Deutsche Telekom has recouped its investment in Bellevue-based T-Mobile US, with an increase of the unit’s value compensating for a 7.4 billion-euro ($10 billion) writedown in 2012, according to the German company’s CEO.

Timotheus Hoettges made the assessment as Deutsche Telekom once again studies selling its holding in the fourth-largest U.S. carrier.

Since a failed disposal of the business to AT&T in 2011 for $39 billion, Deutsche Telekom has made T-Mobile the country’s fastest-growing wireless provider by merging it with MetroPCS Communications, expanding its network and introducing cheaper and more flexible plans.

“We already have increased the value to what it was at the sale,” Hoettges said Sunday.
“That means with 67 percent of a company that’s worth $42 billion, we’re already back at the value of the AT&T deal.”

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SoftBank seeks to combine its Sprint unit with T-Mobile and is talking with Deutsche Telekom to resolve obstacles to a potential deal, people with knowledge of the matter said. T-Mobile has an equity value of $26 billion and total debt of about $13.6 billion, according to Bloomberg data.

Hoettges declined to comment on any discussions over a potential sale of T-Mobile.

The 51-year-old executive, who succeeded Rene Obermann as Bonn-based Deutsche Telekom’s CEO this month, was personally involved in negotiating the transactions with AT&T and MetroPCS.

Deutsche Telekom wants an all-cash offer for T-Mobile, and SoftBank is trying to finance a deal to provide as much cash as possible, one of the people said.

Merging Sprint and T-Mobile would create a strengthened rival to Verizon Wireless and AT&T, but a deal may face obstacles from regulators concerned about reducing the number of national operators.