What is the purpose of a project charter?

The purpose of a project charter is to formalize project initiation and grant authority. It serves as a foundational document that authorizes the project and provides a clear framework for what the project entails. This document not only defines the project’s objectives and scope but also identifies the key stakeholders and their roles in the project. By establishing the project manager's authority to allocate resources and make project decisions, the charter acts as a crucial reference point throughout the project lifecycle.

While the other options address important aspects of project management, they do not capture the primary function of a project charter. Outlining roles and responsibilities, identifying potential risks, and detailing cost estimates are crucial elements in project planning and execution, but they are typically addressed in different documents, such as the project management plan or risk management plan. The charter's specific role in initiating and legitimizing the project is what makes this option the correct choice.