We consider firms with privately-known production efficiencies, captured in their cost structure, bidding for a road concession agreement with a government seeking to maximize the expected public welfare generated by the project. The setting is motivated by the increasing trend in road privatization around the world, and the need to design auctions leading to efficient outcomes: firm selection, government payments, toll and capacity schedules, which determine public welfare and firm profits.In this paper, we characterize optimal direct revelation mechanisms for cases with and without restrictions on government payments. Because, in practice, it may be difficult or unappealing for firms to reveal their cost structure, we derive a scoring function that allows for the implementation of the optimal mechanism as a first-score auction where bids consist of toll, capacity, and government payment levels. The function accounts for distortions stemming from firms’ incentives to exploit their private information. We use the results to benchmark the performance of simple, but sub-optimal mechanisms: (i) predetermined toll and capacity bidding, (ii) auctions where the public welfare function is used to score bids, and (iii) a demand pricing mechanism aimed at maximizing patronage.