Ammonia is increasingly recognized as a potential emission-lean and sustainable energy carrier. Producing fossil-free ammonia from variable renewable energy sources (VRES) through water electrolysis may soon become economically viable. Ammonia is a comparatively cheap and safe medium for hydrogen transport and storage, allowing to cope with the variability of the renewable energy supply in time and space and facilitating the penetration of VRES in the energy systems. Moreover, ammonia features promising properties as a fuel, allowing retrieving stored energy by means of direct combustion or fuel cell use to satisfy heat and power demand during VRES production lows. In particular, its high octane rating makes it suitable for use in spark-ignition (SI) engines, which may be a low-cost, low-complexity, high-reliability solution for local heat and power generation. Power-to-Ammonia-to-Power and Heat (P2A2P+H) could thus be an interesting bridging concept in new energy systems. However, such technologies present a low maturity level and their economic performance is highly uncertain and hard to quantify, thus slowing down their implementation. Therefore, the present work proposes a cost assessment of a grid-assisted P2A2P+H system based on a wind farm, an ammonia production and storage plant and a SI engine generator providing power and heat to a residential district. The optimal system designs are investigated by means of a multi-objective optimization method based on a genetic algorithm. Results show that such systems may be commercially competitive if the grid prices increase, and allow a local energy system to be highly self-sufficient, thus preventing risks of shutdowns associated with increasing shares of VRES. Seasonal storage appears particularly relevant and the ammonia system provides non-negligible amounts of heat to the consumers.