The market found a reason to believe in Apple Computer ( AAPL) again: the prospect of a second-half rebound.The first half of this year -- and a bit more - has been nothing to write home about for shareholders, with Apple's stock falling 42% this year through last week. But investors found reason to hope again on Thursday, sending Apple's stock up more than 13% in recent trading. What's changed? The company's fiscal third-quarter earnings, which the company reported Wednesday night, were much better than expected. But more than that, the report indicated to investors that there are more good times to come. Apple's transition to Intel ( INTC)-based processors at the heart of its Macintosh computers finally seems to be bearing some fruit in terms of market-share gains. Add to that the expected refreshes of the company's iPod lineup and the potential for new products, and the company looks poised to post strong results in coming quarters, bulls say. And that should send the company's stock soaring again. "If you look across the universe and ask which stock has the best promise for the second half, this is definitely one of them," says Jim Grossman, a portfolio manager at Thrivent Investment Management, which is long Apple. For many bulls, the big bright spot of Apple's report was the performance of its computer business. Total shipments were up 12% year over year, outpacing the worldwide market. But Apple could do much better in coming quarters, bulls argue. The growth in the latest quarter came despite even though the company didn't start shipping its new Intel-based consumer notebooks until partway through the quarter. And the growth came even though the company has yet to update its professional line of desktop computers, a factor that likely contributed to the 23% year-over-year decline in desktop computer shipments.