Costco (NASDAQ:COST) has been on a continuous growth trajectory for the last few decades. As the company has expanded to become one of the biggest retailers in the world, its stock price has soared as well.

I am a big fan of Costco's business model, which centers on keeping costs low through high productivity, and passing the savings on to customers. However, Costco stock is fairly pricey -- it currently trades for more than 24 times forward earnings.

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Costco will have to navigate several major challenges in the next five to 10 years. Photo: The Motley Fool.

Furthermore, Costco will face a few major challenges in the next decade. If it cannot come up with good solutions to these potential issues, Costco stock could fall in the years ahead.

Amazon.com is moving into groceries

The first (and biggest) long-term threat to Costco is the growth of Amazon.com (NASDAQ:AMZN). Amazon is similar to Costco in many ways. Both companies constantly work to reduce costs, gain scale, and pass the savings on to customers in order to build long-term loyalty.

Recently, Amazon has taken steps to become a bigger player in the grocery business, which accounts for about half of Costco's revenue. In Seattle, Amazon has operated its AmazonFresh pilot grocery delivery program since 2007. More recently, it began adding new cities, and the company could be on the verge of a broader AmazonFresh rollout.

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Amazon.com is moving way beyond books and movies. Photo: The Motley Fool.

While an annual AmazonFresh membership costs a pricey $299, it is convenient for people who are constantly on the go. Moreover, Amazon has a history of cutting prices as it drives down costs through economies of scale. In the next five to 10 years, AmazonFresh could become much cheaper, and thus a greater threat to Costco.

In the meantime, Amazon is also offering a cheaper alternative called Prime Pantry. This service excludes perishable items, but offers $6 flat-rate shipping for up to 45 pounds of other groceries. This allows customers to stock up on bulky items without having to lug them home. Additionally, Prime Pantry items come in regular sizes, while Costco sells in bulk.

Today, Amazon is a relatively small player in the trillion-dollar U.S. grocery industry. However, its AmazonFresh and Prime Pantry programs could eventually make the online retailer a serious threat to Costco in the grocery business.

Appealing to new customers

A second issue for Costco is its aging customer base. Baby boomers remain Costco's core demographic group. Costco tends to locate its stores in (or near) wealthy suburban communities, where it can appeal to this audience.

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Buying in bulk doesn't make sense if you live in an apartment and don't have a car. Photo: The Motley Fool.

By contrast, millennials shop much less at Costco. Many people in their 20s and 30s appear to be less interested than previous generations in car ownership, homeownership, and suburbia. All of these trends are bad news for Costco. If millennials continue to prefer living in the city and relying on bikes and public transportation as they age, they aren't likely to find Costco memberships very useful.

Of course, it is likely that many millennials will become more like their parents over time. Still, it isn't clear to what extent these generational differences are temporary rather than permanent.

To draw in younger shoppers, Costco has introduced some new items that appeal to millennials, such as organic beef and kale. Costco is also working to improve its e-commerce operation. However, Amazon.com is way ahead in serving younger consumers. If these people remain loyal to Amazon throughout their lives, that would be a big problem for Costco.

Where is the next generation of leaders?

Finally, like its customer base, Costco's executive team is aging. Costco co-founder Jim Sinegal retired as CEO a few years ago, but he remains fairly active in the company, as does co-founder Jeff Brotman. Both are in their 70s. Costco's other leaders are mainly in their late 50s and early 60s.

Many of these people have held senior leadership roles at Costco for most of its corporate history. For example, Richard Galanti has been Costco's CFO since January 1985 -- a little over one year after the company was founded.

In the next decade or so, many of Costco's long-serving executives are likely to retire. Costco has traditionally maintained its culture by promoting from within, but it's unclear if the company is developing a new generation of leaders. This could impact the company's ability to navigate the other challenges it faces in the coming years.

Foolish takeaway

Costco has developed a great business model, but it is now being threatened by a few trends. First, e-commerce pioneer Amazon is moving more aggressively into the grocery business with its  AmazonFresh and Prime Pantry programs.

Second, younger consumers -- particularly the millennial generation -- are adopting lifestyles that don't fit well with Costco's business model. For people living car-free in the city, Amazon offers a convenient service, unlike Costco. Lastly, Costco might not be developing the future leaders needed to counter these threats.

It's possible that Costco's large scale and commitment to price leadership will be sufficient to safeguard its market position in the long run. Nevertheless, investors should be aware that Costco faces risks that could develop into significant problems for the company and its stock.

Adam Levine-Weinberg owns shares of Costco Wholesale. The Motley Fool recommends Amazon.com and Costco Wholesale. The Motley Fool owns shares of Amazon.com and Costco Wholesale. 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.