ABSTRACT
§ 11-1. In §9-5 of Chapter 9, we developed an equity pricing formula based on the clean surplus identity, which, it will be recalled, is an equation that links the increment in the book value of a firm’s equity to the accounting (i.e. book) profit that the firm earns over any given period of time. In particular, clean surplus accounting requires that all profits earned and all losses incurred by a firm are recorded in the firm’s profit and loss account and that increments in the book value of the firm’s equity are composed of the profit (or loss) appearing on the firm’s profit and loss account less any provisions that have been made for the payment of dividends. Here we need to note, however, that there are occasions when accounting standards require firms to exclude certain profits and/or losses from the ‘bottom’ line earnings (i.e. profit or loss) figure reported in their financial statements (e.g. profits and losses on the disposal of fixed assets). This in turn will mean that the increment in the book value of the firm’s equity will not be equal to the earnings figure appearing on the firm’s profit and loss account for the period. Given this, our first brief in this chapter is to generalize the canonical equity pricing formula developed in Chapter 9 to remove its dependence on the clean surplus identity. Our analysis of this issue is based on two dirty surplus propositions. The first of these shows how the recursion value of equity is determined when the clean surplus identity does not hold, that is, when there is a form of dirty surplus accounting. The second proposition outlines how the system of stochastic differential equations that characterize the firm’s investment opportunity set must be modified so as to encompass dirty surplus accounting. Our analysis of this second proposition is based on a multiplicity of determining variables. We do this because it is highly likely that in practice the market value of a firm’s equity will hinge on a large number of determining variables and not just the two (abnormal earnings and the information variable) on which the canonical pricing formula developed in Chapter 9 is based. We then move on to assess the impact that the explicit incorporation of dividend payments into our modelling procedures can have on equity valuation. In common with results reported in the real options literature, our analysis shows that whilst the recursion value of equity does not hinge on the firm’s dividend policy, the adaptation value of equity will in general be affected by the dividend policy invoked by the firm. Against this, our analysis also shows that, for parsimonious dividend payout assumptions (e.g. dividend payments that are proportional to the recursion value of equity), the ‘structure’ of the equity valuation formula is similar (although with some very important differences) to the canonical equity valuation formula developed in Chapter 9.
