ABSTRACT
§ 12-1. In previous chapters, we have developed equity pricing formulae based on the assumption that that there are two complementary aspects to the valuation of a firm’s equity. The first of these is determined by discounting the stream of expected future operating cash flows, or equivalently the dividends that the firm expects to pay, under the assumption that the firm will apply its existing investment opportunity set indefinitely into the future. This is usually referred to as the ‘recursion value’ of equity. The second component of equity value arises out of the fact that the firm will normally have the option to change or modify its investment opportunity set in order that it can use its resources in alternative and potentially more profitable ways. There are a variety of ways in which the firm can exercise this option to change its investment opportunity set, including liquidations, sell-offs, spin-offs, divestitures, CEO changes, mergers, takeovers, bankruptcies, restructurings and new capital investments. The potential to make changes like these gives rise to what is known as the ‘adaptation value’ of equity. Earlier chapters have assumed that if the recursion value falls away to nothing then the firm will be able to exchange its current investment opportunity set for a suite of assets and/or capital projects that have an inter-temporally known and constant adaptation value. However, it is highly likely that the adaptation value of equity will mirror recursion value in evolving stochastically through time. Unfortunately, the equity pricing formulae developed in previous chapters do not fully take account of the valuation implications arising from stochastic variations in the adaptation value of equity. Moreover, our analysis in earlier chapters also assumed that a firm’s cash flows evolve through an investment opportunity set defined in terms of a first-order system of stochastic differential equations. However, there is mounting empirical evidence showing that the momentum and acceleration (i.e. the first and second derivatives) of the variables comprising the firm’s investment opportunity set can also have a significant impact on the market value of a firm’s equity. Unfortunately, when an investment opportunity set is defined in terms of a first-order system of stochastic differential equations, it cannot take account of these momentum and acceleration phenomena.
