Cost?

What is the charges of designing a website banner similar to this: http://www.igotitcovered.org/ [See banner at the top]

That depends on what the designer charges, obviously, as there is no fixed pricing scheme for design elements.

Why not look for designers’ portfolios and ask them this directly?

Actually, I have not asked any designer yet, I am just figuring out how much it would cost? Any rough idea?

That’s my point, though. It’s not possible to figure it out because how much it costs will depend on who will do it, where that person comes from (or rather where that person lives), how much the designer charges. You might find somebody who’d do it for $100 and you might find someone who does it for $500. There is no way anyone can tell you what to estimate except for the designer you quote for the specific task at hand.