Shares of Apple Inc. jumped Wednesday to a new all-time high following the company’s blow-out results for its first fiscal quarter, in which earnings more than doubled on strong sales of the iPhone and iPad.

After the opening bell, the stock rose more than 7% to pass the $450 mark — making for a gain of more than 30% over the last 12 months. The stock was last up 6.8% to $449.

Late Tuesday, Apple AAPL +6.65%  reported that earnings more than doubled in the December quarter, as the company sold more than 37 million iPhones, blowing past analysts’ estimates for the period. The typically conservative company also issued a forecast for the current period that was above Wall Street’s forecasts.

Brokerage analysts, who were already heavily bullish on the stock, amped up their estimates for the company’s current fiscal year as well as their price targets for the stock.

The changes brought the median Street target to $550 from $520 — about 22% above the share’s current level. At least 14 analysts have price targets at the $600 level and higher.

“We expect another stellar product cycle this year with an iPad refresh in March, followed by the much anticipated LTE-capable iPhone 5 mid-year,” wrote Richard Gardner of Citigroup, who raised his price target on the stock to $600 from $500 following the report.

Despite the stock’s high price, Apple’s valuation is actually relatively low, especially given its massive cash war chest that is approaching the $100 billion mark. The stock trades about 11 times estimated earnings for the next four quarters, though the multiple is only 8.4 times estimates when the cash is backed out.

Calling the results “stunning on many levels,” Mark Moskowitz of J.P. Morgan pushed his price target to $625 from $525.

“We think that underlying strength related to iPhone and iPad market penetration has staying power,” he wrote, adding that he expects investors “to be intrigued by Apple preemptively commenting that it is actively assessing cash usage options.”

Apple said it ended the quarter with cash, equivalents and long-term securities totaling $97.6 billion. Several analysts asked the company about discussions regarding a possible dividend or share buyback, but Apple executives remained non-committal on the subject, saying only that the board of directors was having “active discussions” on the topic.

Katy Huberty of Morgan Stanley wrote that Apple “appears committed to making a decision on cash return in the near-term,” and said a dividend would likely help the valuation and “could re-rate the stock toward IBM’s multiple range of 12-13x P/E.”

For the 2012 calendar year, most analysts are baking in a new iPad 3 launch — expected sometime in the March-April time frame — as well as the iPhone 5 in late summer. Several are also expecting the launch of an Apple-branded TV later in the year. Apple, per its usual secrecy, has given no details on up-coming products.

“We see the biggest growth opportunity coming from expanding the iPhone’s reach internationally and deeper into the mid-tier,” wrote Ittai Kidron of Oppenheimer. “But there’s good room for iPad growth, more Mac expansion and new markets with smart TVs a clear opportunity.”

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