With Apple (AAPL) shares having recently topped $500, how soon might they hit $1,000?

That is an impatient thought for an investor, perhaps. But Apple shareholders have gotten used to fast gratification: The share price has doubled five times in the past decade.

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Although Apple already is America's largest company by stock-market value, there are several reasons to believe that it can grow much larger. But it is far from a sure thing, and prospective buyers already may have more exposure to the stock than they think if they own index funds.

Apple's recent growth is the envy of most companies, large and small. Sales jumped 73% and earnings more than doubled during its quarter ended Dec. 31.

 Will Apple Shares Hit $1,000?3:39

Apple can grow much bigger but it's not a sure thing, SmartMoney's Jack Hough argues on Markets Hub. Photo: Getty Images.

By one measure, Apple stock remains reasonably priced. It sells for just under 15 times the company's earnings over the past four quarters, according to Thomson Reuters data. That is in line with the historic average for U.S. stocks and below the current median of nearly 17 for companies in the Standard & Poor's 500-stock index.

"Apple is priced like a slow grower because investors aren't used to dealing with a company this big that's growing this fast," says Daniel Ernst, an analyst at Hudson Square Research in New York.

Mr. Ernst, whose price targets on the stock have long been among Wall Street's highest, says Apple should be worth $700 a share today.

A doubling of the stock price from Friday's $522.41 would put Apple's market value at over $900 billion. No U.S. company has ever been that large.

Such a value seems plausible, however. Microsoft (MSFT) reached a value of around $600 billion in late 1999, which is more than $800 billion in today's dollars. It was helped by a tech-stock boom, but Apple today produces more than triple the profit that Microsoft did back then, not adjusted for inflation.

Gaining Market Share

Another important difference: Microsoft in late 1999 controlled more than 90% of the market for personal-computer operating systems, according to some estimates. Apple controlled 26.6% of the mobile-computing market in the fourth quarter of 2011, including notebooks and tablets, according to NPD DisplaySearch, which provides research for the display industry. Its smartphone market share was 23.9% in the fourth quarter, according to Strategy Analytics, a technology consultant.

"Apple has plenty of room to gain market share in the U.S., and even more in emerging markets like China," says Michael Walkley, who covers Apple for Toronto investment bank Canaccord Genuity.

Mr. Ernst and Mr. Walkley both say Apple stock could hit $1,000 within three years. That would require an extraordinary return of close to 25% a year. The 50-year average for the S&P 500 is about 9% a year, not adjusted for inflation.

Both analysts cite Apple's record of creating large new markets (iPods, smartphones, tablet computers) and its cash and investments of nearly $100 billion. Both also think a dividend payment could attract a new crowd of buyers to shares, especially among income-seeking mutual funds.

Apple pays no dividend and hasn't announced plans to start, but Chief Executive Tim Cook told shareholders Thursday the cash is "more than we need to run the company" and that management is thinking "very deeply" about what to do with it.

Only five of 57 analysts with published recommendations on Apple are neutral or negative. Colin Gillis at BGC Partners in New York, who calls the stock a "hold," says that for Apple to impress investors from here it must "smash earnings forecasts to pieces, and that's a difficult position."

Edward Zabitsky, founder of Toronto-based ACI Research, says these days he often is referred to as "the guy who says to sell Apple," being the only analyst with that recommendation. "It feels a little lonely," he says.

Betting on Mobile Broadband

In Mr. Zabitsky's view, Apple will lose its pricing power as mobile Web browsers become more powerful, because users will no longer need phones and tablets that support a large universe of specialized programs. Stock buyers should bet on mobile broadband companies like Verizon Communications (VZ) and AT&T (T) and on content owners like Walt Disney (DIS), he says.

Who's right? Brian Lazorishak says he isn't sure, but a 52% run-up in the stock over the past year has left him with more exposure than he wants as a portfolio manager at Chase Investment Counsel in Charlottesville, Va., which oversees $700 million. He is selling a portion of his position.

Other investors may likewise find they have more Apple exposure than they want or know. The stock makes up nearly 4% of the S&P 500 index, which weights companies by size. And Apple contributed about 6% of the index's fourth-quarter earnings, according to Howard Silverblatt, senior index analyst at S&P.

Without Apple beating Wall Street forecasts by 37% last quarter, the 500 index would be on track to fall 3% short of earnings forecasts, instead of meeting them, Mr. Silverblatt says.

Investors who are determined to bet on one more doubling for Apple stock might want to content themselves with buying the Technology Select Sector SPDR (XLK), an exchange-traded fund. It tracks the tech sector of the S&P 500, in which Apple has a nearly one-fifth weighting. But it also has plenty of exposure to companies like International Business Machines (IBM), Google (GOOG), Microsoft and AT&T, just in case Apple stumbles.

After all, giants like Apple face long odds. Between 1952 and 2009, shares of the largest companies in their sectors by market value each year tended to underperform peers over the following decade by more than three percentage points a year, according to Robert Arnott, founder of Research Affiliates, a Newport Beach, Calif., money manager.

Apple has recently shown a knack for beating such odds. But most stock investors probably already have enough of a stake in the company's success, whether they hold individual shares or not.

—Jack Hough is a columnist at SmartMoney.com. Email: jack.hough@dowjones.com