A Real-World Way to Manage Real Options^{5}
Suppose a firm is considering building a new chemical plant. Permits and preparation for the plant cost $60 million. At the end of year 1, the firm has the right to invest $400 million on the design phase. Upon completion of the design, the firm has another right to invest $800 million in building the plant over the next two years. The firm’s risk-adjusted discount rate is 10.83%. If the plant existed today, its market value would be $1 billion. The volatility of the plant’s value (\sigma) is 18.23%. The risk-free interest rate is known to be 8%. Determine the NPW of the project, the option values at each stage of the decision point, and the combined-option value of the project.
Strategy: Note that there are three investment phases: the permit-and-preparation phase (phase 0), which provides an option to invest in the design phase; (2) the design phase (phase 1), which provides the option to invest in plant construction; and (3) the construction phase (phase 2). Each phase depends upon a decision made during the previous phase. Therefore, investing in phase 2 is contingent upon investing in phase 1, which in turn is contingent upon the results of phase 0. The first task at hand is to develop an event tree or a binomial lattice tree to see how the project’s value changes over time. We need two parameters: upward movement u and downward movement d. Since the time unit is one year, \Delta t = 1; and since \sigma = 0.1823, we compute u and d as
u = e^{\sigma \sqrt{\Delta t} } = e^{0.1823\sqrt{1} } = 1.2
d = \frac{1}{u} = 0.833
The lattice evolution of the underlying project value will look like the event tree shown in Figure 13.28.
