Accurate forward budgeting and subsequent cost containment, as well as achieving and proving value for money, are generally high on a clients' priority list.
The Cost Consultant's role is basically to estimate the cost of a Brief then derive value for money on behalf of the client during the various phases of the project, ultimately containing overall outturn costs. They also provide an independent audit trail for the client's records or to act as justification to others (maybe seniors) within the organisation.
Initial cost appraisals are carried out pre-design phase, based upon the client's description of desired outcome and the consultants detailed knowledge of realistic pricing levels. This can start an iterative process whereby the client may tweak back their plans once they realise the likely expenditure (or vice-versa)
Budgets naturally evolve throughout the life of the project set-up phase, developing in detail and accuracy as more information becomes available and client decisions are made about the nature of the project/ design specifications. However it is always advisable that as many decisions as possible are made up front so that the Brief and Budget may become frozen prior to commitment to a contractor.