Pricing the Idiosyncratic Risk in the Cost of Capital: A Comprehensive Model

Abstract

Despite the mixed evidence, recent empirical works highlight the importance of idiosyncratic risk in the stock market. On this basis, this note elaborates an approach to price directly the specific risk in the cost of capital, both for scientific empirical purposes and practitioner's investment valuation. For extremely high leverage values, the cost of risky debt tends to approximate the unlevered cost of capital. Exploiting a Merton model, we show a simple solution to calculate in practice every cost of capital version, providing a comprehensive framework. A worked example is provided to simplify the concrete application.

Cost of Capital for Private Firms

“…The model presented in this paper recognizes the different risk position for equity in respect of debt financing at the probability of default level, exploiting a framework in line with past studies (Solomon, 1963;Baxter, 1967;Copeland et al, 2005;Turner, 2014;Beltrame et al, 2014;Beltrame & Zorzi, 2022). In addition, we empirically highlight the ability of the model to incorporate both systematic and size premiums.…”

“…As a consequence, the cost of capital determination is just a special case of cost of debt estimation (Beltrame & Zorzi, 2022).…”