Some 36 million shares in the company, based in San Francisco, were sold Thursday for $21 apiece, higher than the range of $18 to $20 a share that the company’s investment bankers had recently envisioned. Founded in 2007 by two Massachusetts Institute of Technology computer science students, Drew Houston and Arash Ferdowsi, Dropbox sells software subscriptions that let users collaborate and share files online. Until now, it was financed by private investors — including venture capital firms Sequoia Capital and Accel Partners — who valued the start-up at $9.4 billion, according to the research firm CB Insights.