It does not matter if they have a promotion like BOGO, if the rebrand cost $3m and they create an incremental $73 per game and get 1,000 people (that otherwise would not have bought season tickets) for 1 season, than the rebrand is paid for. The fact that those people would have free tickets the next season is irrelevant to the ROI because the ROI will have already been achieved.
Not going to argue with you over how many extra season ticket holders a name change would generate because neither of us know.
The baseline for most businesses to see an ROI for a project is 5 years. If the Bobcats used 5 years, they would only need to generate 200 incremental fans per season that avg. Spending $73 per game to break even(not factoring the time value of money or NPV or discounted cash flows) 200 fans over 5 years, please don't tell me you think that's a stretch as my family represents 2% of that total.
Again, none of that factors in any incremental revenue from merchandising.
You can argue that the team shouldn't do it for any reason you want and I respect your opinion. However, I analyze and am responsible for approving capital projects for a living and a 1 or 2 year return is a slam dunk yes every time.
They may choose not to do it but, i cant fathom it would be for economic reasons that stopped them.( if 3 million is indeed the total rebrand costs)