There is a lot of savings in its low administration costs. Since it would replace a number of social programs that have high administration costs, a UBI actually saves money.

There can be additional cost savings in UBI (and even in existing social programs) if it is structured to incentivise people to work. Many existing social programs actually disincentivise people from working because they lose the income from the social program if they work (too much) and it results in a net loss for them, so they don't bother working.

If a social program is structured so that people don't lose all of their social program income when they work, then they realize a net gain in their income and they continue working. The longer they continue working, the more likely it is that they will gain experience allowing them to make more income on their own, resulting in a further reduction of their social program income.

A very simplistic example would be to remove 50 cents for every dollar they make at their job. If they received $500/month when not working, by the time they're making $1000/month at their job, they're receiving no social program income anymore.