Thecostofdebtforafirmisafunctionofthefirm’sdefault
risk.Asafirmborrowsmore,itsdefaultriskwillincreaseand
sowillthecostofdebt.Ifweusebondratingsasourmeasure
ofdefaultrisk,wecanestimatethecostofdebtinthreesteps.
First,weestimateafirm’sdollardebtandinterestexpensesat
eachdebtratio;asfirmsincreasetheirdebtratio,bothdollar
debt and interest expenses willrise. Second, at each debt
level,wecomputeafinancialratioorratiosthatmeasure(s)
defaultrisk,andusetheratio(s)toestimatearatingforthe
firm;again,as firmsborrowmore,this ratingwilldecline.
Third, a default spread, based on the estimated rating, is
addedtotherisk-freeratetoarriveatthepretaxcostofdebt.
Applyingthemarginaltaxrateto thispretaxcostyieldsan
after-tax cost of debt.
Onceweestimatethecostsofequityanddebtateachdebt
level,weweightthembasedontheproportionsusedofeach
toestimatethecostofcapital.Whilewehavenotexplicitly
allowedforapreferredstockcomponentinthisprocess,we
canhavepreferredstockasa partofcapital.However, we
havetokeepthepreferredstockportionfixed,whilechanging
theweightsondebtandequity.Thedebtratioatwhichthe
cost of capital is minimized is the optimal debt ratio.
In this approach,theeffect on firmvalue ofchanging the
capitalstructureisisolatedbykeepingtheoperatingincome
fixedandvaryingonlythecostofcapital.Inpracticalterms,
thisrequiresustomaketwoassumptions.First,thedebtratio
is decreased by raising new equity and/or retiring debt;
conversely,thedebtratioisincreasedbyborrowingmoney
andbuyingbackstock.Thisprocessiscalledrecapitalization.