AT&T (T -0.37%) pays a high dividend that yields 7.6%. At that level of payout, investors owning a little more than $13,100 in stock would collect $1,000 in annual dividend income. But when it comes to yields that high, there's often some risk, and that's no exception with AT&T. The risk for AT&T is that the business may face some big expenditures related to lead-covered cables, and its financials haven't always been that great.

But there are reasons to feel better about AT&T and its dividend. Here's why the stock might be worth picking up right now, and why the dividend looks a whole lot safer.

AT&T's recent earnings report was encouraging

On July 26, AT&T reported its second-quarter earnings, for the period ending June 30. And there were multiple positives to pull from it, including the following:

  • Revenue of $29.9 billion was up by almost 1% from the same period last year.
  • It was the 14th straight quarter where the business had at least 200,000 fiber net additions.
  • Mobility service revenue was up by almost 5% year over year to $15.7 billion.
  • Free cash flow rose by over $1 billion year over year through the first six months of the year, and the company is on track to hit its goal of $16 billion for the full year.
  • Operating income of $6.4 billion rose by 29% from the prior year.

AT&T's business is proving to be resilient and this all bodes well for the dividend. AT&T pays over $8 billion in dividends over the course of a full year. If it hits its free-cash-flow target of $16 billion, investors should feel much more comfortable about the safety of the dividend. And at this rate, the business looks to be in solid shape.

AT&T found another $2 billion in cost savings

Although AT&T's business is coming off a good quarter, there's an urgency for the company to do even better. That's because AT&T faces concerns that it may need to spend billions of dollars on cleaning up lead-covered cables. The issue arose from a recent report from The Wall Street Journal. 

It's too early to tell if it'll cost the company anything, or if AT&T will have to shell out billions to clean up the old cables. The company said that the "cables pose no public health risk," although it is performing additional tests.

The good news for investors is that the company is finding more ways to trim costs. It projects that over the next three years, it will able to shave off $2 billion in annual expenses. AT&T has already been in cost-cutting mode by closing down stores and offices and replacing old infrastructure. Achieving even more cost savings can help make the dividend look even safer, especially if the company ends up needing to set aside money for potential cleanup costs.

Should you invest in AT&T's stock today?

Shares of AT&T hit 30-year lows on the news of its potential liability surrounding lead-covered cables. Investors may, however, be overreacting to the developments as there is not even any certainty that AT&T will face a big cleanup cost or liability. Even if there is a liability, the cost to fix the issue will likely be spread out over several years.

Investors look to be simply bracing for the worst. And as the old Warren Buffett saying goes, investors might want to "be greedy when others are fearful." Now may be that time to do just that as AT&T's stock is trading at only 6 times its estimated future earnings.

There's some risk with the dividend stock, but investors shouldn't be pressing the panic button right now, as it could prove to be a premature move. Despite the bad news, AT&T still looks like a good buy right now.