A model of investment in projects with uncertain construction time is presented in which both the cash-flows 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.

提出了一个建设时间不确定的项目投资模型，其中完工现金流和建设进度都被建模为扩散。决策者有三个连续的选择：(i) 开始施工，(ii) 在施工期间放弃项目，以及 (ii) 开始运营或完成后放弃。证明了解的存在性及其一些定性性质。引入了马尔可夫链近似以数值近似该解。该模型应用于现实世界的铁路项目，发现它不代表物有所值 (VfM)，并且在未来十年内不太可能这样做。比较静态分析表明，放弃选项的存在可以显着增加项目价值，并可以加快投资。最后，有人认为，常用的收益成本比 (BCR) 不是总结项目 VfM 的适当措施。相反，建议使用价值比率 (VR) 作为替代方案。