No one is sure why Apple (AAPL) shares are so cheap. The stock's price-to-earnings ratio is 13.14 (on a trailing basis) -- near the lowest level in the past five years and less than the average for the S&P 500, which is 19. 

During that same time period, as Apple changed the world with the iPod, iPhone and iPad, shares have soared more than 300%. And Wall Street analysts think the good times aren't going to end anytime soon. They have an average price target of $505.94. The high estimate is $700.

Apple's share value makes little sense compared with its peers. Analysts expect the company's revenue to rise 41.7% to $31.9 billion in the current quarter. Google (GOOG) and IBM (IBM) trade at richer multiples, of 19.19 and 14.01 respectively, even though their revenue growth rates are inferior. During the current quarter, Google is expected to increase revenue by 31.2% to $8.36 billion, and IBM's sales are forecast to rise 2.6% only to $29.78 billion.

Explanations abound about why Apple shares are so undervalued. The blog Bullish Cross argued Apple is the most "undervalued and underappreciated large-cap growth company in America."  Felix Salmon of Reuters recently offered a few theories, ranging from "it's run out of buyers" to "the headline share price is high" to "Steve Jobs is dead." Salmon admitted none of his explanations were "particularly compelling" and he is right.

One plausible explanation came from Pat Becker Jr., a manager who follows the tech sector at Portland, Oregon-based Becker Capital Management Inc., which oversees $2.2 billion in assets. "It looks like they are well-positioned on a number of fronts," Becker, a value investor who does not hold Apple but admires the company, said in an interview. "It's a question of what do they do for their next hit."

Indeed, the Cupertino, Calif. company has reinvented the music business with the iTunes and the iPod. Then it reimagined the smartphone with the iPhone and recreated tablet computing with the iPad. These products are all wildly successful. Apple's market share in the digital music business is about 70%. Sales of the iPhone 4S, the newest model, topped 4 million in the first weekend of sales in October. It was Apple's fastest selling device. The company is on target to sell 40_million iPads this year even as rivals, including Amazon (AMZN), ratchet up the competition in the tablet market.

The only recent Apple product that has not wowed investors has been Apple TV, which despite good reviews has only captured about 4% of the video streaming market. The Apple Television, though, could be a game-changer if half the scuttlebutt that has been published about it in the blogosphere is true. The Apple Television -- dubbed iTV -- is expected to be available in 2012. AppleInsider recently reported that the competition is "scrambling" to match this yet-unreleased product.

Investors have a simple choice: They can either buy Apple shares now in the hopes that the company will come up with another ground-breaking product, or they can wait until the company makes a rare misstep and purchase the shares on the dips. Either way, the stock remains a compelling value.

--Follow Jonathan Berr on Twitter @jdberr.