Diversification in Firm Valuation: A Multivariate Copula Approach

We introduce a new discounted cash flow model which adopts the diversification effect of multi-business firms. We face two challenges: One is examining how different diversification extents can affect the 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 businesses that a firm operates in. 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 a firm's diversification determined by a low dependence between the firm's business segments leads to a lower probability of firm default which results in a higher firm value through reduced bankruptcy costs. We demonstrate this effect by comparing the values of three U.S. firms when modeling independence, dependence with copulas, and perfect dependence between businesses.