Path-dependency and leverage effect on capital return in periodic growth processes

Probability theory is applied to the finances of periodic growth processes. 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 of the 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 area-average of internal rate of return is not representative for the rate of return on capital within an estate. It is shown that the rotation cycle length maximizing the return rate on equity is independent of market interest rate. Correspondingly, from the viewpoint of wealth accumulation, the often-suggested dependency of suitable rotation length on discount rate appears to be a modeling artifact. Leverage effect enters the microeconomics of the growth processes through a separate leverage equation, where the leverage coefficient may reach positive or negative values. The leverage effect on the internal rate of return and the net present value are discussed. Both effects are solvable, resulting in incorrect estimates.