Problem
Consider two firms, A and B. A and B each generate identical annual earnings before interest, taxes, and depreciation of X per year in perpetuity, starting in a year from today. X is random, but is never less than XL > 0. Both A and 8 also had identical past capital expenditure, which now generates a fixed annual depreciation expense of d > 0 for each firm (for simplicity, in perpetuity), where d is constant and d < XL. Firm A is all equity financed. Firm 8 is financed through a combination of debt and equity. In particular, B's financing includes a risk-free perpetual bond with a face value D such that Orf < XL - d, where rf is the risk free rate. There are no further capital expenditures or changes in net working capital. The corporate tax rate is t > 0 and interest is tax deductible. There are no other taxes. Compute the difference in total market value of A and B, showing your steps and explaining your reasoning. Provide intuition for your answer.