In my opinion, in all the stages, except closing. The formal appraisal is done before Planning , but you could reject an initiative during any stage. That depends on maturity of the government organization and its processes and the approach. Oil and Gas companies follow an stage-gate process called front-end loading (water-fall kind), with formal rules before a project gets the execution phase.
To accept or reject the project you do the appraisal in the two first phases, I mean initiation and planning, afterwards during execution you apply some methodology to keep the project working, specially in the advancement, the time and the cost
I would agree with Hernan and it really depends on the project management set-up in your company.
The first asessment should be conducted in the initiation phase. There are companies requiring an elaborate business case before making a decision on rejection or acceptance of a project. In some cases it can also be done in the planning phase. You need to keep the effort for performing each phase in mind. If planning already requires a reasonable amount of resources, there should be a solid justification for the project in the initialisation phase already.
Also depending on the context (as well as changes in the context) and the size of the project, it has to be assessed after each stage. This is not very popular in many organisations but projects should be stopped if they got obsolete or the benefit cannot be achieved considering effort to be spent.
The assessment of whether a project is viable is an interative process. At each step except closing, decision are made on going foward and the scope of the project. An initial scope is developed and then priced. Based upon the pricing the project may go foward, be decreased in scope or increased. This process continues as the design develops and the cost are assessed. If the cost or funding change significantly the project scope is evaluated and adjusted including putting it on hold or just designing and not building. Even during construction if cost rise due to claims by a contractor that may be legitimate the scope may be revised. I have experienced all of this and in the worse case been under construction on a multistory building that the owner decided not to finish several floors due to funding.
Assessment of the viability of any given project is an evergreen process that starts from initiation and continues through to close-out. Circumstances can sometimes change quite dramatically, even for a previously feasible project.