Investing in an up-and-coming growth stock can be a surefire way to generate some significant gains for your portfolio. One to consider now is Axsome Therapeutics (AXSM -1.10%), a small biotech with big potential thanks to a couple of promising products. The company seems to be headed in the right direction. Is this a stock that has the potential to make you a millionaire? Let's find out.

It has two promising products

Axsome has a narcolepsy medication, Sunosi, which contributed just under $45 million in revenue last year -- and this wasn't even for a full year as the company only acquired the medication from Jazz Pharmaceuticals in May 2022. 

What's even more promising is Axsome's treatment for major depressive disorder, Auvelity. The U.S. Food and Drug Administration approved it last year, and at its peak, it could bring in roughly $2 billion in sales. The medication has shown positive results in patients after only one week of use. Axsome launched the product in October 2022, and it generated $5.2 million in sales by the end of the year.

Axsome also has other products in its pipeline as well, including a migraine medication, AXS-07, that it plans to submit a new drug application for later this year. 

Reaching the million-dollar mark

To gauge whether your investment can grow to $1 million, you need to factor in the investment amount, the potential returns, and the number of investing years you have left. If you don't have many investing years left, for example, then you may need to compensate for that by investing more money, or focusing on stocks with high potential returns (riskier investments).

For a $25,000 investment to grow to $1 million, it would need to be worth 40 times its original value. Earning such a mammoth return is a daunting task, but over a window of 25 years, the average return would need to be around 16%. And over a period of 30 years, you would need an average return of a little over 13%.

The trouble here is that the S&P 500 averages an annual return of around 10%. So for Axsome to turn a $25,000 investment into $1 million within 25 to 30 years, it would need to consistently outperform the S&P 500, by at least a few percentage points. It's tough to be able to predict that, especially for a business like Axsome that's still in its early growth stages. Over the past 12 months, the stock has delivered some impressive gains of around 50%. Whether it can continue to outperform over several years, and potentially decades, is a big question mark.

At 40 times its value, that also means this would need to eventually be a $100 billion business. It's hard to picture that today. Axsome does have attractive growth potential, but I wouldn't expect it to get to that high of a valuation based on where the company is right now. Unless you're investing $100,000 or more into the stock, I wouldn't expect Axsome to get you to $1 million all on its own.

Should you buy Axsome's stock?

The big advantage of investing in a mid-cap stock such as Axsome is that if the business is successful, you could potentially be sitting on a 10-bagger or better. Analysts see the stock rising by as much as 72% over the next year based on price targets of around $104. So even in the short term, some significant returns could be made from owning the healthcare stock.

Axsome has a strong base to build on, with Sunosi and now Auvelity potentially generating billions in revenue for the business in the future. That makes the company's $2.6 billion valuation look cheap right now, and even if it doesn't end up making you a millionaire, this can still be an excellent investment to buy and hold.