* Sunrise sets IPO price range at 58-78 Sfr per share
* Market capitalisation implied at 2.8-3.3 bln Sfr
* Backer CVC says not in conversations on a trade sale (Recasts, adds quotes, context)
By Oliver Hirt and Freya Berry
ZURICH/LONDON, Jan 27 (Reuters) - Sunrise, Switzerland's second-biggest telecoms operator, expects to be valued at up to 3.3 billion Swiss francs ($3.7 billion) in a stock market debut aimed at paying down debt and stepping up its challenge to bigger rival Swisscom.
Sunrise, which counts Swiss tennis star Roger Federer as an ambassador, on Tuesday set a price range for its initial public offering (IPO) of 58-78 francs per share, giving it an implied market value of 2.8-3.3 billion francs.
The company, backed by European buyout house CVC, has said it wants to raise 1.35 billion francs to cut debt and exploit growth opportunities, in Switzerland's biggest flotation since 2006.
Gripped by a wave of dealmaking, the telecoms sector has seen few new share issues. Europe saw just five telecoms IPOs in 2014 -- only 0.7 percent of the region's total issuance, according to Thomson Reuters data.
Both Sunrise and rival Orange Switzerland have struggled to wrest market share from government-backed Swisscom.
They have toyed with a merger in the past, but the plan was blocked by Swiss competition regulators in 2010. Last year, Orange Switzerland was sold by private equity firm Apax to telecoms tycoon Xavier Niel's NJJ Capital.
"We are a Swiss company and have no intentions for adventures abroad," Sunrise finance chief Andre Krause told reporters on Tuesday. "The big question is whether there is a consolidation opportunity in Switzerland."
Industry sources have said a tie-up could now be viewed more favourably by regulators, as a bigger firm could improve investment and consumer choice in "converged" services that offer both mobile and fixed-line products.
However, CVC partner Lorne Somerville told reporters there were currently no talks on selling Sunrise.
Convergence has become a buzzword recently, with customers increasingly demanding a range of services from a single provider. Last year, British telecoms firm BT entered exclusive talks to buy mobile operator EE to widen its product range.
Swisscom's current market capitalization values it at about 6.2 times its expected 2014 earnings. At the midpoint of its IPO price range, Sunrise would be valued at about 5 times.
Sunrise had earnings before interest, tax, depreciation and amortisation (EBITDA) of 621 million francs in the 12 months to Sept. 14. It is committed to a dividend of at least 135 million francs for 2015, and is planning further payouts once it hits a target of 2.5 times net debt to EBITDA.
Debt will be at 2.7 times immediately following the IPO, with the first day of trading on the SIX Swiss Exchange expected on or before Feb. 6.
$1 = 0.9027 Swiss francs Additional reporting by Alice Baghdjian and Katharina Bart; Editing by David Holmes and Mark Potter