Time Warner Inc's board, in rejecting 21st Century Fox Inc's $80 billion bid, insisted the offer undervalued the media conglomerate and raised fears about the dominating role that Rupert Murdoch's family would play, a person close to the situation said on Wednesday. The board worried about the future value of Fox's shares, which represented 60 percent of the cash-and-stock proposal. Those fears were magnified by the lack of voting rights that would come with the shares, the source said, as that would concentrate too much power in the hands of Murdoch and his sons.