Do you charge for creativity?

I wonder at this. Does one charge for the creative process? Say I am tasked with making something creative. A logo, an icon, a PowerPoint background (shudder). I hem, I haw, I try somethings, I troll the web, I try again, I change the colors, and eventually I come up with an idea.

Do I charge an hourly rate for the time it took me to come up with that idea? That is, for the hem and haw?

Or do I assume that my brilliance is assumed (why I was tasked with this) and build that expectation into my hourly rate?

Or do I charge a flat fee for brilliance? “My creativity is worth $500 per.”

Once the idea is generated, charging for the grunt work of production is a no-brainer. I just don’t know what to do on the front end.

Ideas?