62 ©2000, Association for Investment Management and Research Rational Pricing of Internet Companies Eduardo S. Schwartz and Mark Moon We apply real-options theory and capital-budgeting techniques to the problem of valuing an Internet company. We formulate the model in continuous time, form a discrete time approximation, estimate the model parameters, solve the model by simulation, and then perform sensitivity analysis. We report that, depending on the parameters chosen, the value of an Internet stock may be rational if growth rates in revenues are high enough. Even with a real chance that a company may go bankrupt, if the initial growth rates are sufficiently high and if this growth rate contains enough volatility over time, then valuations can reach a level that would otherwise appear dramatically high. In addition, the valuation is highly sensitive to initial conditions and exact specification of the parameters, which is consistent with observations that the returns of Internet stocks have been strikingly volatile. robably no recent investment topic elicits stronger feelings than Internet stocks. The skyrocketing valuations of these compa- nies have made millionaires and billion- aires out of many Internet entrepreneurs while the actual companies were generating significant, and often growing, losses. Interestingly, as the Internet has grown, so have the means by which individuals can trade over the Internet easily and with rela- tively low transaction costs. The view among some traditional money man- agers is that Internet stocks have been bid upward irrationally by individual day traders sitting at home at their computers and buying any stock that begins with “e-” or ends with “.com.” Such managers see the current frenzy as a spectacular example of a market bubble, the likes of which many will witness only once in a lifetime. These traditionalists fear significant negative consequences to the real econ- omy after this bubble bursts. Others see the Internet as dramatically transforming the way in which busi- ness is transacted. These investors believe that some of the upstart Internet companies will rapidly grow to dominate and even make irrelevant their tradi- tional bricks-and-mortar competitors. We apply real-options theory and modern capital-budgeting techniques to the problem of val- uing an Internet stock. We formulate the model in continuous time, form a discrete time approxima- tion, estimate the model parameters, solve the model by simulation, and then perform sensitivity analysis. Continuous-Time Model In developing the simple model to value Internet stocks, for simplicity, we initially describe the model in continuous time. Its implementation, however, will use the quarterly accounting data available from Internet companies and be in discrete time. Consider an Internet company with instanta- neous rate of revenues (or sales) at time t given by R t . Assume that the dynamics of these revenues are given by the stochastic differential equation , (1) where μ t , the drift, is the expected rate of growth in revenues and is assumed to follow a mean-reverting process with a long-term average drift ; σ is vola- tility in the rate of revenue growth; and z 1 is a ran- dom variable that reflects the draw from a normal distribution. That is, the initial very high growth rates of the Internet company are assumed to con- verge stochastically to the more reasonable and sus- tainable rate of growth for the industry to which the company belongs: (2) where η 0 is the initial volatility of expected rates of growth in revenues. The mean-reversion coeffi- cient, κ, describes the rate at which the growth is Eduardo S. Schwartz is professor of finance at the Anderson School at the University of California at Los Angeles. Mark Moon is vice president and portfolio manager at Fuller and Thaler Asset Management. P dR t R t ------- μ t dt σ t dz 1 + = μ d μ t κμ μ t – ( ) dt η t dz 2 , + =