Shares of educational software maker Blackboard (NASDAQ:BBBB) pulled out of their post-earnings free-fall Friday. But for the life of me, I cannot fathom why they were falling in the first place.

As usual, this Motley Fool Hidden Gems recommendation aced its quarterly exam, nailing analysts' expected 35% pace of sales growth and beating earnings expectations -- just as it's done all year long. Other companies whose wealth depends on the health of state and municipal tax bases -- Oshkosh (NYSE:OSK) and Mine Safety (NYSE:MSA), for example -- may be struggling, but Blackboard keeps adding new public-school customers to a list already populated with private names like Strayer (NASDAQ:STRA), ITT Educational (NYSE:ESI), and DeVry (NYSE:DV).

True, Blackboard also cut guidance, pointing to the weak K-12 market in explanation. Even so, analysts tracking the company continue to expect it to grow profits at the rate of 26% per year over the next half decade. And as I pointed out last week, the crucial test that management needed to pass lay not in proving its independence from the troubles affecting the American economy. Rather, we just wanted management to show that it knew what it was talking about when it predicted it would turn free cash flow-positive this year.

It passed that test.

Blackboard generated cash profits of $55.4 million in Q3, enough to completely erase the deficit from the year's first half. The company's now up $33.1 million year-to-date -- a respectable 16% increase when compared to its position at this time last year.

Q3's superb performance gives me confidence in management's promise to generate $80 million to $85 million in cash from operations this year. Subtract from that the year's capex, which is currently trending toward $30 million by year-end. Based on the resulting $50 million to $55 million in free cash flow, and analyst projections of 26% long-term growth, I think anywhere in the neighborhood of $1.3 billion to $1.4 billion is a fine price to pay for Blackboard.

And seeing as the stock's selling for just over half that price today, I'm writing Blackboard up as a buy.

Does the Motley Fool Hidden Gems team agree? They recommended the stock in the first place, after all. Find out if they still consider this one the teacher's pet when you take a free trial.

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Fool contributor Rich Smith owns shares of Oshkosh. Blackboard is a Motley Fool Hidden Gems selection. The Motley Fool has a disclosure policy.