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* Shares in BT were hit by Brexit vote
* Deutsche Telekom reports rise in German core profit
* Proposes 9 pct hike in dividend for 2016 to 0.60 eur/shr (Adds details on BT stake, fourth quarter, dividend, outlook)
BONN, Germany, March 2 (Reuters) - Deutsche Telekom wrote down the value of its 12 percent stake in Britain's BT by 2.2 billion euros ($2.3 billion), pushing it to a fourth-quarter net loss of 2.12 billion euros from a profit of 946 million euros a year earlier.
Shares in the UK's biggest telecoms provider fell by about a fifth over the course of 2016, hurt by Britain's vote to leave the European Union. The BT stake is now valued at 5.1 billion euros in Deutsche Telekom's books.
Deutsche Telekom reported a 2 percent increase in fourth-quarter adjusted core profit (EBITDA) to 5.26 billion euros on Thursday, driven by its T-Mobile US unit but also lifted by a 3 percent increase in German adjusted EBITDA.
The profit in Germany of 2.14 billion euros was better than the average estimate of 2.12 billion euros in a Reuters poll and represented the first rise in several years, lifted by broadband and stabilising mobile service prices.
Europe's biggest telecoms group by revenue proposed a 9 percent increase in its 2016 dividend to 0.60 euros per share, below the Reuters poll average but equal to the median estimate. Free cash flow also rose by 9 percent over the year.
Deutsche Telekom said 2017 sales should grow by an unspecified amount but consistent with its 1-2 expected average for 2014-16, and adjusted EBITDA should rise by just under 4 percent, with a 12 percent increase in free cash flow.
$1 = 0.9497 euros Reporting by Georgina Prodhan; Editing by Maria Sheahan