Diversification in Firm Valuation: A Multivariate Copula Approach

We introduce a new discounted cash flow model which adopts the diversification effectof multi-business firms. We face two challenges: One is examining how different diversificationextents can affect the firm value due to risk reduction, and the other is modelingsegment-specific cash flows and discount rates to reflect the differences in risk and growthcharacteristics across the different businesses that a firm operates in. Since the co-movementof business segments depends on the state of the economy, we use a multivariate copulaapproach 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’sbusiness segments leads to a lower probability of firm default which results in a higher firmvalue through reduced bankruptcy costs. We demonstrate this effect by comparing the valuesof three U.S. firms when modeling independence, dependence with copulas, and perfectdependence between businesses.