Apple's new chief executive Tim Cook vowed to stick to Apple's "unique principles and values" as investors marked his first day as successor to founder Steve Jobs by selling shares and marking the company's value down by more than 5%, or about £10bn.

In taking over from Jobs, widely regarded as a genius for giving the world such groundbreaking products as the iPod and iPhone, Cook faces one of the toughest challenges in corporate history as he strives to maintain Apple's position as the world's foremost technology firm. Earlier this month Apple briefly passed the oil behemoth Exxon to become the world's most valuable company just 14 years after flirting with bankruptcy.

In a company-wide email on Thursday, Cook, who has been at Apple for 13 years, told staff: "I want you to be confident that Apple is not going to change. I cherish and celebrate Apple's unique principles and values. Steve built a company and culture that is unlike any other in the world and we are going to stay true to that – it is in our DNA. We are going to continue to make the best products in the world that delight our customers and make our employees incredibly proud of what they do."

The first challenge for Cook's reign will be the expected unveiling of the next versions of the iPhone, widely anticipated within the next six weeks as Apple aims to capitalise on its leadership of the mobile phone industry, where it has risen from nothing to having the largest revenue and profits in just under five years. In the computer market, its small sales have still grown faster than the rest of the Windows-based market for 20 successive quarters. And its iPad tablet still dominates the fast-growing market, despite competition from dozens of rivals using Google's free Android operating system.

Reports said that Jobs spent his final day as chief executive at the Apple campus in Cupertino, California, where he worked a full day, and that he intended to be an "active" chairman of the company.

Although he gave no reason for his departure, announced late on Wednesday, medical observers believe it is linked to the rare neuroendocrine cancer for which he was treated in 2004, and the liver transplant he received in April 2009.

Cook, 50, was until Wednesday the company's chief operating officer, and had been acting CEO since January. He has long been seen as the natural successor.

But even as investors were selling the stock – it later recovered to be down only 1.1% – business analysts were insisting that Cook would have at least two years in which to rely on products that Apple will already have under development.

The departure of Jobs, the visionary who has set out Apple's philosophy for decades – first between 1975 and 1985, and then from 1997 to this year – had been seen by some investors as cause for alarm at the company, which is now more valuable than rivals such as Microsoft, Dell and Intel.

But Gartner Research analyst Michael Gartenberg suggested that customers would continue to be loyal to the brand. Without Jobs, he believes the company's challenge will be the same as it was with him: continuing to find ways to raise the bar with its consumer electronics.

"Yes, this is quite some transition… but it doesn't mean Apple itself will fundamentally change," he said. "Certainly Apple's competition would be foolish to think this is a situation they could somehow capitalise on."

Richard Windsor at Nomura said: "By its own admission, Apple's pipeline is several years long, so if innovation were to stop dead overnight it would still be some time before the effect was felt. That said, the launch of the next iPhone already delayed from the anticipated July launch will be even more important now than it already was. If the hardware is not impressive ... then the company may be seen to be losing momentum."

Richard Gardner at Citigroup advised investors to buy the stock if it drops, saying Jobs had laid a strong foundation, and that he expected it to gain market share for years. "In our view, [Cook] is a tough but well-regarded leader who will continue to hold Apple employees to an extremely high standard of performance," he wrote."

The quiet man with similar goals

Steve Jobs is famous for his temper, while Tim Cook is described as soft-spoken. Jobs is a Californian known for his new age interest in vegetarianism and spirituality, but Cook, who is from Alabama, loves American football. And while Jobs enjoyed rockstar-like fame, the intensely private Cook toiled for years in obscurity, an operations wonk who made the proverbial trains run on time.

But now it may be the things that Cook shares with Jobs that will matter most as he takes over as boss of one of the world's coolest companies. One of those characteristics is said to be sheer competitiveness. "He's not in it for the fame or the ego or the money. He's in it to win," said Greg Petsch, his boss at Compaq Computer during the late 90s.

"The guy is just a phenomenal operating executive," said Mark Briggs, who was Cook's boss at Intelligent Electronics from 1994 to 1997. Briggs remembers a highly analytical executive, focused on metrics, who overhauled the company's supply chain. "He just works all the time, that's his life."

Cook has a strong record as a stand-in. When Jobs was first ill in 2004 Cook took charge and things went so well he was made chief operating officer. In his second stint, Apple's stock rose 62%.

Charles Arthur and agencies