CHAPTER 9. BANKRUPTCY PROCEDURES Bebchuk, Lucian. "A New Approach to Corporate reorganizations Harvard Law Review 101(1988)775-804 9.3 An equilibrium model of bankruptcy Suppose there is a single bid for the firm consisting of>0 units of cash and the equity in the re-organized firm. If the bid is all cash then the distribution problem is trivial, so there is no loss of generality in assuming that the amount of equity is positive. Without loss of generality we can normalize the number of shares to equal one There are n classes of debt(i=1, ..., n) arranged in decreasing order of seniority. The face value of the i-th class of debt is denoted by Di>0. The quity in the original firm is the(n+1)-th class security. There is assumed to be one share in the original firm There is a(non-atomic) continuum of agents A=0, 1 endowed with Lebesgue measure. The assumption that agents form a non-atomic contin- uum implies that an individual has no"market power". Each agent a has w(a) units of cash, di (a) units of the i-th class of debt, and dn+1(a) units of equity. Let d(a=(d1(a),., dn+1(a)) represent the portfolio of agent a Each agent has a linear utility function for cash and equity. If agent a holds a units of cash and e units of equity his utility is +v(ae. In other words, v(a) is the monetary value agent a places on one unit of equity in the re-organized firn We assume that the functions v(),()and d() are Lebesgue integrable 9.3.1 Competitive equilibrium An allocation is a measurable function f: A-R+XR+, where f(a)=(a, e) is the portfolio of cash and equity allocated to agent a. An allocation f is attainable if f(a)da=(W+C,1), where W=Jw(a)da is the aggregate initial endowment of cash Let v be the equilibrium value of the equity. The equilibrium price of4 CHAPTER 9. BANKRUPTCY PROCEDURES Bebchuk, Lucian. “A New Approach to Corporate Reorganizations,” Harvard Law Review 101 (1988) 775-804. 9.3 An equilibrium model of bankruptcy Suppose there is a single bid for the firm consisting of C ≥ 0 units of cash and the equity in the re-organized firm. If the bid is all cash then the distribution problem is trivial, so there is no loss of generality in assuming that the amount of equity is positive. Without loss of generality we can normalize the number of shares to equal one. There are n classes of debt (i = 1, ..., n) arranged in decreasing order of seniority. The face value of the i-th class of debt is denoted by Di > 0. The equity in the original firm is the (n + 1)-th class security. There is assumed to be one share in the original firm. There is a (non-atomic) continuum of agents A = [0, 1] endowed with Lebesgue measure. The assumption that agents form a non-atomic contin￾uum implies that an individual has no “market power”. Each agent a has w(a) units of cash, di(a) units of the i-th class of debt, and dn+1(a) units of equity. Let d(a) ≡ (d1(a), ..., dn+1(a)) represent the portfolio of agent a. Each agent has a linear utility function for cash and equity. If agent a holds x units of cash and e units of equity his utility is x + v(a)e. In other words, v(a) is the monetary value agent a places on one unit of equity in the re-organized firm. We assume that the functions v(·), w(·) and d(·) are Lebesgue integrable. 9.3.1 Competitive equilibrium An allocation is a measurable function f : A → R+×R+, where f(a)=(x, e) is the portfolio of cash and equity allocated to agent a. An allocation f is attainable if Z f(a)da = (W + C, 1), where W = R w(a)da is the aggregate initial endowment of cash. Let V be the equilibrium value of the equity. The equilibrium price of