'Budget' is an ugly, harsh word. It implies limitations and constraints, long before any creative process is underway.
For me, it's not so much a case of knowing a clients budget, but rather understanding the 'value' they place on the exercise. By focusing on the 'value' it can help to define and justify a budget.
What makes me affordable is my approach. Budgets vary in size and each brings their own limitations, however, I work closely with my clients to identify how best to allocate their budget, ensure the right value is invested in the right places and that specific goals are achieved.