Suppose, for instance, that this right lies with a fiscal authority, as has been the case over long stretches of history. The fiscal authority could finance state expenditure by raising taxes; but this would require the establishment of costly administrative structures. It could even finance spending via its printing press.
In a fiat money regime, at the margin, the cost attached to this operation would be close to zero. The benefit, however, would be positive and equal to the value of the new public undertaking multiplied by the opportunity cost of financing the new public function with taxes. The pecuniary value of that benefit to the government issuing money is called seigniorage.