ABSTRACT
Our analysis to date assumes that thefirm is constrained to apply its existing investment opportunity set indefinitely into the future. We have previously noted, however, that firms will normally have the option of changing or modifying their investment opportunity sets in order to use the resources available to them in alternative and potentially more profitable ways. There are a variety of ways in which firms can exercise the option to change their investment opportunity sets, including liquidations, sell-offs, spin-offs, divestitures, CEO changes, mergers, takeovers, bankruptcies, restructurings and new capital investments. We have also previously noted (as in §9-1 above) that the potential to make changes like these gives rise to a second element of equity value, which is known as the adaptation value of equity. We now demonstrate the procedures that are used to determine the adaptation value of a firm’s equity. We begin by defining P(η(t)) to be the market value of the firm’s equity at time t in terms of its recursion value η(t). It will be recalled from §9-5 above that the recursion value of the firm’s equity at time t is given by
η(t) = b(t)+ (r − c22)a(t) (r − c11)(r − c22)− c12c21 +
c12ν(t)
(r − c11)(r − c22)− c12c21 where b(t) is the book value of the firm’s equity, a(t) is the abnormal earnings associated with the firm’s equity and ν(t) is an information variable that captures all the information that is relevant to the value of the firm’s equity but that has not, as yet, been incorporated into the firm’s accounting records. Moreover, r is the cost of equity capital and c11, c12, c21 and c22 are the structural coefficients associated with the firm’s investment opportunity set.
