Path-dependency of capital return in periodic growth processes

Periodic growth processes are investigated. The expected value of the profit rate, on accrual basis, does not directly depend on divestments, neither on the capitalization path. The expected value of capitalization is path dependent. Because of the path-dependent capitalization, the return rate on capital is path-dependent, and the time-average return rate on capital differs from the expected-value return rate on capital for the growth cycle. In the absence of intermediate divestments, the internal rate of return is path-independent, thereby differing from the expected value of the rate of return on capital. It is shown that the rotation cycle length maximizing the return rate on equity is independent of market interest rate. Leveraging effect enters the microeconomics of the growth processes through a separate leveraging equation, where the leverage coefficient may reach positive or negative values. Correspondingly, from the viewpoint of wealth accumulation, the often-suggested dependency of suitable rotation length on discount rate appears to be a modeling artifact. In other words, the net present value computation is based on maximization of consumption utility, instead of a capital growth objective; borrowing is obligatory, but the leverage effect is absent.