Discount Rates for Closely Held Businesses: Recognizing Managerial Choice and Option Value
Abstract
FFor many decades, the portfolio theory that originated with Harry Markowitz (1952, 1959) has been the dominant paradigm for setting discount rates for business valuation and commercial damages. It is based on broad presumptions that long-lived investors consider the risk and return on a portfolio of investments; that these investors can readily diversify their holdings across publicly-traded stocks and a risk-free bond; and that this limited asset set is a good proxy for the wealth of households.The CAPM of Sharpe (1964) and Lintner (1965) developed this into an equation involving an equity market return, a “beta” factor, and a risk-free rate. Variations on the CAPM remain staples of corporate finance and valuation. Consistent with this theory, business discount rates are commonly estimated using aggregate equity returns over long periods of time. In a similar manner, lost personal earnings are commonly estimated using aggregate wage increases over time.
However dominant the portfolio theory, its broad presumptions cannot be reconciled with the fact that most private employers are closely held businesses; that investors in most such enterprises cannot substantially diversify their holdings; and that “idiosyncratic” risks are often primary for these investor-entrepreneurs. Furthermore, as Fama and French (1992) and many others have demonstrated, additional factors empirically predict stock market returns. The literature arising from this approach now provides arguments for estimating widely varying discount rates for the same company, as well as an assortment of alleged discounts and premia. We conclude that practitioners are largely unconstrained by the dominant theory, and pronounce this a sad state of affairs.
We propose an alternative to the portfolio theory, which originates from the value functional approach to business valuation outlined in Anderson (2012) that is rooted in the decision models of Bellman (1957) and the asset pricing model of Lucas (1978). This novel approach focuses on an entrepreneur solving a sequential decision problem, not an investor managing a passive investment portfolio. Such a decision problem can incorporate the liquidity constraints and asymmetric risks that most businesses face. We provide simple illustrations showing how many businesses—as well as many workers—face choices that can be modeled as sequential decision problems involving a series on one-period-ahead discount and growth assumptions. We argue that this theory is much closer to reality than the portfolio approach, and can often provide better estimates of actual value and loss.
We recommend further development of other methods that recognize managerial choice, idiosyncratic risk, and liquidity constraints as an alternative to standard portfolio models for businesses and wage growth indices for workers. We note a limited number of successful uses of this method, and emphasize the matching principle between net growth and discount rates.