Customers enter an Apple Store in San Francisco, California

Apple became the first US company to record a stock market valuation above $700bn at the close of trading, prompting its chief executive Tim Cook to say it could overcome the “law of large numbers” and keep growing rapidly.

Shares in the world’s most valuable company closed up 1.9 per cent at $122.02 on Tuesday, giving it a market capitalisation of more than $710bn. Apple is now valued at $300bn more than ExxonMobil, the next most valuable US company, and just exceeds the combined value of Google and Microsoft, its fiercest tech-industry rivals.

Apple can continue to grow at speeds more akin to a start-up than the world’s most valuable company, even after reporting the most profitable quarter on record with a 46 per cent jump in iPhone sales, Mr Cook suggested at the Goldman Sachs technology and internet conference in San Francisco.

“We don’t believe in such laws as laws of large numbers. This is sort of an old dogma that was cooked up by somebody,” he said. “Steve [Jobs, Apple co-founder] did a lot of things for us over many years but one of the things he ingrained in us is that putting limits on your thinking is never good.”

For example, Apple Pay, the iPhone’s mobile-payments service, is growing “much faster” than expected after launching in October, Mr Cook said.

In conversation with Gary Cohn, chief operating officer at Goldman Sachs, Mr Cook said that Apple would not “hoard” its $142bn net cash pile and would announce its latest plans for returning capital to shareholders during its next earnings call in April.

“By and large, my view is for cash that we don’t need, with some level of buffer, we want to give it back,” Mr Cook said. “It may come across that we are but we are not hoarders.”

However, he said that any cash returns would come only after investing in research and development, making acquisitions, expanding its stores and maintaining its infrastructure.

Apple announced an $850m investment to build a 1,300-acre solar-power farm in California that Mr Cook said would provide renewable energy for its new campus, other offices and retail stores in the state.

“We are doing this because it’s right to do,” he said, but added that it would also create “very significant savings” in Apple’s energy costs.

Another area of investment is China, where Mr Cook said Apple was “still kind of not too far from the surface”, suggesting it still had an “enormous opportunity” for growth there.

“There’s such an amazing number of people moving into the middle class, it’s something like I’ve never seen in my lifetime before,” he said.

India holds similar potential but Apple has not put “as much energy” there yet, he said.

However, he dismissed suggestions that Apple should make a cheaper iPhone just to appeal to consumers in emerging markets as “a bunch of bull”.

“People everywhere in this world want a great product. That doesn’t mean every single person in the world can afford one yet, but everyone wants one,” he said.

“We’ve stayed true to that and blocked out the noise of everybody saying you’ve got to do this, you’ve got do that. We’re pretty good at blocking the noise out.”

Apple’s next leg of growth will depend on the success of its Watch, which is scheduled for release in April. Mr Cook dismissed existing smartwatches from the likes of Samsung, Motorola and LG and said that Apple customers would be surprised by the “breadth of what it will do”, from health tracking to communication and apps.

“There are several things that are called smartwatches that are shipping but I’m not sure you could name any,” he told Mr Cohn. “I think you’re going to think ‘Wow, I can’t live without it’.”

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