Warren Buffett has a challenging problem. He has too much money. Berkshire Hathaway (BRK.A) has $50 billion cash in the bank. In order to show improving earnings, Buffett has to put that money to work and have it make more money for him.

He needs to buy stocks that go up and companies that improve their book value and cash flows. He needs to take in insurance premiums that he never gives back as payments (in other words, the insurance company should be conservative on the risks it takes, something Buffett has been notoriously good at for 40 years). And all of his current businesses, such as MidAmerican, NetJets, Fruit of the Loom, Dairy Queen, etc. need to do well.

Buffett has so much cash, though, that it’s hard to find a suitable investment to satisfy his voracious appetite. He can’t just make tiny investments, like buying 1% of a company, and hope it does well on the stock market. He has to swallow companies whole and trust that he’s paying a cheap enough price for a good enough management, that the company satisfies his desires for growth.

Some things he won’t do, however.

-- He’ll stay out of China (no Baidu (BIDU) for him).

-- He loves health care; his recent investments in Sanofi-Aventis (SNY) and Johnson & Johnson (JNJ) are examples, but I don’t think he’ll buy those companies outright.

-- He’ll stay out of Internet tech (despite once owning bonds on both Amazon.com (AMZN) and Level 3 Communications (LVLT), I can’t see him making an extensive foray into this arena).

-- He’ll probably not swallow up any of his bank investments (Wells Fargo (WFC), US Bancorp (USB) or Bank of America (BAC) are all underwater this year but represent good investments).

-- And while I’m sure he’s a big fan of his bridge partner Bill Gates’ company, Microsoft (MSFT), he’ll probably leave that one alone also. (Note: Gates is on the Berkshire board.)

First up: ConAgra Foods (CAG). The company makes packaged foods ranging from Orville Redenbacher’s popcorn (mmm, I’m getting hungry writing this) to Hebrew National hot dogs. With Wall Street worried about food inflation, CAG’s stock price has tanked in the past year, falling almost 30% from its high, vs. 20% for the Dow.

The company has beaten analyst estimates four quarters in a row. Analysts have also been raising estimates recently for this quarter and the full year. CAG trades at a price-to-earnings (P/E) ratio of just 12. Insiders have bought back more than $600,000 worth of stock recently, showing their faith in the company. And the company has also announced that it will be buying back $900 million worth of stock.

Furthermore, the company, founded in 1919, is based in Buffett’s hometown of Omaha, Neb. Buffett’s son, Howard, (future chairman of Berkshire Hathaway) sits on the board of ConAgra.

This is a safe buy at these prices, and even if Buffett doesn’t acquire the company, you can sit back and collect your 3.7% dividend while you wait.

Next up is First Industrial Realty (FR). It might seem odd to say that Buffett might be interested in buying a real estate investment trust, or REIT, given the pain and suffering that real estate has gone through recently. FR owns and operates industrial real estate properties such as warehouses, manufacturing properties, etc.

The stock, at $24, is down from a recent high of $42. At today’s price, the company yields 12.6%. The company has never cut its dividend and has raised it every year since it went public in 1994. In the past few days, the CEO, Michael Brennan, has bought $160,000 worth of stock on the open market; and in April, a director, Robert Newman, bought $217,00 worth of stock at much higher prices.

Why do I think Buffett would be interested? Well, in 1999, Buffett auctioned off his wallet to charity. In his wallet he had a stock tip. John Morgan paid $210,000 for the wallet. Morgan announced that the stock tip was First Industrial. Nobody was buying REITs in 1999 when the Internet fervor was raging. At the time, First Industrial was trading slightly higher than where it is today, at $25, and was yielding around 10%. Buffett was holding this stock in his personal portfolio (he no longer keeps a personal portfolio but did then) and the stock later doubled to $50 in 2006.

Buffett knows the company and the stock, it’s trading down at 1999 levels with much higher earnings than it had in 1999 (analysts expect $4.51 earnings per share this year, vs. $2.41 in 1999). Again, with a 12.6% dividend yield you can afford to sit back and wait and see if Buffett will dip his shoes into this company again.

By James Altucher. At the time of publication, Altucher and/or his fund was long Bank of America, although positions may change at any time.