Exercise 5 Shareholders Debtholders conflicts (20 pts, 5 by question) There is no tax (corporate tax rate 0 ) F has generates a single cash flow in one year This cash flow depends on the strategy chosen by the management The safe strategy yields a certain cash flow of $1,200, The risky strategy yields a high cash flow 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 If the bond is non convertible, which strategy does the management choose Suppose now that the bond is convertible until maturity (that is, the bondholder can observe the year 1 cash flow before converting) with a conversion ratio of 3 (coupon and maturity are unchanged) Will the bondholder convert if the final cash flow is $1,200 Same question if final cash flow is $3000, and if it is $300 If the bond is convertible until maturity with a conversion ratio of 3, which strategy does the management choose 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

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Exercise 5: Shareholders/Debtholders conflicts (20 pts, 5 by question)

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

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

-The safe strategy yields a certain cash-flow of $1,200,
-The risky strategy yields a high cash-flow 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.

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