I wouldn't go for it. Suppose my budget is Y and I could reduce it to Y/2 and get X%*Y/2 as a bonus. But in subsequent years I would only get a budget of Y/2. With half the budget I can only employ half the staff and be half as important. I don't think it works out.
edit: on the other hand: If I'm going to quit the job next year and I don't like my successor I'm definitely going to cut corners and budget.