Apple is now worth more than $700bn

Apple’s market cap surpassed $700bn (£447bn) for the first time when the Nasdaq opened for trading on Tuesday morning, as shares in the company opened slightly higher at $119.07.

The record valuation follows the rise in Apple’s share price above $118 for the first time on Monday, a 1.85pc increase from Friday’s closing price.

Several investors said last week that they expect Apple to continue gaining in value.

Speaking at the Reuters Global Investment Outlook Summit in New York, Michael Corcelli, head of the Miami-based fund Alexander Alternative Capital, said he "absolutely, without a doubt" expects Apple's market cap to reach $1 trillion next year.

At the same event, the activist investor Carl Icahn, who owns more than 50m shares in Apple, said the company is still undervalued.

A record fourth quarter helped boost Apple's shares in mid-October after they had been hovering around the $100 mark since the summer.

Apple shipped 39.27m smartphones in the fourth quarter, compared to 33.79m in the same period last year, helping drive profits up 13pc to $8.47bn. Chief executive Tim Cook said demand for the iPhone 6 was "off the charts" and that 2014 would be "one for the record books".

The company expects to sell more products in the Christmas quarter this year than it did in the whole of 2010.

Apple first became the most valuable publicy traded company in the world in August 2011, overtaking Exxon when its market cap dropped to $337.2bn but the energy giant’s fell more, to $330.8bn.

The two business have tousled for top spot since, with Apple again emerging victorious in August 2013 when falling oil prices and weak earnings weighed on Exxon and allowed Apple’s 14pc surge in July to take the Cupertino-based company to number one.

Exxon’s current market cap is $404.3bn, compared to Apple’s $702.2bn. Microsoft, the third most valuable publicly traded company in the world after briefling taking second place earlier this month, is worth $394.8bn. Google's valuation is $370bn, while Berkshire Hathaway, in fifth place, is worth $363.6bn.

In mid-November, Apple's market cap surpassed the value of all Russian public companies for the first time in history.