -1.07%) is in the same boat as Walgreens. The telecom giant has declined over a several-year period as growth has been stagnant, and it's made strategic errors and lost market share to T-Mobile US.

However, Verizon's most recent earnings report showed it may finally be turning after a disappointing run. It had 100,000 postpaid phone net additions or customers who pay every month, and it's seeing strong growth in the broadband segment. Meanwhile, it acquired spectrum to help fix its coverage and connectivity issues.

While growth is essentially flat, Verizon's profits should be reasonably stable at this point as the company competes in a triopoly with T-Mobile and AT&T, and high barriers to entry have afforded the telecom operators strong operating margins, even though there's a high level of competition among those three companies.

Verizon is now valued at a price-to-earnings ratio of just 7.6, and it seems like the worst is behind the company, especially with interest rates expected to fall. Verizon looks like a solid bet for dividend investors.

3. 3M (5.75% dividend yield)

3M's (MMM -0.10%) stock price has also shrunk as the company has faced multibillion-dollar lawsuits, stagnant sales growth, and a culture that seems to have shifted away from new products and innovation.

The conglomerate plans to spin off its healthcare division by the end of the year, which could help breathe new life into the company, but the healthcare segment has also been its best-performing segment.

Unlike Verizon and Walgreens, 3M is more of a cyclical business, and the company could benefit from a recovery in the economy. There's no sign of that thus far. The company sees revenue for the full year falling 5% as management has cited weak demand due to macroeconomic challenges and poor results in China.

One of the biggest challenges facing 3M is its settlements over PFAS (a kind of synthetic chemical) and faulty earplugs, which will cost it billions of dollars in cash payments over the next decade and could weigh on its ability to invest in the business and raise its dividend. Considering that drain on cash flow, dividend investors may be better off looking elsewhere.