Apple’s 78% surge in profit has helped alleviate — at least a bit — concerns about the company’s future as CEO Steve Jobs takes a medical leave of absence and Chief Operating Office Tim Cook heads the ship.

On Tuesday Apple announced the financial results for its fiscal 2011 first quarter that ended Dec. 25, 2010. The company posted record revenue of US$26.74 billion and record net quarterly profit of $6 billion, or $6.43 per diluted share.

These results compare to revenue of $15.68 billion and net quarterly profit of $3.38 billion, or $3.67 per diluted share, in the year-ago quarter. Gross margin was 38.5% compared to 40.9 % in the year-ago quarter. International sales accounted for 62% of the quarter’s revenue.

Apple sold 4.13 million Macs during the quarter, a 23% unit increase over the year-ago quarter. The company sold 16.24 million iPhones in the quarter, representing 86%t unit growth over the year-ago quarter. Apple sold 19.45 million iPods during the quarter, representing a 7% unit decline from the year-ago quarter. The company also sold 7.33 million iPads during the quarter.

The results indicate that Apple will perform well even as Jobs hands day-to-day operations to Cook, Bill Kreher, an analyst at Edward Jones, told “Bloomberg” ( Apple gained $3.05 to $343.70 at 9:38 a.m. New York time in Nasdaq Stock Market trading. The shares climbed 53% last year.

“These results will help shift focus away from Steve Jobs’s health and to the company’s long-term earnings power,” Kreher says. “Investors have become increasingly more comfortable with life after Jobs.”

While some analysts question how long Apple can maintain its run of products without Jobs’ day-to-day oversight, most agree the company can keep going apace for the next few years with updates to the iPad, iPhone and other devices already in the pipeline, notes the “Associated Press” ( The Sellers Research Firm (that’s me) maintains that the momentum will continue long past that with Jobs’ hand-picked team in pace.

“The quarter was remarkable,” Shaw Wu, a Kaufman Bros. analyst told the “AP.” The analyst thinks investors will give Apple more credit for the quarter in the coming days or weeks. As for Jobs’ health, he said investors are “not as fixated on it,” Wu adds.

— Dennis Sellers