In this model we provide a theoretical justification for why the functional relationship between earnings and value will be non linear. Moreover in our stylised model we derive a closed form for the relationship and show why earnings response coefficients are lower for firms that are contracting or expanding relative to those firms that are maintaining a steady investment strategy. We extend earlier research which posits a simple convex relationship based upon fixed abandonment values and also generalize research which uses real-options valuation models based upon the assumption that firms only ever exercise one real investment option (and then are committed to that strategy ad infinitum). In particular, since in some empirical settings the special case of `fixed' abandonment will not apply, we show how the form of convexity changes. Secondly, in our model firms are allowed to dynamically change investment strategies, for instance expanding in one period followed by contraction in the subsequent period. Given an objective of deriving comparative statics results for earnings response coefficients, our more flexible dynamic model is able to capture more accurately real investment behaviour than a model in which firms only ever decide to expand or contract once. Our model provides both an alternative rationale for accounting measures having information content and an alternative framework for the empirical specification of tests of `accounting value relevance' based upon finite mixture (regime-switching) distributions.
The model combines discrete and continuous elements. Accounting activity is discrete and in any period that period's revenue is generated by a production function consuming some input and storing remaining units to the next period. Input available for consumption arises from the opening stock of inputs for the period, which may be expanded by additional purchase at a unit price (which is geometric Brownian), or contracted by selling at a discount. The purchase price is not observable except by the management. Embedded options are evaluated using a Cobb-Douglas production; generalizations are available, in particular the fact that: the equity value comprises opening cash, q-re-valued opening stock, current q-income and future q-income.