Eli Lilly (LLY 1.19%) isn't as popular a stock as Tesla (TSLA -1.11%), and it might seem unlikely that the pharma company could ever grow to become larger than the hottest car stock of the decade so far. Nonetheless, thanks to a handful of ongoing drivers for big growth, there's a good chance that it'll top Tesla by 2027.

Here's why.

Lilly has the heft to overtake Tesla

At the moment, Tesla's market cap is about $745 billion, whereas Lilly is around $565 billion. Assuming both companies are fairly valued, Tesla is worth about 32% more than Lilly right now. Yet over the last three years, the pharmaceutical giant grew more than 300%, while Elon Musk's company grew by only 65%. So, at the pace Eli Lilly is galloping, it's a real possibility that it could become worth more than the electric vehicle manufacturer in the future.

In terms of drivers for earnings, Eli Lilly has plenty. There are three markets in particular where it'll focus over the next three or so years: obesity, diabetes, and Alzheimer's disease.

Leading the charge in the first two markets will be its medicine Mounjaro, which is already approved to treat type 2 diabetes, and which brought in nearly $3 billion in sales during the first three quarters of 2023. The drug could soon gain regulatory approval to treat obesity as well, and it may be followed by a pair of other programs that are currently in phase 3 clinical trials. The company also has a pair of late-stage programs for diabetes in the works, not to mention a candidate for treating Alzheimer's in regulatory review.

Some of those attempts might fail. But given Lilly's track record of bringing multiple blockbusters to the market, the probability of future success is high. And success is two-pronged: An initial boost in the share price on the good news of a drug candidate's approval by regulators, and second, in all probability, seeing shares rise further based on highly successful sales of the drug until its patent expires.

Tesla's shares may exhibit similar behavior in the event that new vehicles or major new features are announced. But if the ongoing delays and tepid discourse surrounding the launch of the often-lampooned Cybertruck are any indication, investors and car buyers alike are starting to view Tesla's products with much more skepticism.

Both companies have very high valuations compared to others in their industries, as well as to the market's average; the drug developer's price-to-earnings (P/E) ratio is 110, whereas the automaker's is 78. That means there would need to be significant earnings growth over the coming years for their stocks to continue rising, assuming the market's impressions of their future value remain roughly the same as where they are today. But crucially, both players have the benefit of at least some hype in the media; that means there could still be buyers willing to pay a premium even if valuations go even higher -- at least until the excitement peters out.

On average, Wall Street analysts are predicting Tesla's diluted earnings per share (EPS) to grow, from $3.62 in 2022, to just over $5.50 by the end of fiscal 2025. In contrast, they anticipate Eli Lilly's EPS will rise from last year's $6.90 to $17.10 over the same period. So its rate of earnings growth is anticipated to accelerate significantly, but Tesla's isn't. Combining that factor with those discussed above, it looks like the pharma giant is likely to be the bigger company within a few years.

But Tesla won't be sitting idle

There are a few wild cards that might prevent Eli Lilly from becoming larger than Tesla. The first is that the electric-vehicle maker has plans of its own, and it can announce changes to those plans that will affect its shares. Both expanding into international markets and convincing investors that it'll soon make its cars more profitably than before could lead to its shares becoming more highly valued. But not every factor is in its favor. In addition, Tesla plans to move beyond its core business of auto manufacturing, such as commercializing its Dojo supercoumputer. While it's early days to precisely estimate how much these additional sources of revenue will contribute to Tesla's value, it's safe to say they will be non-trivial.

In the event of an economic downturn, consumers would no doubt be more inclined to spend their diminishing funds on medicine than on new vehicles. At the same time, there is a lot of discourse about Tesla's CEO Elon Musk that, while not strictly related to his company's ability to generate more earnings in the future, still affects the valuation of its shares. And lately, that impact has tended to be more detrimental than positive.

So if things continue as they're going, Eli Lilly could likely become the larger business by 2027. It's entirely possible that its being bigger will be a temporary phenomenon. Still, if you're looking for a growth stock to buy and hold for the next few years and beyond, Eli Lilly could be a good fit.