The classic funding mechanism that matches best with that model is municipal bond issues, where private funders get to tap into the future revenue stream of the region as a whole and the local government get cash up front to spend on capital investment. Since the government does capture revenue from those positive externalities (via a more robust tax base) it aligns incentives nicely. Not sure why they seem to have gone out of favor to be replaced with public-private-partnership type arrangements, where the private entity gets just profits from tolls or tickets in exchange for fronting some cash.