Final answer:
The accounting branch focused on recording and managing costs for internal use is Cost Accounting, which is crucial for organizational decision-making and control.
Step-by-step explanation:
The branch of accounting that is primarily concerned with recording, classifying, allocating, and reporting current and prospective costs is Cost Accounting. This field is focused on the internal management of costs and how these costs influence decision-making within an organization. It deals with the analysis of variable and fixed costs, direct and indirect costs, and overhead allocation.
Managerial Accounting also deals with these aspects but is broader, encompassing strategic financial planning and control. Financial Accounting is concerned with the preparation of financial statements for external use, and Auditing involves the examination of these financial records to ensure their accuracy and compliance with accounting standards.