lecture3-MM__CAPM___Black___Scholes

# lecture3-MM__CAPM___Black___Scholes - MM CAPM Black Scholes...

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Corporate Liabilities as Options 19 September 2005

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Debt and Equity as Options Consider: A firm with a zero coupon debt outstanding, with face value F Value of the firm is V at maturity Payoffs: Bondholders: » F if V F » V if V < F Equity holders: » V – F if V F » 0, if bankrupt = Min (V, F) = V – max (0, V – F) = Max (0, V – F)
Debt and Equity as Options 0 F Firm Value Payoffs Equity Debt

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Debt and Equity as Options From above: Value of a risky bond = V – E By put – call parity: V – E = Riskless bond – Put Both together: Riskless bond = Risky bond + Put Option Where the put option is on the firm’s value, with same parameters as stock.
Debt and Equity as Options 0 F Firm Value Payoffs Risky Bond Riskless Bond

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In formulas Using this, we can rewrite equity beta as: V S r S V dV dS V dV S V dV dS S dS r = = = ( 29 V m m V m m V m m S S S V dV dS r Var r r Cov S V dV dS r Var r r S V dV dS Cov r Var r r Cov β = = = = = ) ( , ) ( , ) ( ) , (
In formulas dS/dV we can get from the B&S formula, Therefore ) ( ) ( ) ( 1 2 1 d N dV dS d DN e d VN S T r f = - = - V V S S V d N V S dV dS β ) ( 1 = =

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Old formulas revised Plugging into CAPM formula, we get And using that we get Which is similar to MM II S V d N r r r r r r r f m V f f m S f S ) ( ) ( ) ( 1 - + = - + = β f m f V V r r r r - - = (a) ) ( ) ( ) ( 1 S V d N r r r r r r r f V f f m S f S - + = - + =
Cost of debt By the same token: V m m B B B V dV dB r Var r r Cov β = = ) ( ) , ( ) ( 1 , ) ( ) ( 1 2 1 d N dV dB S V B d DN e d VN S T r f - = - = - = -

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Cost of debt And: B V d N r r r r r r r f m V f f m B f B )) ( 1 )( ( ) ( 1 - - + = - + = β (b) )) ( 1 )( ( ) ( 1 B V d N r r r r r r r f V f f m B f B - - + = - + =
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## This note was uploaded on 11/22/2010 for the course FINANCE 100104 taught by Professor Pfofessorking during the Spring '10 term at Erusmus University Rotterdam .

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lecture3-MM__CAPM___Black___Scholes - MM CAPM Black Scholes...

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