Even though the S&P 500 is down about 11% over the past 12 months, bargains are still few and far between. For instance, the average price-to-earnings (P/E) ratio of stocks in the S&P 500 is 18. Even more, stocks in the Nasdaq-100 trade at 26 times earnings, on average. But for investors willing to be contrarian and consider some of the stocks that have been beaten down particularly hard, there are some stocks with valuations that may have crossed into bargain territory.

Two stocks that have been hit extremely hard recently are 3M (MMM 0.71%) and Verizon (VZ 0.35%). Indeed, the two stocks' recent underperformance has been so bad that they are now trading at levels lower than where they were trading 10 years ago. Over the last year, specifically, 3M and Verizon stocks are down about 32% and 24%, respectively. Over the last 10 years, they are down 3% and 19%, respectively.

For investors willing to give these unloved stocks a closer look, there are some good reasons to consider investing in them. Their dividends, in particular, make for a good bull case for the stocks.

3M: Nearly a 6% dividend yield

Given how high 3M's dividend yield is, you might expect the stock to look like a risky dividend investment upon close examination. For instance, high-yielding dividend stocks often have payout ratios of 100% or more, suggesting the current dividend level may be unsustainable. But 3M, which sells a diversified selection of safety, industrial, medical, and consumer products, has an easily manageable payout ratio of 58%.

Furthermore, the stock trades at a very cheap P/E multiple of just 10.

Some key risks, however, include a recent sales slowdown in many of the items that previously saw a lift from COVID-19. Furthermore, the company is currently dealing with some high-profile litigation, which could negatively impact financials.

Verizon: Nearly a 7% dividend yield

Telecom giant Verizon has an even higher dividend yield of 7% and a lower payout ratio of 50%. This means Verizon is paying out only half of its earnings in dividends despite consistently rewarding shareholders with a juicy quarterly payout.

Like 3M, Verizon stock is also cheap on a P/E basis. The stock's P/E ratio is just 8.

On the surface, this may look like the opportunity of a lifetime to some investors. But a deeper look reveals a key reason why the stock fails to command a significantly higher valuation: debt. Verizon, which has a $170 billion market capitalization, has more than $143 billion of long-term debt on its balance sheet. Its interest expense is running at $3.6 billion annually.

Despite this ugly debt load, Verizon stock may still be a buy at its current valuation. Consider that the company's trailing-12-month net income was $21.7 billion. In other words, Verizon's stable and profitable business can easily handle large levels of debt.

Moreover, management is currently prioritizing paying down its debt. Indeed, it's holding back on share repurchases until it has paid it down to a level it is more comfortable with.

Overall, both 3M and Verizon look like good dividend stocks. While there are risks to owning both, the two stocks' cheap valuations seem to more than account for those risks.