lecture16a - Economics 202A Lecture Outline(version 1.2...

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Economics 202A Lecture Outline, November 13, 2007 (version 1.2) Maurice Obstfeld Financing the Firm: Modigliani-Miller Firms raise capital by issuing debt as well as equity. Above we priced equity claims to a °rm±s output. If all claims on a °rm are equity claims ²claims to dividends ²then the value of the °rm clearly is the present value derived above. Consider a °rm facing complete markets and a riskless real interest rate of r . There are two periods and S states of nature in period 2. The °rm can issue bonds B and equity shares E to °nance its investment in capital K: The payo/ to this investment tomorrow is A ( s ) F ( K ) , for s 2 S : Since the °rm may be unable fully to repay its bondholders on date 2, its borrowing rate ~ r (the corporate bond rate) will generally exceed r . For simplicity (and without any real loss of generality) assume the depreci- ation rate of capital is ° = 1 . Let the °rm borrow B on date 1. It will then owe its bondholders (1+~ r ) B in every state of nature s 2 S ; but it declares bankruptcy if it cannot repay them in full : Let S b be the set of bankruptcy states and S n be the set of nonbankruptcy states, so that S = S b [ S n : By de°nition, in a bankruptcy state, the total output of the °rm is insu¢ cient to cover debt payments: A ( s ) F ( K ) < (1+ ~ r ) B: In this case, bondholders are senior claimants and get whatever there is, while equity holders get nothing. Thus equity holder payo/ = ° A ( s ) F ( K ) ° (1 + ~ r ) B for s 2 S n 0 for s 2 S b ; whereas bond holder payo/ = ° (1 + ~ r ) B for s 2 S n A ( s ) F ( K ) for s 2 S b : At the Arrow-Debreu prices, the value of the °rm±s equity, sold on date 1, is E = X s 2S n p ( s ) 1 + r [ A ( s ) F ( K ) ° (1 + ~ r ) B ] = K ° B: (1)
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