Think Apple (AAPL) shares are running out of steam?

Think different, advises Sterne Agee analyst Shaw Wu.

Wu, a long-time Apple bull who recently joined Sterne from Kaufman Bros., this morning assumed coverage of the stock at his new employer, lifting the firm’s price target on the stock to $445, from $400. He writes in a research note this morning that Apple “has emerged as the most beloved and feared provider of PCs and mobile devices and one of the world’s leading distributors of digital content.” He says the new price target reflects a 15x multiple on his calendar 2011 EPS forecast of $25.39, plus net cash.

Wu has a multi-part thesis on why you should own the stock.

Apple, he says, is “the ultimate platform adoption story. “When we look at AAPL’s share of PCs and mobile phones, it is still relatively small in the grand scheme with China and international emerging as vast opportunities that could rival its strong U.S. business.”

He sees “plenty of headroom” for Macs and iPads. “The beauty with the AAPL story is that the company doesn’t need to win everyone over to continue its success,” he writes. “The company just needs to continue winning a fair share of its vast end markets.” He notes that global Mac share is only about 4.5% – and that the total can potentially double to 8%-10%. And that’s not counting the iPad. Include tablets, he says, and Apple’s share can reach 15%-17%, close to that of HP and ahead of Dell, Acer, Lenovo and Toshiba.

Meanwhile, he also sees more growth potential for the iPhone, noting that smart phones are just 20% of the market, up from 15% a year ago, and 5%-7% a few years ago. He thinks smart phones will take 50%-60% of the market in the next 3-5 years – and he adds that Apple has “plenty of room for growth,” holding just a quarter of the smart phone market and only 3% of the total mobile phone market.

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