In 2015, the World Bank claimed that rich-country private capital could: (i) close the infrastructure services gap in poor countries, (ii) achieve the sustainable development goals, and (iii) make money by moving from "billions to trillions" of investment in poor-country infrastructure. Our framework distinguishes those poor countries in which the Bank's claim is tenable from those where it is not. For a given poor country, the framework reveals that investing a dollar in infrastructure is efficient if the social rate of return on infrastructure clears two hurdles: (a) the social rate of return on private capital in the poor country, and (b) the social rate of return on private capital in rich countries. Applying the framework to the only comprehensive, cross-country dataset of social rates of return on infrastructure indicates that in 1985 just 7 of 53 poor countries cleared the dual hurdles in both paved roads and electricity.