Investors buying shares of Apple (Nasdaq: AAPL) at current prices are betting the company will double to roughly $850 billion in market value, and perhaps $1 trillion not long after that.

Are they right? Can the Mac maker become the world's first trillion-dollar enterprise? Only if 48-year-old John Browett is able to transform a 361-store fiefdom into a global retail empire. CEO Tim Cook is betting that he can.

Browett, formerly the head of Dixons Retail in the UK, replaces Ron Johnson as the head of Apple's retail operations. Johnson last year took the top job at JCPenney after helping the late Steve Jobs create one of the world's top-performing retail concepts.

At last count, each Apple store generates $4,709 in merchandise sales per square foot annually. Tiffany & Co. (NYSE: TIF) ranks a distant second at just $2,974 per square foot. Electronics retailer Best Buy (NYSE: BBY) was moving just $831 per square foot as of August, according to researcher RetailSails. This is the legacy Browett inherits.

He won't be able to live up to it.

That's not necessarily a bad thing. Browett already has retail experience in overseas markets -- including parts of Asia -- a key area of focus for the Mac maker. Pricing is bound to vary widely across a more expansive worldwide chain that includes locations in wage-poor economies. Average selling prices per square foot would probably dip as a result.

The bigger concern is how fast Browett would move. If he moves fast, will he able to preserve the high-tech premium experience Jobs and Johnson worked so hard to cultivate? Dixons isn't the Tiffany & Co. of electronics retailers in the UK the way that Apple is here in the U.S.

I'm optimistic, if only because Browett brought Apple to Dixons and built what amount to Genius Bars at locations that sold the company's products, Bloomberg BusinessWeek reports. The implication? He already has a sense of what Mac users and wannabes expect; I believe he'll deliver.

Of course, Apple isn't the only American enterprise branching out. The Motley Fool recently identified 3 U.S. companies making waves worldwide for investors looking for safe ways to diversify internationally. Click here to get access to the research now -- it's 100% free for a limited time.

Fool contributor Tim Beyers is a member of the Motley Fool Rule Breakers stock-picking team. He owned shares of Apple at the time of publication. Check out Tim's web home, portfolio holdings and Foolish writings, or connect with him on Google+ or Twitter, where he goes by @milehighfool. You can also get his insights delivered directly to your RSS reader.

The Motley Fool owns shares of Best Buy and Apple. Motley Fool newsletter services have recommended buying shares of Apple. Motley Fool newsletter services have recommended creating a bull call spread position in Apple. Motley Fool newsletter services have recommended writing covered calls in Best Buy. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.