reflecttheunderlyinguncertaintywefacein estimatingthe
inputs to the valuation.
There have generally been two impediments to good
simulations. The first is informational: Estimating
distributions of values for each input into a valuation is
difficulttodo.Inotherwords,itisfareasiertoestimatean
expectedgrowthrateof 8 percentinrevenuesforthenextfive
yearsthanitistospecifythedistributionofexpectedgrowth
rates—the type of distribution and parameters of that
distribution—forrevenues.Simulationstendtoworkbestin
cases wherethereiseither historicaldata(different growth
ratesover time) orcross-sectional data(a rangeof growth
ratesacrosscomparablecompanies)thatmakeitfeasibleto
estimate distribution characteristics. The second is
computational; until the advent of personal computers,
simulationstendedtobetootimeandresourceintensivefor
thetypicalanalyst.Boththeseconstraintshaveeasedinrecent
years, and simulations have become more feasible.
As simulations become more common, analysts have to
confront three potential problems. The first is that the
distributionsforinputsareoftenincorrectlyspecifiedinterms
ofbothtypeandparameters;itisgarbagein,garbageout.The
second is the misconception that the cash flows from
simulationsaresomehowrisk-adjustedbecausetheyfactorin
thelikelihoodofpooroutcomes.Theexpectedcashflowsare
supposedtofactorinthelikelihoodofpooroutcomesandare
notrisk-adjusted.Westillneedtouserisk-adjusteddiscount
ratesto gettothevaluetoday.Thethirdproblemthatboth
scenarioanalysisandsimulationshareisthatanalystsoften
doublecountriskbyfirstcomputinganexpectedvalueusing
risk-adjusted discount rates and then considering the