whereπGoingconcern,tisthecumulativeprobabilitythatthe
firmwillcontinueasagoingconcernthroughperiodt.The
probabilities ofdistress willhaveto be estimatedfor each
year,andthecumulativeprobabilityofsurvivingasagoing
concern can then be written as follows:
whereπDistress,nistheprobabilitythatthefirmwillbecome
distressedinperiodn.Forexample,ifafirmhasa 20 percent
chance of distress in year 1 and a 10 percent chance of
distressinyear2,thecumulativeprobabilityofsurvivingasa
going concern over two years can be written as:
Estimating Discount Rates
Inconventionalvaluation,weoftenestimatethecostofequity
usingaregressionbetaandthecostofdebtbylookingatthe
marketinterestratesonpubliclytradedbondsissuedbythe
firm.Forfirmswithasignificantprobabilityofdistress,these
approachescanleadtoinconsistentestimates.Considerfirst
theuseofregressionbetas.Sinceregressionbetasarebased
on past prices over long periods (two to five years, for
instance), anddistress occursover shorter periods,we will
find that these betas will understate the true risk in the
distressed firm.
5 Withtheinterest ratesoncorporatebonds,werunintoa
different problem. Theyields to maturityon thecorporate
bondsoffirmsthatareviewedasdistressedreachextremely
highlevels, largelybecausetheinterest ratesarecomputed