Price Modeling of Eucalyptus Wood under Different Silvicultural Management for Real Options Approach

Choosing the ideal number of rotations of planted forests under a silvicultural management regime results in uncertainties in the cash flows of forest investment projects. We verified if there is parity in the Eucalyptus wood price modeling through fractional Brownian motion and geometric Brownian motion to incorporate managerial flexibilities into investment projects in planted forests. We use empirical data from three production cycles of forests planted with Eucalyptus grandis × E. urophylla in the projection of discounted cash flows. The Eucalyptus wood price, assumed as uncertainty, was modeled using fractional and geometric Brownian motion. The discrete-time pricing of European options was obtained using the Monte Carlo method. The root mean square error of fractional and geometric Brownian motions was USD 1.4 and USD 2.2, respectively. The real options approach gave the investment projects, with fractional and geometric Brownian motion, an expanded present value of USD 8,157,706 and USD 9,162,202, respectively. Furthermore, in both models, the optimal harvest ages execution was three rotations. Thus, with an indication of overvaluation of 4.9% when assimilating the geometric Brownian motion, there is no parity between stochastic processes, and three production cycles of Eucalyptus planted forests are economically viable.