Consider a single period binomial setting where the riskless interest rate is ze
ID: 2794223 • Letter: C
Question
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.
Explanation / Answer
Answer :- Initially the expected Payoff to Equity is 0.5 (210-50) +.5 (80-50) = 95 .So the Price per share is 95/100 = $ .95.
In the good state ,both the new debt and old debt are paid in full.In the bad state,the debt holders split the $ 80 available equally because the new debt has equal priority with the old debt and both are owed $ 50. Thus, the new debt has a value of .50($ 50) + .50( $ 40) = $ 45.
After the capital structure change, the expected value of the remaining equity is
.5($ 210-100) +.5($ 0) = $ 55
To find out the price per share,we must find out how many shares n were repurchased at this price. We solve the following two equations :
ns = $ 45 and (100-n)s = $ 55
The first says that the new debt is used to repurchase shares,and the second is that the value of the shares remaining must equal the value of the remaining equity calculated above.Solving these gives s = $ 1 and n = 45 which means that the firm uses the proceeds of the new debt to buy back 45 shares at a price of $ 1 Each. The share price jumps from $ 0.95 per share to $ 1.The shareholders make a gain .