Shares of rooftop solar installer SolarCity surged Thursday in their market debut after the offer priced well below its original expectations.

The stock rose $3.09, or 38.6 percent, to $11.09 in afternoon trading, after reaching as high as $11.35 earlier.

The San Mateo, Calif., company, started by PayPal founder Elon Musk, cut its expectations for the offer on Wednesday. It issued 11.5 million shares at $8 per share, for proceeds of $92 million. It originally hoped to offer 10.1 million shares at $13 to $15 per share, with proceeds of $141 million.

SolarCity offers homeowners a "solar lease" that allows them to pay for the panels and electricity that they generate over time, often for less than it would cost to buy electricity from a local utility.

The company has been growing quickly, aided by a huge decline in the price of solar panels. While that has crushed solar panel makers' profits, lower prices have also boosted installers' prospects by allowing them to sell solar-generated electricity cheaper than grid power with no upfront investment.