Buying a site

Not so long ago, I was approached by a representative of one of the major festivals. The audience of this action at the moment in the region of 30,000 people. The purpose of his visit was that they launch a new series of festivals after NG and change a lot both in terms of organization and in terms of the style of festivals. The festival site on this one is something of the 90s. In this connection, they want to refresh the site, update something in terms of design, etc. and etc.
All would be nothing, but like most "customers" they want to get, if not for free, arguing that you owe us for what we have come to you, then for a soooo limited budget. Standardly we send such clever men to similar companies so that people understand how much it costs and what it is, but usually there are different kinds of BUT. In this case, I myself am interested in doing this project, but the proposed budget does not suit me at all. He is not that small, he is actually not at all as such. Therefore, after thinking with my team, it was decided to offer customers to buy the rights to the site because I really see great prospects in it.
Such an idea came at the time of the customer representatives and the most leading core. And again, a different kind of BUT arise. I am ready to take the site completely under my wing, I am ready to update it, to refresh it, to start looking towards possible monetization, BUT, the design of the site uses a logo which is a registered trademark. I can not remove it, otherwise the site will lose its face, just so I can not keep it too. There is an idea to sign an agreement on the use of TM for a certain period, after which it is necessary to think where to steer further. Therefore, I would like to know / ask / consult with the community who thinks about this. Thank you in advance.