We consider a repeated contract game between a sponsor (principal) and a contractor (agent) concerning a large scale project, where the project requires a number of tasks to be completed before the benefit from the project can be realized. There is cost uncertainty and the contractor has private, task specific information which is relevant in cost determination. Thus, the sponsor must resolve an adverse selection problem in designing the remuneration scheme offered to the contractor. We focus on the case where the sponsor cannot precommit to compensation per task and where the contractor is not bound to complete the project. We demonstrate that the contractor does not achieve cost minimization in equilibrium and that both the distribution of cost per task, given that the task is completed, and the compensation scheme rise as the project nears completion, giving the appearance of cost overruns towards the tail end of the project. We also consider the possibility of project delay as an alternative screening device.