Capital Structure (20 Points)

a. Every student loves the Nobel-prize-winning theory of capital structure irrelevance in a world of perfect competition without taxes or private information (and no transactions costs), formulated by Modigliani and Miller, or MM for short. Suppose there are no personal or corporate taxes and no transactions costs nor private information. In this perfect world, the David Dennison Organization (DD) and the Peggy Peterson Company (PP) are identical in all respects, except that PP is unlevered and DD has $5,000,000 of 5% bonds outstanding. (After all, DD, or the alter ego DJT, boasts to be the "King of Debt".) Assume that EBIT is $1,000,000 for both, and that the cost of equity to PP is 10% and the cost of equity to DD is 15%. Next assume that VPP = $10,000,000 and VDD = $12,000,000. Using the MM propositions, demonstrate how to make a riskless profit from DD and PP without investing a penny of one's own wealth. (10 points)

b. Now in the same world without personal or corporate taxes and no transactions costs, assume a firm's debt is risk-free, so that the cost of debt RD equals the risk-free rate Rf. Define A as the firm's asset beta - that is, the systematic risk of the firm's assets. Define E to be the beta of the firm's equity. Use the CAPM along with M&M's Proposition II to find the relationship between A and E. (10 points)