The deal — one of the biggest of the year — would give the Japanese company control of a firm whose chip designs can be found in most of the world’s mobile gadgets, from iPhones and drones to a growing array of smart devices and appliances for the home.

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When Masayoshi Son, the billionaire Japanese technology investor, solidified his control over his SoftBank internet conglomerate last month, he told shareholders he still wanted to “work on a few more crazy ideas.”

One of those ideas materialized Monday, when SoftBank unveiled an audacious $32 billion deal to acquire ARM Holdings, the British semiconductor designer. The deal — one of the biggest of the year — would give the Japanese company control of a firm whose chip designs can be found in most of the world’s mobile gadgets, from iPhones and drones to a growing array of smart devices and appliances for the home.

The deal is the first major cross-border transaction in Britain since it voted to exit the European Union last month. Worries over the impact to the British economy have weakened the value of the country’s currency and made it cheaper for foreign companies like SoftBank to hunt for deals there. Compared with this same time in 2015, for example, pound-denominated assets are 30 percent cheaper for buyers holding yen.

For SoftBank, the deal signals another reinvention, this time with a major bet on a future filled with interconnected devices. While major technology companies see a future in smart thermostats and toasters, the technology has not yet become widely available. At the same time, global sales of smartphones have slowed, showing the mobile future has limits.

“ARM and SoftBank have an overlap on how we see the future,” Simon A. Segars, ARM’s chief executive, said in an interview. But he left the door open for another offer. “Now that the offer is in the public domain, if anyone wants to make a counteroffer, they are more than welcome to do so,” he said. “There’s always a possibility of someone counterbidding.”

British leaders, under pressure to address global worries about the country’s future outside the European Union, portrayed the deal as an endorsement. SoftBank’s “decision confirms that Britain remains one of the most attractive destinations globally for investors to create jobs and wealth,” Philip Hammond, the new chancellor of the Exchequer, said in a statement.

Son said he was a “strong believer in the U.K.”

The deal is the third-largest proposed corporate merger this year, behind Bayer’s offer for Monsanto and a Chinese state-owned company’s proposal for Syngenta, according to the deal-tracking firm Dealogic. If completed, it would also be the second-largest chip deal on record, after Avago Technologies’ $37 billion deal for Broadcom.

SoftBank already has ties to ARM through Sprint, the U.S. wireless carrier that it controls. Son said he first spoke with ARM’s chairman about two weeks ago regarding a possible takeover, and added that the deal came together quickly. The two sides eventually agreed to a price — more than 70 times ARM’s net earnings in 2015. The deal is expected to close in November.

Son described the deal as a bet on the “internet of things,” a new stage in the evolution of network technology, when cars, buildings and household items may be connected through embedded electronics.

Started in 1990 as a spinoff from Acorn Computers, a now-defunct British computer maker, ARM has gone from a small startup of fewer than 20 people to a global leader whose technology is used in more than 90 percent of smartphones produced by Apple and Samsung, among others.

ARM took an early lead on chips for mobile devices, while the growing popularity of smartphones and tablets has been more challenging to traditional chip makers like Intel.

Unlike Intel, ARM forgoes the high margins — and equally high production costs — of directly manufacturing microchips. Instead, its engineers design chips, which are then licensed to larger technology companies like Qualcomm that pay ARM fees and royalties for manufacturing the chips.