Consider a single period problem 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 probability and the covariance of these states with the market portfolio is zero (no systematic risk). initially, the firm has 100 shares outstanding and debt with a face value of $50 due at the end of the period.
a.) what is the share price of this firm? (hint: you need to calculate cash flows to equity holders in the good state and at the bad state of the economy separately. after that, you compute the expected cash flow. also, don’t forget that debt holders are paid first in both states of the world.)
suppose the firm 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.
b.) what is the market price of the new debt? (hint: in case of bankruptcy, old and new debt holders will split the cash flow proportional to the face value because they have debt of the same seniority.)
c.) just after the announcement, what will happen to the price of the equity shares?
d.) what has happened to the total value of the firm? does the modigliani-miller (mm) theorem hold in this case?