The Implied Private Company Pricing Line (IPCPL): On the Nature, Scope, and Assumptions of IPCPL Theory

Abstract

The Implied Private Company Pricing Line (IPCPL) was introduced to the business valuation literature by Dohmeyer, Burkert, and Butler (2013) and Dohmeyer and Butler (2012) as a means of using public equity market data to estimate the (fair market) value of small- and medium-sized privately-held enterprises. The IPCPL is based on the fundamental assumption that no arbitrage opportunities exist, between privately-held and publicly-held equity. This is the fundamental assumption underlying modern asset pricing theory. Although Dohmeyer, Burkert, and Butler (2013) present a detailed general discussion and example of applying their IPCPL model, a formal theoretical development and reconciliation of their model to existing asset pricing theory does not exist in the literature. We (i) present a formal development of IPCPL theory based on arbitrage pricing theory (Ross 1976), (ii) derive the assumptions under which the theory holds and the essential empirical predictions of the model, and (iii) present an empirical model which can be used to test the theory and estimate parameters useful in estimating the value of privately-held equity interests.