Other way around. Right now there exists a negative incentive to go under budget, being that if you need extra budget next year you suddenly don't have a buffer.

The correct way to fix things is to simultaneously prohibiting end-of-FY budget-keeping purchases (e.g. by mandatory reviewing of purchases) while at the same time allocating a company/organization wide buffer for stuff that needs immediate / projected stuff that was not in the planned budget.

Obviously for common routes such as Sf to la, nyc to sf...etc they hard coded values.

for every $1 under the cap you received 50cent to use on a future travel plan over the calculated cap.

You could fly economy on an international flight saving money, then bank 50% of savings to buy a first class ticket some other time.

This created a negative feedback loop keeping travel costs in check.