We consider the case of scheduling a project under the threat of a catastrophic disruption where the likelihood and timing of the disruption are independent of the project schedule and if the disruption occurs, the project is completely canceled. In such scenarios, there is high managerial interest to know the maximum investment at risk at any time during project execution. This can be answered using the alphorn of uncertainty which maps the maximum and minimum possible project costs during project execution when activity durations and, correspondingly, cash flows are random. We prove the NP-hardness of calculating the alphorn of uncertainty and provide a mixed integer linear program for calculating it. The mixed integer linear program is shown to be able to calculate the alphorn for projects with up to 145 activities efficiently. We also show that using railway scheduling as opposed to roadrunner scheduling can significantly reduce the maximum possible investment at risk without significantly delaying the project.