There is no tax (corporate tax rate = 0%).

F has generates a single cash-ow in one year. This cash-ow depends on the strategy chosen by the management:

• The safe strategy yields a certain cash-ow of $1,200,
• The risky strategy yields a high cash-ow of $3,000 with probability 0.3, and a low cash-flow of $300 with probability 0.7.

F has one stock outstanding and one bond, with a $900 face value, a 5% annual coupon and a one-year maturity. The management chooses the strategy that maximizes the final expected cash flow for the stockholder.

A bond can be non-convertible. In that case, it is a classical bond.

A bond can also be convertible. In that case, the holder of the bond has the possibility (but not the obligation) to convert the bond at predetermined time in a predetermined number of shares x (the conversion ratio) at no cost. The shares are issued by the firm for the occasion. For instance, in the context of this example, if the conversion ratio is x, there will be 1+x shares after the conversion. If he converts, the bondholder will receive the payoff associated with having x shares. The bondholder chooses to convert or not to maximize its expected final cash-flow

a. If the bond is non-convertible, which strategy does the management choose?

b. Suppose now that the bond is convertible until maturity (that is, the bondholder can observe the year 1 cash-ow before converting) with a conversion ratio of 3 (coupon and maturity are unchanged). Will the bondholder convert if the final cash-ow is $1,200? Same question if final cash-flow is $3000, and if it is $300.

c. If the bond is convertible until maturity with a conversion ratio of 3, which strategy does the management choose?

d. Assuming debtholders do not convert when the firm chooses the safe strategy, what is the smallest conversion ratio xmin(not accounting for decimals, xmin is an integer) such that the management chooses the safe strategy? Based on this exercise, what is according to you the purpose of convertible bonds?