ABSTRACT
§10-1. Previous analysis (as in Chapter 9) shows that adaptation options can play a significant role in the valuation of a firm’s equity. If a firm has the option of abandoning poorly performing capital projects, it can increase the market value of its equity well beyond the traditional benchmark as given by the expected present value of its future cash flows under its existing investment opportunity set. Moreover, one can use the fact that the market value of a firm’s equity is the sum of its recursion value and its adaptation value to show that there will be a highly convex and non-linear relationship between the market value of the firm’s equity on the one hand and the variables comprising its investment opportunity set on the other. Given this, it is somewhat surprising that both empirical and analytical work on the relationship between equity value and its determining variables continues to be based on models that establish the value of a firm’s equity exclusively in terms of the present value of its future cash flows, since this ignores the adaptation option effects associated with the firm’s ability to modify or even abandon its existing investment opportunity set. Hence, in the present chapter, our first task is to use the equity valuation procedures developed in Chapter 9 to determine the likely form and magnitude of the biases that arise when researchers assume that the market value of a firm’s equity is composed exclusively of its recursion value and therefore is linear in its determining variables. We analyse the biases that arise from assuming that the market value of a firm’s equity is composed exclusively of its recursion value by employing an orthogonal polynomial fitting procedure for identifying the relative contribution that the linear and non-linear components of the relationship between equity value and its determining variables make towards overall equity value. The evidence from this procedure is that the non-linearities in equity valuation can be large and significant, particularly for firms where the recursion value of equity is comparatively small. Moreover, empirical work conducted in the area is invariably based on market and/or accounting (book) variables that have been scaled or deflated in order to facilitate comparisons between firms of different size. Given this, it is important that one appreciates how these deflation procedures might alter or even distort the underlying levels relationships that exist between the market value of equity and its determining variables. In particular, our analysis of this issue shows that deflating data before regression procedures are applied can lead to a form of spurious correlation between the regression variables. This in turn can lead a researcher to the conclusion that a non-trivial relationship exists between the regression variables when in fact the data on which the regression analysis is based are completely unrelated. Examples of spurious correlations arising out of the deflation procedures demonstrated here are not difficult to find in the literature and several illustrations are provided in the later sections of this chapter.
