Non‐Additivity in Accounting Valuation: Theory and Applications

Abstract

This paper has three objectives. First, to introduce a theoretical solution to the issue of non‐additivity between assets in place, relying on an accounting‐based valuation approach. Second, to explain how such an approach can be implemented empirically by measuring synergies between assets. Third, to present the properties of this non‐additive valuation technique. We use Choquet capacities, that is, non‐additive aggregation operators, to measure the interactions between assets and apply our methodology to a sample of US firms from the capital goods industry. To operationalize our approach we examine the relationships between synergies—captured by Choquet capacities—and the market‐to‐book ratio (proxying for growth options), and show how interactions between assets are consistently linked to a firm’s market‐to‐book ratio. We also measure firm‐specific productive efficiency relative to the industry and firm size. For large firms, efficiency, as defined by our approach, is positively associated with higher future operating cash flows. For small firms, efficiency is positively associated with higher future sales growth. We document that the non‐additive approach appears to be better able to identify expected relationships between efficiency and future performance than a simpler approach based on the market‐to‐book ratio.

Keywords: Choquet capacities, Goodwill, Growth options, Non‐additive accounting‐based valuation, Productive efficiency, Synergies