Innovative Applications of O.R.Valuing multistage investment projects in the pharmaceutical industry
Introduction
Most capital budgeting problems involve analyzing the tradeoffs between a fixed and certain capital investment and an uncertain stream of future cash flows. On the other hand, a large class of problems, such as the valuation of startup firms, complex industrial and construction ventures, and R&D projects such as software, drugs and technology initiatives, include complications not captured by this simple model. In addition to the uncertainty over the final payoffs of the venture, for this class of problems there is also considerable uncertainty over the cost and timing of the total investment required and over the quality and performance of the final product. The design of an advanced microprocessor chip, the development of a new aircraft, a startup firm or a new drug, for example, all involve investing an uncertain amount of capital and time in order to obtain and to bring to the market a product whose performance characteristics or final quality is uncertain.
Another characteristic of these projects is that by investing, the firm learns about the difficulty of designing and building a new product or of performing research on a new drug, and updates its prospects of a successful development, timely completion and the quality of the final product as it progresses during each development phase. This new information also allows the firm to optimally determine whether to abandon or to continue investing in the project at any time. This gives these projects the characteristics of a contingent claim over the value of the completed project, and we analyze the problem from a real options approach. According to Lo Nigro, Morreale, and Enea (2014), Real Options Analysis is acknowledged as a powerful tool to evaluate uncertain projects that have an intrinsic flexibility. The valuation of multi-staged pharmaceutical R&D ventures, for example, can be interpreted as a chain of nested real options (Cassimon, De Backer, Engelen, Van Wouwe, & Yordanov, 2011), where there is uncertainty of both the true investment costs and the future cash flows the product will generate, as well as managerial flexibility to optimally abandon the development (Managi, Zhang, & Horie, 2016).
These projects are subject to several different types of stochastic cost and demand uncertainties. We model the investment cost as a diffusion process with a negative drift equivalent to the instantaneous rate of investment, in an approach that follows Pindyck (1993), where the firm starts out with an exogenously defined expected cost to completion and updates this expected cost as new information becomes available. There is also uncertainty concerning the changes in the competitive and market environment, both during and after product introduction, that may render the project worthless, such as a preemptive move by a competitor or a technological breakthrough that makes the product obsolete. This is modeled as an exogenous Poisson death process.
We assume the firm has the option to abandon the project continuously at any time during the development process, even before a particular stage is completed. If successfully completed, through additional investment the project provides the firm an opportunity to optimally expand the scope of the project to new market segments that were not originally contemplated, or to derivative products, with the possible extension of patent life. This may involve new uses for the original product or making improvements or modifications that would allow it to be marketed for different uses. As an example, a low power consumption version of a successful cell phone model may expand the original market for this product to include other mobile appliances, or a drug that is targeted to the adult patients may be altered to also be used by children. Obviously, the prerequisite for a profitable expansion is that the development of the original product is successfully completed and that the project has an adequate performance.
Prior to the beginning of the project, the firm specifies a set of performance characteristics the final product is expected to have. This can be the clock speed of a new microprocessor chip design, the operating range of a new aircraft, the maximum sustainable output of a power plant or the effectiveness of a new drug. As the firm invests in the project it also learns about any deviations from the expected performance and updates this information as the project progresses through each stage. We assume that the final product performance is correlated with the deviations from the expected cost and time to completion in each stage. Also, we assume that the project is subject to a finite economic life due to technical obsolescence, increased competition or patent expiration.
We adopt a discrete simulation model to obtain a solution for the value of this more complex multistage investment problem. We first model the more general case of an n-stage investment project subject to several sources of uncertainties and then analyze the case of a three stage drug R&D project in the pharmaceutical industry. We obtain a discrete approximate solution to this application and show the comparative statics.
This paper is organized as follows. In the next section we discuss previous work in this field that is related to our work. In Section 3 we present our basic model, the notation and the valuation equations. In Section 4 we apply the model to value a R&D project in the pharmaceutical industry and show analytical results. In Section 5 we draw our conclusions.
Section snippets
Related work
The valuation of R&D projects as a contingent claim on the value of the completed project has been subject to much interest in the literature. With the increasing complexities related to analyzing uncertainty, R&D decision making has become more difficult for firms seeking to enhance their competitive position and drive their sustainable profitable growth (Song, Di Benedetto, & Nason, 2007). Therefore, real options models can help R&D managers evaluate and determine optimal investment decisions
The model
Consider a multistage investment project where the first R&D stage (1) ends at time t = τ1, the second stage (2) ends at time t = τ2 and the last R&D stage (n) ends at time t = τn. If successfully completed, the project provides the firm with a continuous stream of stochastic cash flows during the subsequent market phase, where t ∈ [τn,τm]. The project is subject to uncertainties concerning the total cost of the investment required to complete each stage, the final quality of the finished
Application: R&D in the pharmaceutical industry
Drugs are a substance or combination of substances presented as having properties for treating or preventing disease in human beings (European Union, 2014). Drugs contain molecules that present biological activity against a targeted disease, and since not all molecules have these properties, the task of the drug maker is to discover which ones are effective against the disease. The development of pharmaceutical drugs has evolved significantly in the last decades and has since become an
Conclusions
The analysis of multistage investment problems is a typical application of real options analysis given the characteristics of a compound option problem. We modeled a R&D investment problem with multiple sources of uncertainty and compound abandon and expansion American options using a simulation approach.
Traditional real options models usually require simplifying assumptions that limit the complexity of the model in order to maintain tractability of the solution. In this sense, the model we
Acknowledgements
The authors wish to thank CNPq Brazil for the support for this article, under grant no 305422/2014-6.
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