State-space approach to capital return in nonlinear growth processes

Abstract

Purpose We introduce a capital return rate function for growth processes, and apply it to financial sustainability considerations in growing multiannual plants. Design A partition function of change rate of capitalization is introduced, as well as that of capitalization itself, and the expected value of capital return rate is produced as the ratio of the two functions. Findings Financial sustainability significantly differs from maximum-yield sustainability, and does not depend on any external interest rate. Research Implications It is proposed that financial considerations should not be based on any arbitrary external interest. Neither should the shape of any yield function be neglected. Constancy of capital return rate in time is not assumed. Practical Implications Two forestry examples show that the capital return rate is sensitive to rotation time, and in particular to the level of initial investment. The proposed procedure can be applied in the absence of periodic boundary conditions in time. Originality The methodology has not been applied in this field previously.