In participatory budgeting the stakeholders collectively decide which projects from a set of proposed projects should be implemented. This decision underlies both time and monetary constraints. In reality it is often impossible to figure out the exact cost of each project in advance, it is only known after a project is finished. To reduce risk, one can implement projects one after the other to be able to react to higher costs of a previous project. However, this will increase execution time drastically. We generalize existing frameworks to capture this setting, study desirable properties of algorithms for this problem, and show that some desirable properties are incompatible. Then we present and analyze algorithms that trade-off desirable properties.