On the estimation of cost of capital and its reliability

Gordon and Shapiro (1956 Management Sci. 10 102–10) first equated the price of a share with the present value of future dividends and derived the well known relationship. Since then, there have been many improvements on the theory. For example, Thompson (1985 Managerial Decis. Economics 6 132–40, 1987 Managerial Decis. Economics 8 321–32) combined the ‘dividend yield plus growth’ method with Box–Jenkins time series analysis of past dividend experience to estimate the cost of capital and its ‘reliability’ for individual firms. Thompson and Wong (1991 Managerial Decis. Economics 12 27–42, 1996 Eng. Economist 41 123–47) proved the existence and uniqueness of the cost of capital and provided a formula to estimate both the cost of capital and its reliability. However, their approaches cannot be used if the ‘reliability’ does not exist or if there are multiple solutions for the ‘reliability’. In this paper, we extend their theory by proving the existence and uniqueness of this reliability. In addition, we propose estimators for the reliability and prove that the estimators converge to a true parameter. The estimation approach is further simplified, hence rendering computation easier. In addition, the properties of the cost of capital and its reliability will be analysed with illustrations of several commonly used Box–Jenkins models.