This thesis studies cost estimation and investment decisions under cost uncertainty of large construction projects. The combination of these two topics intends to satisfy the Master’s theses of Civil Engineering at the Delft University of Technology and Quantitative Finance (Econometrics) at the Erasmus University Rotterdam. The first part relates to the Delft University of Technology, the second to the Erasmus University Rotterdam. Both parts are interrelated but can be read separately. Part A develops a model for APM Terminals to estimate costs of new terminals investments. Present-day estimates of APM Terminals insufficiently incorporate risk. Therefore, the study formulates and analyses six (new) estimation models. Differences in the model include the use of error distribution function or the incorporation of interdependency. The analysis subjects the models to various constraints and selects the most appropriate model for APM Terminals. The selected model requires little input information, uses normally distributed error distributions and accounts for shocks. Moreover, the study points out shocks are of great importance in the estimation of costs. Shocks increase expected costs and mainly determine cost uncertainty. The change of estimation model and occurrence of shocks implies that APM Terminals changes its estimation process. The new approach requires an estimate of both expected cost and uncertainty to estimate construction costs. Part B studies investments of projects subjected to cost uncertainty. Prior to construction investors have an idea of the value but not of the costs. Academic research assumes that cost uncertainty is composed of technical and input uncertainty (Pindyck (1993)). Technical uncertainty covers the physical difficulty to complete the project and is only known after completion. Input uncertainty relates to the pricing uncertainty of the required commodities to complete the project and is known beforehand. This study adds shocks to uncertainty because of the significant contribution to uncertainty (Part A). The research argues that shocks are a special form of technical uncertainty. Shocks occur after investing and complicate physical completion. But where technical uncertainty can accelerate construction, shocks solely delay progress. The study uses option theory to examine investments subjected to the different types of uncertainty. The analysis defines optimal investments and shows shocks increase the aversion to invest.