A budget is the amount of money that one estimates will be needed to realize a specific task. Every infrastructure project has to be planned and budgeted, often already for the planning and building authorization, or even before you get mandated to do it. Many Masterplans also give a first financial idea of part-projects. The fine budget happens at the time that the mandator asks the builder for an offer. It is then, after eventually discussed and adapted, accepted from both partners. It has to represent the final financial costs, including at best all the potential additional costs. As many mandates are attributed trough an offer appeal, the whole process is a question of not being too high to receive the mandate, and not being too low to be rentable and build a sustainable trail.
For the builder, the goal is to be as congruent as possible with the costs that he is going to have to support. Some parts of the budget are fix (taxes, etc.), some can be fix or not (trips, accommodation, etc.), some can vary. Differences are to be noticed between countries, as in some places you will find, for example, stricter norms for what a builder has to earn for his job.
Site note: As added value of a proper Trailbuilding is not always / everywhere recognized, it is difficult for a small trail builder company to “race against” bigger construction companies with the prize. Those latter have scale economies and, as they often don’t know the job as well, tend to offer less time to do the job and, as the concept of rider experience isn’t central, underestimate a lot of points. For example, it is easier to dig a 50 meters straight line into the terrain, than adapt the trail to it.