Q 18.16. Consider a project similar to the firm in Exhibit 18.3, but change the risk- neutral required interest rate to 0%. The firm is worth either $100 or $120. The bond promises $90. We shall consider two cases: one in which the bond is convertible into 75% of the firm's equity, and one in which it is not. 1. Work out the value of the firm. For the bond, create three rows for each state:

a) If bondholders never convert (which is also the value for the nonconvertible bond);

b) If bondholders always convert;

c) If bondholders convert only if it is optimal for them (which is also the value for the convertible bond). Does the convertibility feature have any value? 2. Now a new and independent project "BAD" becomes available. It will pay off either +$50 or -$60 with equal probabilities.

a) If the bond is not convertible, is it in the interest of shareholders to undertake "BAD"?

b) If the bond is convertible (into 75% equity), is it in the interest of sharehold- ers to undertake "BAD"? Would you expect to see many conversions if this were the case? How does frequency of actual conversion empirically relate to the value of convertibility?