The math is right, and in terms of cost to the budget, if you pay a tax of $12,000 and receive a $12,000 transfer, the net budgetary cost is zero. However, there will be opportunity costs of carrying out the transfer. A small part of the opportunity cost is the administrative cost of collecting and disbursing the money. The more significant part is the potential deadweight loss from the incentive effects of the taxes and transfers. If the package is constructed badly, both the tax to collect the money and the disbursement of the money will have a disincentive effect on earning income. These effects can be minimized if the tax and transfer is structured properly. For example, the work incentive effects of a true universal basic income (not means-tested in any way) are unambiguously more favorable than those of a negative income tax.