lecture12post - Equity and debt options Other options in...

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Equity and debt options Other options in corporate securities MIM Lecture 12 - Incentives and convertibles BUSI 588, Fall 2011 Diego Garc´ ıa Kenan-Flagler Business School UNC at Chapel Hill October 5th, 2011 c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 12 - Incentives and convertibles 1 / 20
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Equity and debt options Other options in corporate securities MIM Outline 1 Equity and debt options Expected returns of corporate securities 2 Other options in corporate securities Convertible debt 3 MIM Project choice Convertibles Handouts today: Class slides. Case 12 solutions. c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 12 - Incentives and convertibles 2 / 20
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Equity and debt options Other options in corporate securities MIM Cost of debt versus expected return on debt Consider example from previous class. Firm with $80m in assets, senior debt with face value $50m, junior debt with face value $10m. Both debt issues have two year maturity and zero-coupon. Firm assets have 30% volatility, risk-free rate at 10%. Assume firm is average, i.e. β A = 1, and that E [ r m ] - r f = 5%, so r A = 15%. First, are yields the same as expected returns? D = F (1 + r D ) T No - we are not computing expected cash flows. c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 12 - Incentives and convertibles 3 / 20
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Equity and debt options Other options in corporate securities MIM Expected returns on corporate securities In principle (from basic principles) D = E [ CF ] (1 + r D ) T Sounds like a hard problem: computing probabilities of default, recovery rates, . . . , in order to back out discount rate. Try using option analogies: Senior debt is like risk-free debt minus a put. Junior debt is like a call K = F S minus a call K = F S + F J . Equity is like a call K = F S + F J . Notation: Δ 1 is the delta of the call with K = F S and Δ 2 is the delta of the call with K = F S + F J . c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 12 - Incentives and convertibles 4 / 20
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Equity and debt options Other options in corporate securities MIM Expected returns on corporate securities Equity expected returns should be equal to the expected return on a call K = F S + F J . E = C = Δ 2 A - B ; β E = Δ 2 A C β A Junior debt expected returns should be equal to the expected returns on a portfolio that is long a call K = F S and short a call K = F S + F J . D J = C 1 - C 2 = Δ 1 A - B 1 - Δ 2 A + B 2 ; β J = 1 - Δ 2 ) A D J β A Senior debt expected returns should be equal to the expected returns on risk-free debt minus the expected returns on a put K = F S .
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