If you think about a grant as 100% loss, that is actually the higher cost. For an SIB as an example, you don't spend anything until the social outcome is achieved. The government spends nothing until you actually see the results. This money that the government spends is actually the savings to the government.
If you reduce welfare rolls, the government is saving money in welfare cheques. You're not paying that in transfer payments. You pay a percentage of what you had saved to the intermediary; it's not a new outlay of capital.