A model of investment in projects with uncertain construction time is presented in which both the cashflows upon completion and construction progress are modeled as diffusions. The decision maker has three sequential options: (i) to start construction, (ii) to abandon the project during construction, and (ii) to start operations or abandon after completion. Existence of a solution and some of its qualitative properties are proved. A Markov-chain approximation is used to numerically approximate the solution is introduced. The model is applied to a real-world railway project for which it is found that it does not represent value for money (VfM) and is unlikely to do so in the next decade. A comparative statics analysis reveals that the presence of an abandonment option can increase project value substantially and can speed up investment. Finally, it is argued that the commonly-used benefit-to-cost ratio (BCR) is not an appropriate measure to summarize a project’s VfM. Instead, the value ratio (VR) is suggested as an alternative.