PMBoK begins with developing a Project Charter, then proceeds with stakeholders identification, collecting requirements, etc.
Below is the excerpts from PMBoK's 4.1 Develop Project Charter:
The project charter establishes a partnership between the performing and requesting organizations. In the case of external projects, a formal contract is typically the preferred way to establish an agreement.
The approved project charter formally initiates the project.
Obviously no sum of money can be agreed in the contract because the requirements are not collected, the scope is not defined, etc. What a formal contract is PMBoK talking about? And which PMBoK process is devoted to signing a contract that specifies scope, time and price?