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Even if you find yourself in an environment where it is not expected that you develop a project budget (instead you are asked to primarily manage schedule and scope), I strongly encourage you to do two things:
Do it anyway— Develop a project budget anyway. This exercise builds your project management skills, enables you to recognize project performance issues sooner, and better prepares you for senior management discussions about your project.
Follow the money— You should have determined this as part of project definition, but just in case you haven’t, make sure you are totally clear on who is financially sponsoring the project and who controls any financial-based decisions to be made about your project. This awareness is key in your efforts to manage expectations and to understand the political aspects of your project.