Real options with synergies: static versus dynamic policies

Abstract

We develop a model for determining whether a firm should exercise two real options individually or simultaneously. The simultaneous exercise of both options has synergy of cost savings, while the separate exercise of each option benefits from project flexibility. This trade-off determines the optimal exercise policy. We compare static and dynamic management of multiple real options. A firm under static management determines the type of exercise of real options ex ante; on the other hand, a firm under dynamic management makes the decision at the time of exercise. We show that highly correlated projects increase the option values under both styles of management because a firm is more likely to enjoy the synergy gains of joint investment. We also highlight the advantage of dynamic management over static management for weakly correlated projects.

Keywords:

• multiple real options
• synergy
• static versus dynamic
• optimal stopping
• exercise region

Acknowledgements

The author like to thank anonymous referees for helpful comments. This work was supported by KAKENHI 20710116 and 22710142.

Notes

1 Another stream of real options development is combined with game theory. Strategic interactions among several firms are investigated in Grenadier (1996), Grenadier (2002), Lambrecht and Perraudin (2003), Nishihara and Shibata (2010), while agency problems in a single firm are investigated in Grenadier and Wang (2005), Mauer and Sarkar (2005), Shibata and Nishihara (2010).

2 Although Trigeorgis (1993) investigates the non-additivity of the value of multiple real options, he does not consider the problem of whether multiple real options are exercised individually or simultaneously. In addition, the analysis is based on a one-dimensional process.

3 If we consider a more specific problem, a proper function may be identified. If it takes a linear function, we can gain the same insights. If it takes a more complex and nonlinear form, the results are ambiguous.

4 For example, Samsung is famous for its managerial capability for more dynamic and rapid decision-making than its rivals such as Sony.

5 For instance, UNIQLO, the Japanese casual wear brand which has already launched operations in China in 2002, Hong Kong and South Korea in 2005, and Singapore in 2009, announced its plans to enter markets in Indonesia, Thailand, and Malaysia within a couple of years.

6 Another approach to strategic interactions is the game-theoretic approach (eg, Grenadier, 1996; Huisman, 2001). For example, Nishihara (2009) investigates a duopoly real options game concerning two projects.

7 An alternative modeling for learning is the filtering approach (eg, Bernardo and Chowdhry, 2002; Décamps et al, 2005). Extending our model to a filtering model will be a difficult but important challenge in future work.

8 These parameter values are similar to Geltner et al (1996) and Detemple (2006). We carried out a lot of computations with varying parameter values and distilled robust results into this section.

9 We make a discretization with 100 time steps per 1 year following a bivariate version of the lattice binomial method (see Boyle, 1988).

10 For technical reasons we define f(x) as the non-negative function. This does not matter because a firm never exercises the option that yields a negative payoff.