Return to a project similar to the firm in Table 18.3. The risk-neutral required interest rate is 10%. 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 shareholders 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?
