Diversification in Firm Valuation: A Multivariate Copula Approach

Abstract

We introduce a new discounted cash flow model which integrates the diversification effect of multi-business firms. We face two challenges. One is examining how different degrees of diversification can affect firm value due to risk reduction, and the other is modeling segment-specific cash flows and discount rates to reflect the differences in risk and growth characteristics across the different business sectors in which a firm operates. Since the co-movement of business segments depends on the state of the economy, we use a multivariate copula approach, taking the state-varying dependence of business segments explicitly into account. A high level of corporate diversification caused by a low dependence between the firm's business segments yields a lower default probability, which results in a higher firm value through reduced bankruptcy costs. We demonstrate this effect by comparing the values of three U.S. firms in modeling independence, dependence with copulas, and perfect dependence between businesses.