Decision-making in sequential projects: expected time-to-build and probability of failure

The main purpose of this paper is to account for the two most basic options in the context of a sequential investment project, the option to adjust investment speed and the exit option. Current models of sequential investment ignore the role of a minimal investment rate that must be sustained as long as the project is not abandoned. In most real projects, a positive minimal investment rate provides an incentive for (irreversible) exit from the project. On the other hand, the minimal investment rate still leaves room for adjustment of the investment speed. Therefore, models with realistic (non-extreme) assumptions about the minimal investment should account for both, the exit option and the option to adjust investment speed. In this paper we set up the equations for this dual-option scenario in a continuous (PDE) framework. The resulting model is characterized by the presence of two thresholds describing the optimal decision-making. We provide a robust numerical procedure for the determination of both thresholds. Our analysis reveals that the minimal investment rate creates an endogenous incentive for fast completion that complements the corresponding exogenous incentives. This ??incentive-enhancement effect?? of the minimal investment rate is reflected by the fundamental statistical characteristics of the sequential project. As a direct consequence of this effect, an increase of the minimal investment rate will always lead to a reduction of the expected time-to-build. Another, striking consequence is that the minimal investment rate can also have a positive effect on the probability of failure (default-risk). This effect occurs under the condition of a low exogenous incentive for fast completion, represented e.g. by poor market expectations for the product to be developed.