Reduction of valuation risk by Kalman filtering in business valuation models

A recursive free cash flow model (FCFF) is proposed to determine the corporate value of a company in an efficient market in which new market and company-specific information is modelled by additive white noise. The stochastic equations of the FCFF model are solved explicitly to obtain the average corporate value and valuation risk. It is pointed out that valuation risk can be reduced significantly by implementing a conventional two-step Kalman filter in the recursive FCFF model, thus improving its predictive power. Systematic errors of the Kalman filter, caused by intermediate changes in risk and hence in the weighted average cost of capital (WACC), are detected by measuring the residuals. By including an additional adjustment step in the conventional Kalman filtering algorithm, it is shown that systematic errors can be eliminated by recursively adjusting the WACC. The performance of the three-step adaptive Kalman filter is tested by Monte Carlo simulation which demonstrates the reliability and robustness against systematic errors. It is also proved that the conventional and adaptive Kalman filtering algorithms can be implemented into other valuation models such as the economic value added model (EVA) and free cash flow to equity model (FCFE).