For long-term investors, compounding growth at high rates is the name of the game. If you can buy a company that compounds earnings and cash flows at high rates for a long period, odds are you will have a very comfortable retirement.

While the markets have recovered somewhat in 2023, there are still high-quality growth stocks out there that look undervalued. Time to buy or add the following three names.

Amazon

Investors underestimate Amazon.com (AMZN 3.43%) at their peril. The e-commerce and cloud leader has been a relative laggard among big tech stocks during this recovery period and is still 31% below its all-time highs -- worse than most other FAANG names.

Some might be thinking Amazon hasn't kept up with changing artificial intelligence (AI) trends, but it's pretty early to say that just eight months after the introduction of ChatGPT. And while OpenAI's chatbot is quite exciting, Amazon also sells lots of AI-as-a-service offerings as well, both from its own large-language models to those from start-ups on the Amazon Web Services (AWS) marketplace, including AI21 labs, Anthropic, and Stability.ai. In addition, Amazon has its own custom silicon, Trainium and Inferentia -- custom accelerators that can lower the costs of training and running large and expensive models.

Moreover, investors may be underrating how much AI will benefit Amazon's e-commerce operations and other aspects of its business. After all, Amazon is by far the largest and dominant e-commerce company in the U.S. and a growing player around the world, with streaming video and shipping. So, its data on customer interests and trends is likely unmatched. Given that AI and machine learning improve with more quality data, companies with large and proprietary datasets that other companies can't match are likely to be advantaged in the AI era. That means Amazon's non-cloud businesses should benefit from AI too, making the stock a buy today.

Microchip Technology

Besides generative AI, another long-term trend is in electrification and automation amid climate change and labor-shortage concerns. That means sustained growth prospects for makers of industrial and auto semiconductors.

Microchip Technology (MCHP 1.51%) has a long history of success growing market share and expanding margins in these industries as a leader in programmable microcontrollers, the tiny computers that go into just about every machine across a variety of end markets. In its most recent fiscal year, Microchip got 41% of revenue from industrial chips, 17% from automotive chips, and 19% of revenue from data centers, which have exposure to AI.

Even though Microchip has appreciated to near all-time highs, 2023 is a good year to double down on this high-quality, high-margin semiconductor stock -- for two reasons. First, Microchip has recently completed a de-leveraging cycle that began all the way back in 2018 after the large acquisition of Microsemi. Now having reached its leverage target, the company will programmatically increase cash returns to shareholders, growing from 62.5% of free cash flow last quarter to 100% of free cash flow by March 2025.

When that happens, it's possible Microchip's valuation discount to other analog and microcontroller peers will close. Currently, larger and more established players in the field that return roughly 100% of free cash flow to shareholders trade at valuations almost 50% higher than Microchip, which trades at less than 14 times next year's earnings estimates. But as Microchip's cash returns ramp, not only will shareholders see a dividend that could grow every quarter, but a re-rating to a higher valuation too. That makes Microchip a great add before that happens.

Farfetch

Of the sectors that may be lagging the market's strong recovery, consumer-discretionary stocks may be the last to recover once recession fears have passed.

Currently, sentiment for luxury goods e-commerce platform Farfetch (FTCH -2.22%) is pretty low. High interest rates and recession fears in the U.S., as well as bad economic figures out of China, seem to have dampened sentiment around luxury goods stocks.

Still, Farfetch has a secular-growth story, as it seems to have solidified itself as the winner in the online luxury space. While luxury is a laggard in terms of going digital, e-commerce sales should make up a greater and greater share of the luxury market going forward. Last quarter, Farfetch was able to defy the skepticism around the sector, and the stock rocketed higher. However, after luxury goods giant (and Farfetch investor) Richemont (OTC: CFRUY) and LVMH (LVMUY 0.82%) reported some soft-ish numbers this month, Farfetch's stock has retreated again.

Still, long-term investors should probably use the share-price weakness -- with the stock down more than 90% off its all-time high and shares trading at just one times sales -- to add shares of this market leader.

This year, Farfetch will be lapping the closing of the Russia business and Chinese lockdowns in the first quarter of 2022, as well as last year's super-strong dollar, which depressed revenue and profits in international markets. So, Farfetch should post accelerating growth, which may defy skeptics. Moreover, partnerships with brands Ferragamo and Reebok just launched last quarter, which should fuel this year's growth. And Farfetch's digital partnership with Neiman Marcus will be launching in the second half of this year, propelling results into 2024.

Finally, the company's pending acquisition of rival Yoox Net-a-Porter, owned by Richemont, should go through this year, consolidating Farfetch with its main rival and establishing Farfetch as the de facto dominant platform for luxury. That should increase Farfetch's flywheel and network effects, leading to long-term growth and profit improvement. There is also a chance China stimulates its economy, which may reverse the current sour mood on China's consumption by the end of the year.

All of these company-specific factors should allow Farfetch to thrive over the long term, making this year's recession worries an opportunity to add this high-quality growth stock to your portfolio.