1. Consider a single period binomial setting where the riskless interest rate is zero, and there are no taxes. A firm consists of a machine that will produce cash flows of $210 if the economy is good and $80 if the economy is bad. The good and bad states occur with equal risk-neutral probability. Initially, the firm has 100 shares outstanding and debt with a face value of $50 due at the end of the period. What is the share price of the firm? (In this question please ignore any risk adjustments and discount expected cash flows at a rate of 0%. In calculating expected cash flows, use probabilities 0.5 for the good and 0.5 for the bad states).
2. Suppose the firm in Q1 unexpectedly announces that it will issue additional debt, with the same seniority as existing debt and a face value of $50. The firm will use the entire proceeds to repurchase some of the outstanding shares. (Hint: In part c of the question, “undoing the leverage change” means that the investor sells some of her shares to get back to 20% ownership ratio, i.e., as before the leverage change).
a. What is the market price of the new debt?
b. Just after the announcement, what will the price of a share jump to?
c. Show how a shareholder with 20 percent of the shares outstanding is better off as a result of this transaction when he or she undoes the leverage change.
d. Show how the Modigliani-Miller Theorem still holds.