Complex economics of simple periodic systems

This paper investigates the financial economics of simple periodic systems. Well-established financial procedures appear to be complicated, and lead to partially biased results. Probability theory is applied, and the focus is on the finances of simple periodic growth processes, in the absence of intermediate divestments. The expected value of the profit rate, derived from accounting measures on an accrual basis, does not depend 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. The internal rate of return, defined through a compounding equation, is path-independent, thereby differing from the expected value of the rate of return on capital. It is shown that within a production estate, the area-average of internal rate of return is not representative of the rate of return on capital. The growth cycle length maximizing the return rate on equity is independent of market interest rate. 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.Author Summary: Economics of periodic growth systems are investigated. In such systems, no time instant is of special importance, and expected values of observables within any period are of interest. The rate of return on capital (RROC), on an accrual basis, differs remarkably from the internal rate of return (IRR) on a cash flow basis. Both differ from the net present value of cash flows (NPV), which further depends on the selection of the “present time”. Suitable period durations do not depend on external interest rates. Leverage effects on RROC are successfully introduced, whereas both IRR and NPV fail to show a meaningful leverage effect.