In an interview Tuesday on CNBC's "Squawk Box," Miller made a case for why he thinks Apple shares are trading at ridiculously low levels of about $476 each as of Monday's closing price. "It just makes no sense for Apple to trade where it is: Seven times enterprise value to free cash flow."
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He also said, "Microsoft has been a terrible stock for a decade. It started out stupidly overpriced and now it's stupidly underpriced." In the past 10 years, Microsoft stock has gained 18 percent. But year-to-date, it's up 25 percent.
Miller is portfolio manager of the Legg Mason Opportunity Trust, which returned nearly 40 percent in 2012. The fund—with $1.5 billion in assets under management—owns shares of Apple and Microsoft.
He said an Apple "double is probably not likely" in the next 12 to 24 months. "[But] if it takes two years to get back to where it was a year ago, it's 50 percent" higher from current levels. Apple stock has dropped more than 30 percent since its all time highs of more than $700 a share back in September 2012.
On Microsoft, he said, "They raised the dividend actually 15.9 percent per year on average for the last five years. But the last dividend increase was 22 percent. And I think it's much more likely the dividend increase is going to be 20 percent or more the next five years."
Miller explained, the psychology game surrounding a stock can turn around on a dime. "When Netflix was at $60 and now it's $300, that was a year ago. Best Buy was $13, now it's $38. The psychology can change quickly."
A couple of other major value investors also appeared on "Squawk Box" Tuesday and they decided to look at Apple after Miller's call.
John Rogers Jr., chairman and CEO of Ariel Investments, said: "Bill has made a very compelling case. … We have to re-look at Apple for our large cap product."
"Bill Miller said Apple's a no-brainer. I think I'll buy some Apple today," said Harvey Eisen, chairman and CEO of Wright Investors' Service Holdings. He's also chairman of Bedford Oak Advisors.
Eisen also likes Microsoft and gave a shout out to billionaire Warren Buffett. "Hi Warren, how are you?"
"You just gave $50 billion to a guy named Bill Gates," Eisen continued. "Microsoft trades at 10 times earnings and yields 3.5 percent and raises the dividend 15 percent a year. Even you Warren, can buy with your position."
Asked about his recommendation for Buffett, Rogers recommended a stock he owns: "International Speedway, they own those Nascar tracks. They got a new contract, up 46 percent with Fox and NBC. It's terrific."
The broader market and the Fed
(Read more: Did the Fed just pop the stock market bubble?)
"Last year, you could buy things and we bought them last fall—Netflix in the $60s, Best Buy at $13 a share—where it was pretty obvious," said Miller.
"The risk-reward was fantastic," he continued. "[But] it's very hard to find things that you can say would reasonably have a chance to be up 50 percent to 100 percent in the next 12 to 24 months."
On the Federal Reserve, Miller said he had no idea if the central bank will start to taper its $85-billion-a-month bond-buying program sometime this year. The Fed declined to make changes at its September meeting. Policymakers meet again this month and in December.
"The Fed is running a giant experiment, and we don't know what the answer to the experiment is going to be," he said. "We're playing it out in real time."