The value of liquidity ultimately has to derive from the
investorbeingabletosellatsomepredeterminedpriceduring
thenontradingperiodratherthanbeingforcedtohold until
theend of theperiod.Thelook-back optionapproach that
assumes a perfect market timer, explained earlier in the
chapter,assumesthatthesalewouldhaveoccurredatthehigh
priceandallowsustoestimateanupperboundonthevalue.
Canweuseoptionpricingmodelstovalueilliquiditywithout
assuming perfect market timing? Consider one alternative.
Assumethatyouhaveadisciplinedinvestorwhoalwayssells
investmentswhenthepricerises 25 percentabovetheoriginal
buyingprice.Notbeingabletotradeonthisinvestmentfora
period(saytwoyears)undercutsthisdisciplineanditcanbe
arguedthatthevalueofilliq-uidityistheproductofthevalue
oftheputoption(estimatedusingastrikepriceset 25 percent
above the purchase price and a two-year life) and the
probabilitythatthestockpricewillrise 25 percentormore
over the next two years.
If you decide to apply option pricing models to value
illiquidityinprivatebusinesses,thevalueoftheunderlying
asset (which is the private business) and the standard
deviation in that value will be required inputs. While
estimatingthemforaprivatebusinessismoredifficulttodo
thanforapubliclytradedfirm,wecanalwaysuseindustry
averages.
ILLUSTRATION 14.1: Estimating the Illiquidity Discount
for a Private Firm
Kristin Kandy is a privately owned candy manufacturing
businessthatgenerated$500,000inpretaxoperatingincome
on$3millioninrevenuesinthemostrecentfinancialyear.