We analyze the welfare effects of voucher provision in the DC Opportunity Scholarship Program (OSP), a school voucher program in Washington, DC, that randomly allocated vouchers to students. To do so, we develop new discrete choice tools to show how to use data with random allocation of school vouchers to characterize what we can learn about the welfare benefits of providing a voucher of a given amount, as measured by the average willingness to pay for that voucher, and these benefits net of the costs of providing that voucher. A novel feature of our tools is that they allow specifying the relationship of the demand for the various schools with respect to prices to be entirely nonparametric or to be parameterized in a flexible manner, both of which do not necessarily imply that the welfare parameters are point identified. Applying our tools to the OSP data, we find that provision of the status-quo as well as a wide range of counterfactual voucher amounts has a positive net average benefit. We find these positive results arise due to the presence of many low-tuition schools in the program, removing these schools from the program can result in a negative net average benefit.