4 r 010 t 10 years value using the bsm model equity

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Unformatted text preview: I: R. J. Hawkins Econ 136: Financial Economics 19/ 21 The Contingent-Claim Valuation Paradigm Mapping Capital Structure to Option Pricing Input Firm Data Assets valued at \$100 MM Face value of ZCB debt is \$80 MM Asset value standard deviation of 40% 10-year Treasury bond rate is 10% Maturity of debt is 10 years Option Interpretation S = \$100 MM K = \$80 MM σ = 0.4 r = 0.10 t = 10 years Value using the BSM model: Equity = SN (d1 ) − Ke −rt N (d2 ) + r + 1 σ2 t √2 = 1.5994 ⇒ N (d1 ) = 0.9451 σt √ d2 = d1 − σ t = 0.3345 ⇒ N (d2 ) = 0.6310 d1 = ln S K Equity = \$100 × 0.9451 − \$80e −0.1×10 × 0.6310 = \$75.94MM Equities II: R. J. Hawkins Econ 136: Financial Economics 2/ 16 The Contingent-Claim Valuation Paradigm Implications for Debt: Given equity as a call option with a value of \$75.49 MM: The value of the debt is a covered call: Debt = S − C = \$100 − \$75.49 = \$24.06 MM The interest rate on the debt follows from e −Rt = 1 R = − ln t Debt Value Face Value =− 1 ln 10 \$24.06 \$80 Debt Value Face Value = 12.01% and the default spread s of the bond fol...
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This note was uploaded on 01/23/2014 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at University of California, Berkeley.

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