It, of course, depends on the minutes produced. I've not heard of anyone charging by the finished minute in 20 years. IMO, you should charge by the hour or by the day. Based on your pre pro meetings, you should know how much time you will ut into it so you could quote a flat price for the finished video up front. I believe that's all the client is wanting in this case... and in most cases for that matter. When they ask how much, they really are looking for a dolalr figure so they can move forward or retreat.
I quoted 5k yesterday for a 24 minute show pilot. This will not be 20 layers of compisites though. It's a reality documentary. One day of shooting, 3 days of post, one day for possible revisions. That was my simple formula to be able to spit out "how 'bout 5 grand?"
Had I not been able to do that, they would have bailed.