Why Duolingo Stock Soared 10% on Thursday

Shares of Duolingo (NASDAQ: DUOL) , the AI-powered language learning company, jumped 9.5% through noon ET Thursday after crushing analyst forecasts for second-quarter earnings last night.

Heading into the quarter, Wall Street forecast Duolingo would earn $0.32 per share on sales of $177.1 million. Instead, Duolingo reported a profit of $0.51 per share. Sales were $178.3 million.

Duolingo's Q2 earnings

The news was actually even better than that sounds. While Duolingo beat revenue expectations by only $1.2 million (which sounds small), revenue growth year over year was an astonishing 41%. Profits, already impressive relative to what analysts predicted, grew more than sixfold compared to last year's Q2.

And Duolingo is still growing.

Bookings at the language learning company -- a proxy for future revenue growth -- rose 38% year over year, nearly as fast as sales growth in the quarter. Subscription bookings in particular grew faster than Q2 sales -- up 47%. And the number of people paying for Duolingo grew 52%, with 8 million subscribers now paying to use the otherwise-free language app.

Is Duolingo stock a buy?

Expect all of these numbers to continue growing, too, because according to Duolingo, its app reached 100 million monthly average users last quarter. Not only is that a new record for the company, it means that currently, only 8% of the company's users are paying for the service. That means there's 92 million people left, familiar with Duolingo, that the company can work on trying to convert into paying customers.

Is all this enough, though, to make Duolingo stock a buy at its now-$7.8 billion market capitalization?

Yes, I think it is. Consider that in Q2, Duolingo generated just shy of $55 million in positive free cash flow, implying a run rate of about $220 million annually. On a $7.8 billion market cap, that works out to a price-to-free cash flow ratio of 35.5. Admittedly, that's a high number.

But so long as Duolingo keeps growing at 38%, 41%, 47%, or 52%, I think it's actually a bargain price to own a piece of this growth stock .

Rich Smith has no position in any of the stocks mentioned. The Motley Fool has positions in and recommends Duolingo. The Motley Fool has a disclosure policy .