The Valuation of R&D Projects with on Option to Expand

We model a multistage finite life investment problem subject to several sources of cost and price uncertainty, as typical of start up firms, complex industrial and construction initiatives and research and development projects for software, drugs and technology ventures. Additionally, the firm also has an option to expand the original project to take advantage of derivative investment opportunities once all the development stages are successfully completed, which is modeled as an American style option. An important characteristic of these initiatives is that as the firm incurs cost and invests, it learns both about the difficulty of developing and implementing the project and also about market conditions, and updates its prospects of timely completion and of expansion accordingly. This information can then be used to optimally decide whether further investments is warranted or not, given the expected future revenues of the whole venture.