Everyone has a different hourly rate, or a different way of billing. *Link to billing styles blog*
Some bill by the hour, the project, the value or the outcome.
I have had in the past where clients compare what their experiences have been with other designers and placed that expectation on me. I am not them.
Tell me if you have heard this: “Oh, the last designer did it for $x, can you match that?”. Unless you really need the job, you can say no. That last designer may have undercharged and regrets it or has passed on it because it had scope creep or a difficult client with unrealistic expectations. You don’t want to start off a relationship feeling undervalued, so set that expectation for both yourself and the client.