Cox kicks of mobile service with money back offer

* Cox promises up to $20 back for unused minutes

* Launching in three markets

* Aiming to win market share.

NEW YORK, Nov 19 (Reuters) - Privately held cable provider Cox Communications is kicking off a mobile phone service in its first three markets with an unusual MoneyBack offer for customers who use less than their plan's allotted minutes.

After a year of testing, Atlanta-based Cox opens its mobile phone service to the public on Friday with an aim to winning customers from AT&T Inc (T.N) and Verizon Communications (VZ.N) - its current competitors in video, home phone and Internet service.

As Verizon and AT&T have entered the pay-television market, Cox and its cable counterparts have been fighting back with telecom services such as wireless. Cable firms Comcast Corp (CMCSA.O) and Time Warner Inc (TWX.N) offer wireless via their Clearwire Corp (CLWR.O) venture with Sprint Nextel (S.N).

The new Cox service, which starts at 450 minutes of talk time a month for $40, is roughly comparable to its competitors.

But unlike its rivals Cox is offering to deduct up to $5 off the next bill for customers who do not use all their 450 minutes in a given month. The pay-back comes at a rate of 5 cents per unused minute and has a $20 a month cap for family plan customers.

"We will take market share. It's a growth opportunity for us," Cox Vice President for Wireless Stephen Bye said. He expects value-minded customers to sign up for bundles of Cox services such as television and Internet with wireless.

The Cox offering is most comparable to one from AT&T, which lets consumers "rollover" or add unused minutes to their allotment for the next month. But consumers "may never use those minutes," Bye said.

Since many U.S. cellphone users are subscribed to family plans, Forrester Research analyst Charles Golvin said Cox may have a hard time winning new customers as it is tougher to move an entire family than a single subscriber.

But he said that the money-back offer may appeal to cash-pinched consumers in the same way that some credit card companies have promised some money back once a customer has spent a certain amount on their credit card.

"I think it will have resonance with consumers much in the same way that credit card offers that pay money back on your purchases are popular," Golvin said. "In today's faltering economy the idea of money being put back in your pocket is highly valued by customers."

Cox said it has opened 25 stores in the three markets where it is offering the service: Hampton Roads, Virginia; Omaha, Nebraska and Orange County, California.

Bye said the company competes more often with AT&T's U-Verse video service than Verizon's FiOS video offer. Verizon offers wireless service through its Verizon Wireless venture with Vodafone Group Plc (VOD.L). (Reporting by Sinead Carew; editing by Leslie Gevirtz)