Abstract:

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.