A fuzzy-based approach to residual income equity valuation

Abstract

The decision of whether to buy, hold or sell equities depends on whether the current price reflects the stock’s intrinsic or fundamental value. The residual income valuation model expresses this fundamental value as a function of current book value of equity plus the sum of discounted expected residual income. Although past and present income and book value information is readily available to investors, values taken by essential parameters in this model are unknown ex ante, particularly the cost of equity or discount rate and future residual income. Any point estimate of equities’ fundamental value according to the model may therefore conceal considerable variation around the estimate, even in the presence of minor perturbations in the model’s inputs. In this paper, we introduce a fuzzy-based approach which reflects the imprecision inherent in certain parameters in equity valuation. We extend the limited prior fuzzy-based literature on investment analysis by introducing the concept of fuzzy fundamental equity value, initially on an illustrative example. To further demonstrate this fuzzy representation, illustrative financial statement data for individual UK companies are considered, with fuzzy fundamental equity values evaluated over progressive forecast horizons. Our series of illustrative applications (which encompasses the standard crisp approach) make the inherent uncertainty involved in estimating equity value immediately apparent.