with substantial debt and a significant potential for
bankruptcy,theoptionvalueofequitymaybeinexcessofthe
discounted cash flow value of equity.
Payoff on Equity as an Option
Theequityinafirmisaresidualclaim;thatis,equityholders
layclaim to all cash flowsleft after otherfinancial claim
holders(debt,preferredstock,etc.)havebeensatisfied.Ifa
firmisliquidated,thesameprincipleapplies;equityinvestors
receivethecashthatisleftinthefirmafteralloutstanding
debt and other financial claims have been paid off. With
limitedliability,ifthevalueofthefirmislessthanthevalue
of theoutstanding debt,equity investors cannot lose more
than their investment in the firm. The payoff to equity
investors on liquidation can therefore be written as:
whereV= Liquidation value of the firm
D=Facevalueof theoutstandingdebtand otherexternal
claims
Equitycanthusbeviewedasacalloptiononthefirm,where
exercisingtheoptionrequiresthatthefirmbeliquidatedand
thefacevalueofthedebt(whichcorrespondstotheexercise
price)bepaidoff.Thefirmistheunderlyingassetandthe
option expireswhen thedebt comesdue. Thepayoffs are
shown inFigure 17.1.
FIGURE 17.1Payoff on Equity as Option on a Firm