Commercial projects are undertaken with the expectation of maximizing financial returns. There are a variety of cash flow models in the literature in which payments, whose amounts depend on the type of contract quoted between the contractor and the client, are tied to the project events or to the completion times of activities. These models are of deterministic nature with respect to cash inflows, that is, the amount and timing of the payments, once determined, are fixed. However, there are situations specifically in the housing industry where the contractor is the owner of the project. In this case, the contractor starts with an initial capital to cover the activity expenditures and then, capital is augmented by the sale of flats which take place randomly over the progress of the project. In this risky environment, the contractor has to decide on the rate of expenditure at each decision time in order to maintain a positive cash balance. Hence, activities are represented by multiple performing modes with different activity durations and the same total cost. A heuristic to construct and re-construct schedules during the progress of the project is proposed here with the aim of maximizing the project Net Present Value while completing the project on time. The heuristic incorporates dynamic mode selection criteria which change adaptively according to the current status of the project. Computational experiments with the heuristic demonstrates that it provides satisfactory results regarding the feasibility of the schedules with respect to the project due date and the nonrenewable resource constraints.