During intraday trading on Tuesday, Amazon.com (NASDAQ:AMZN) joined Apple in the $1 trillion market cap club. The achievement highlights Amazon stock's incredible performance recently. To get to this valuation, shares more than doubled over the last 12 months.

Of course, the big milestone raises the question: Is Amazon really worth $1 trillion? The more specific question for investors is: Is Amazon a buy, sell, or hold after rising so sharply? After all, Amazon requires much frothier valuation multiples to be in the $1 trillion club than Apple. Is Amazon's premium valuation justified?

The answer may surprise you.

A smartphone displaying a picture of a shopping cart

Image source: Getty Images.

Looking beyond Amazon's wild valuation metrics

A quick glance at Amazon's valuation metrics without any further context makes the e-commerce giant appear overvalued. Amazon has a price-to-earnings ratio of 183 and a price-to-book ratio of 28 at the time of this writing on Tuesday. For perspective, Apple's P/E is just 20, and its P/B ratio is 10. Some investors may consider the idea of buying a stock with valuation multiples as high as Amazon's to be absurd.

Amazon's underlying business, however, boasts some extraordinary momentum, making a good case for an unconventional valuation. First and foremost, Amazon's earnings per share are skyrocketing. The e-commerce and cloud-computing company's trailing-six-month earnings per share are $8.34, up 346% year over year. 

Another reason Amazon would trade at a much-higher premium to its earnings than Apple: Amazon's earnings growth obliterates Apple's. The iPhone maker's trailing-12-month earnings per share increased 31% year over year. This compares to 178% year-over-year growth for Amazon's earnings per share over the same time frame, according to Reuters data.

Amazon's huge growth in earnings has been fueled by a combination of rapid revenue growth and fatter margins. In Amazon's most recent quarter, for instance, revenue was $52.9 billion, up 39% year over year. Meanwhile, operating income surged from $638 million in the year-ago quarter to $3 billion, crushing management's guidance range for second-quarter operating income between $1.1 billion and $1.9 billion. Amazon's outsize operating income growth was driven by an operating margin that expanded from just 1.7% in the year-ago quarter to 5.6% in Q2.

Playing a key role in Amazon's fast-improving profitability is a thriving cloud computing business. Amazon Web Services, or AWS, is the world's largest cloud services business. It's so far ahead of peers that it can be cost-competitive while simultaneously growing its operating margin. Then there's the fact that AWS, which is Amazon's biggest contributor to its bottom line, is growing much faster than its e-commerce business. AWS' trailing-six-month net sales and operating income are up 49% and 68% year over year, respectively.

Boxes in an Amazon fulfillment center

Image source: Amazon.com.

Buy, sell, or hold

Considering these factors, the premium investors have to pay to buy Amazon looks reasonable. Indeed, when combining these fundamentals with the competitive advantage that comes with Amazon's unprecedented scale in two fast-growing industries -- e-commerce and cloud computing -- the stock continues to look attractive at around $2,050 per share.

Sure, Amazon stock isn't as attractive as it was at $1,000 last May. But even at $2,000, Amazon remains a good bet for buy-and-hold investors.

John Mackey, CEO of Whole Foods Market, an Amazon subsidiary, is a member of The Motley Fool's board of directors. Daniel Sparks owns shares of Apple. The Motley Fool owns shares of and recommends Amazon and Apple. The Motley Fool has the following options: long January 2020 $150 calls on Apple and short January 2020 $155 calls on Apple. The Motley Fool has a disclosure policy.