Barclays sees several challenges ahead for Vodafone post-Verizon Wireless, not least increasingly tough European mobile trends for the group and how it can make best use of its underleveraged balance sheet. More intriguingly, there is the ongoing press speculation that a bid by AT&T is looming for the UK mobile giant.After considering the potential impact on Vodafone of these challenges, Barclays analyst Maurice Patrick and his team see the balance of risk for the stock skewed to the upside, especially with regards to the AT&T scenario given historical M&A precedents. Patrick notes that Vodafone's European mobile service revenues fell a hefty 7.8% in the third quarter and that the group is underperforming its peers on this front. He anticipates an improvement in underlying trends in 2015, due partly to easier comparatives, but cautions that "fundamentals here remain tough due to challenging macro conditions and competition". Project Spring, Vodafone's ambitious multi-billion pound network investment initiative - much of it aimed at Europe - could help the group not only offer a differentiated product, especially versus smaller rivals, but also enable it to make better use of its under-leveraged balance sheet, according to Patrick. But a bid from AT&T would clearly offer more immediate upside. Barclays currently rates Vodafone at 'overweight' with a price target of 260p. This, however, provides only limited upside on any AT&T bid materialising. A fuller valuation analysis by Patrick applies historical European M&A multiples of 7.2 x EV/EBITDA to Vodafone and suggests a take-out price of around 300p for the group. Midday Vodafone shares were ahead 0.3p to 246.5p - a 22% discount to Barclays 300p take-out estimate. KP