The German support for renewable energies in the electricity sector is based on the feed-in tariff for investors that grants guaranteed revenues for their renewable energy supply. Corresponding to differences of granted tariffs and respective market values, a surcharge on consumption covers differential costs. While granted tariffs are bound to fall with advances in renewable energy technologies, the market design and the flexibility of the system influence the expected market values of renewables and the necessary surcharge. We apply the European electricity market equilibrium model EMELIE-ESY to investigate this relationship. We find a crucial dependence of market values of renewables on a high system flexibility and the current so-called energy-only market design. Under these conditions, the market values of renewables sequentially recover with increasing market prices by 2024 and 2034. This allows to limit the increase of the core surcharge to below a quarter of its 2013 value by 2024 despite a doubling of renewables, and to introduce substantial surcharge reductions through 2034. However, the introduction of a capacity market would erode market values of renewable energies and induce a pronounced growth of the core surcharge. Under inflexible supply structures and a capacity market, we find an increase of the core surcharge of more than 50 percent by 2024, a respective loss of the market value of wind power of the same magnitude, and an increase of the generation induced part of the consumer prices of more than a quarter.