I don't have a lot in common with Warren Buffett. For one thing, I'm a lot younger than he is (although he's awfully spry for an 89-year-old man). I don't run one of the world's biggest companies as he does. I can't play the ukelele; Buffett can. I've never played bridge with Bill Gates. And there's the little detail that my net worth amounts to only a fraction of his.

But I now have at least two new things in common with the Oracle of Omaha. Last week, I bought two dirt cheap stocks that Buffett really likes. Here's which stocks I purchased -- and why I plan to buy even more shares in the not-too-distant future.

Warren Buffett with people in the background

Image source: The Motley Fool.

The quintessential Buffett stock

At long last, I'm finally a shareholder of the stock for which Warren Buffett is best known, Berkshire Hathaway (BRK.A -0.36%) (BRK.B 0.11%) itself. Just to set the record straight, I scooped up Berkshire's class B shares. They're just a wee bit more affordable than the class A shares, which currently trade for around $290,000 a pop. 

I've actually been a fan of Buffett and Berkshire for a while. Why did it take me so long to buy the stock? The main reason was that I've invested more heavily over the last few years in stocks that I thought would generate even greater total returns than I expected Berkshire would deliver.  

With the stock market meltdown caused by the COVID-19 pandemic, though, I expect that Berkshire is now clearly in a position to trounce the market going forward. For one thing, the stock is dirt cheap. Berkshire's shares trade at just a little over book value and less than 1.4 times sales. This is the lowest price-to-book level for the stock in the last 10 years and the lowest P/S ratio since early 2013. 

Another reason why I've gotten off the fence with Berkshire is that it's sitting on a massive cash stockpile at a time when there are lots of buying opportunities. Buffett once said, "When it rains gold, put out the bucket, not the thimble." The Weather Channel might not report it, but it's raining gold right now with the coronavirus-fueled bear market. Berkshire had $125 billion in cash and equivalents at the end of 2019. That's a mighty big bucket. 

Will some of Berkshire's businesses suffer during the likely recession caused by the COVID-19 outbreak? Sure. But the company is built to survive and thrive over the long run. I'm confident that Berkshire will be worth a lot more a few years from now than it is today, and I've put my money where my mouth is.

Buffett's favorite bank stock

I already owned shares of Berkshire Hathaway's biggest equity position (Apple). Now I also have Berkshire's second-biggest holding in my portfolio -- Bank of America (BAC -1.25%).

To be honest, I haven't been gung-ho about bank stocks in the past.  But there are several things about Buffett's favorite bank stock that I really like right now.

At the top of the list is its valuation. Although Bank of America shares aren't as cheap as they were a couple of weeks ago, they're still down 30% off the highs from earlier this year. The stock trades well below its book value and at less than nine times expected earnings.

It's certainly true that low interest rates don't present a great environment for banks. With many small businesses shutting down and people losing their jobs, it won't be surprising if Bank of America sees a spike in loan defaults. But the company's financial position remains strong and should enable the company to plow through a temporary rough patch.

Bank of America has made significant strides in improving its operational efficiency and technological prowess. Its mobile app ranks as one of the highest-rated in the industry. I think the stock will surge back as the economy emerges from the COVID-19 crisis.

Just the start

My purchases of Berkshire Hathaway and Bank of America stocks last week were just the start. I fully intend to scoop up more shares of both companies over the next few months.

I won't be surprised if the stock market drops some more after its recent rebound. If that happens, it will present opportunities to buy these high-quality stocks at even more attractive prices. What if the market doesn't fall further? I'll keep on buying shares of Berkshire and Bank of America anyway.

Buffett once said that "it's far better to buy a wonderful company at a fair price than a fair company at a wonderful price." I think that both Berkshire and Bank of America are wonderful companies, and I expect their stocks will be available at fair prices (if not bargain-basement prices) over the near term. Buffett and I will soon have even more in common.