How do I calculate an hourly rate for a Interaction Design/UX Engineer role?

I'm trying to pitch a role on my company's design team by leveraging web animation - something that isn't used much currently. The manager of the team liked what he saw but wants to understand how to budget and price for it by breaking down the costs of building a project to an hourly rate, and how long each project takes in hours.

My question is how would you recommend I assemble this information? So far my searches have returned number that are all over the spectrum. How can I provide an accurate estimate?