Infrastructure investment as a real options game: the case of European airport expansion

Financial Management (Financial Management Association), Winter, 2003 by Han T.J. Smit

B. Competitive Equilibrium Expansion

For expansion, the players face a value-capture game for flights under exogenous stochastic demand. In each period, the airport management has an option to invest in the next module of expansion if demand is high or to defer investment if demand is low. I assume that investment creates additional capacity [DELTA][Q.sub.i,t], measured in flights per year. The cash-flow value of expansion, [DELTA][V.sub.i,t], is the present value of the incremental cash flow ([DELTA]TC[F.sub.i,t]) from the additional capacity. In standard real option theory, such an option to expand would be analogous to a call option, [C.sub.i], on this added cash-flow value [DELTA][V.sub.i]. The exercise price would be equal to the extra investment outlay, [I.sub.i], required to build additional capacity. In the absence of competitive interaction this results in a (non-linear) call option payoff: [C.sub.i]= Max[[DELTA][V.sub.i] - [I.sub.i,] 0].

However, in an option-game valuation, the incremental value of a lumpy (or indivisible) expansion investment involves competitive interactions. Such interactions introduce a discontinuity in this non-linear option payoff, due to preemptive investment. The capacity depends not only on the evolution of yearly demands in flights (with [Q.sub.M] = [Q.sub.A] [Q.sub.B]), but also on the investment of the competitor. Investment in additional capacity [DELTA][Q.sub.i,t], can be temporarily underutilized until demand has grown sufficiently.

I simplify the analysis by assuming that there are only two rivals. The two airports play a repeated expansion game, where in each period they may expand simultaneously by making a lumpy investment (building on the opportunities generated by their infrastructure).

Figure 1 shows a (two-period) example of the repeated capacity expansion game in an extensive form. The alternative actions by the two airports to make the expansion investment (I) or to defer (D) are shown by squares ([]) along the tree branches.

Figure 1. Two-Period Example of the Expansion GAme (in Extensive Form)

The firm may gain an advantageous strategic position as a result of a better infrastructure (or create such a position by making a strategic infrastructure modification). The market structure is assumed to result in a duopoly, where either of two competing firms (A or B) may invest (I) in additional capacity (using their infrastructure) or defer investment (D). The incremental value of an additional lumpy unit of capacity, [DELTA]V - I, depends on the development of demand ([Q.sub.i]) (u or d) and the investment decision in the previous period by the firm and its competitor (D or I). Starting at the terminal nodes, the valuation of growth opportunities (PVGO) works backwards in time to the top summing the state value creation and taking expectations over the future investment opportunity values. The value of the investment opportunity, C, in each "state of the world", is the outcome of an investment subgame: