Valuing the profitability of investment projects plays an important role in the decision-making process. This fact is more evident for investment decisions that are made sequentially, and in a particular order. In this paper we focus on one specific kind of two-stage sequential investments — a compound option to expand. As a result of the real options approach, the project/option values are governed by partial differential equations with two variables, namely, the time and the underlying output price, which is given by a relevant stochastic process. Since the flexibility embedded in the investment project considered is analogous to a call on call option, common pricing techniques from financial engineering can be easily used to solve the governing equations. Therefore, to improve the numerical valuation we solve the corresponding equations by a discontinuous Galerkin approach with a semi-implicit time stepping scheme. We proceed backwards to find the value of the compound option, from the value of the completed project through the value of the option to expand in the second stage to the value of the option to expand in the first stage. Finally, the numerical results obtained are compared within the reference benchmark.

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