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.