2020 is over, but old problems are stubbornly hanging on in 2021. With a pandemic, extreme political unrest, an economy still trying to find its way in the wake of it all, and the stock market near all-time highs, the reasons to invest may appear to be slim.

But there's always opportunity -- especially when negativity is running high -- to purchase shares of quality companies with great long-term prospects. Three Fool.com contributors think Veeva Systems (NYSE:VEEV), Intel (NASDAQ:INTC), and Naspers (OTC:NPSNY) are worth your while at the start of the new year.

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Life sciences race to the "digital transformation" door

Nicholas Rossolillo (Veeva Systems): The future looks bright for life science stocks. For many, 2020 was a big year as pharmaceutical and biotech companies raced to find treatments and vaccines for COVID-19. The fight against the pandemic continues. And new research and development is being aimed at innovative healthcare treatments and methods of patient care. Collectively, trillions of dollars are being spent every year globally to improve health outcomes. From a business standpoint, there will be winners, but there will also be plenty of losers.

That's why Veeva Systems is one of my favorite stocks for the massive life sciences industries. Veeva is a way to participate in the growth of the whole universe rather than try to bet on which companies developing new treatments and health technologies will be the biggest winners. Specifically, Veeva provides cloud-based software and tools for pharmaceutical, biotech, and other health-related companies to manage their operations. 

Besides participating in a general increase in life science research over time, Veeva is focused on helping these organizations make digital transformations -- updating tools and procedures to new digital standards. The software firm provides all sorts of functionality, ranging from clinical trial management to quality control to sensitive data management. It's constantly expanding its capabilities as well, recently adding new features to its far-reaching platform like virtual meetings and AI built into its customer relationship management product. Building on its early success as a software technologist partner for pharmaceutical and biotech companies, Veeva is expanding its platform to help consumer goods, chemical, and cosmetic companies as well.

This is a premium-priced stock at nearly 83 times trailing-12-month free cash flow (revenue minus cash operating expenses and capital expenditures), but for good reason. Veeva has consistently grown its sales at a double-digit percentage pace for years, a rate that accelerated in 2020 during the pandemic, and that shows no signs of slowing anytime soon as the need for new digital tools remains. Put simply, this is a best-in-class business that lies at the intersection of software and health.

This microchip giant is down but not out

Anders Bylund (Intel): Very few technology stocks strike me as great buys right now. The market as a whole looks overheated and many of my favorite stocks may be headed for a sharp correction in the not-too-distant future -- especially in the soaring tech sector. Semiconductor giant Intel is a rare exception to my unusually bearish analysis of the current market.

Intel shares are already trading at a 24% discount to their 52-week highs because Chipzilla has struggled to upgrade its manufacturing facilities to next-generation 7 nanometer technologies. This issue puts Intel on the back foot as many of its closest rivals are producing 7 nm chips with the help of third-party chip foundries led by Taiwan Semiconductor. Activist investor Daniel Loeb is asking Intel to consider breaking away from its time-honored commitment to running its own manufacturing facilities, suggesting that the company could spin its chip factories out as an independent company or even sell them to Taiwan Semi and friends.

Whether or not Intel adopts any of Loeb's ideas of radical change, Intel is well equipped for a return to full health. Nobody else in the semiconductor industry can match the company's massive research and development budget, which added up to $13.3 billion over the last four quarters. That's more than the R&D expenses of Advanced Micro Devices and Qualcomm combined. Innovation is the lifeblood of every technology company worth its salt, and Intel is taking its forward-looking development very seriously.

Intel's stock is priced for absolute disaster at just 10 times trailing earnings and 14 times free cash flows. That's an absolute steal if you believe that Intel is getting its derailed manufacturing upgrades back on track, as I do.

The company is due to report fourth-quarter results in a couple of weeks and I think it's wise to grab a few Intel shares on the cheap before that business update.

Get China's best company at half-price -- without investing in China

Billy Duberstein (Naspers): You don't often get to invest in a top-tier internet giant at half-price, especially in today's frothy tech market, but that's exactly what investors currently find in South African investment company Naspers.  

Naspers used to be a South African media company, but has basically become an emerging-markets venture capital investor over the past 20 years. In late 2019, Naspers spun out its venture investments, which are basically all of its assets, into a separate company called Prosus (OTC:PROSY). As of last quarter, Naspers owned 72.66% of Prosus.

Prosus' main asset is the company's huge 31% stake in Chinese internet giant Tencent -- a stake that is now worth a whopping $226 billion. Not only that, but Prosus also has stakes in other large international food delivery, classifieds, and digital payments companies, which analysts estimate could be worth anther $30 billion.

What's remarkable is that Prosus' market cap is only worth about $173.3 billion today, or about a 32% discount to its asset value. Even more egregious? Naspers only trades at an $85.4 billion valuation, or another 32% below the value of its 72.7% stake in Prosus.

This all adds up to Naspers' market cap being about half its asset value. And while it's hard to say if and when that asset-to-value gap might close, Naspers/Prosus' management is taking advantage, recently announcing a $5 billion share repurchase program back in November.

Tencent has come under some pressure recently as rumors have swirled that the U.S. government may ban citizens from owning shares of some Chinese companies. For those wanting exposure to this best-in-class international growth stock, Naspers offers an indirect way to invest in Tencent without the direct Chinese risk, and at a massive discount, at that.