Film & Television Producer. Disney Channel, AMC, ABC, etc. 25 years planning and executing difficult things with big egos. Perpetual student of technology, culture & science. Leader, mentor, strategist, advisor.
I always take the project size into consideration. Also are they new clients or returning? Studios/Networks will usually make an offer based on the scope of the work and size of the project.
Day rates aren't always the best route because you usually won't have a great idea of what it will take until you get into it and it's easy to underbid your time unless you have worked for them before.
Last note. Don't work on the promise of getting paid when the project goes. Often they don't.