ABSTRACT
Our purpose in this chapter then is to build momentum, acceleration and stochastic variations in the adaptation value of equity into the equity valuation models developed in previous chapters. We begin our analysis of these issues in the next section by reiterating the fundamental proposition that underpins most of the equity valuation formulae developed in this book; namely, that the present value of the stream of future operating cash flows that a firm expects to earn is given by the sum of the book value of its equity and the present value of its stream of expected abnormal earnings. We then move into the main body of the chapter, where it is assumed that the variables comprising the firm’s investment opportunity set evolve in terms of a second-order system of stochastic differential equations. We can use this assumption to show that the present value of the cash flows that a firm expects to earn
can be stated in terms of both the levels and momentum (or first derivative) of the variables comprising the firm’s investment opportunity set. This provides an analytical justification for the emerging empirical work that documents a significant association between earnings momentum and the market value of the firm’s equity. Moreover, this result generalizes when the investment opportunity set is stated in terms of a higher-order system of stochastic differential equations. As a particular example, we show that if the investment opportunity set evolves in terms of a third-order system of stochastic differential equations then the present value of the cash flows that the firm expects to earn will be stated in terms of the levels, momentum (or first derivative) and acceleration (or second derivative) of the variables comprising the firm’s investment opportunity set.
