F operating cash-flows depend on the entry of a competitor. If the competitor enters (proba 0.5), the operating cash-flows at year 1 are equal to $50. If the competitor does not enter (proba 0.5), the operating cash-flows at year 1 are equal to $150.

There are bankruptcy costs. If the firm does not default at time 1, the operating cash-flow in the subsequent years (2, 3, 4 etc. . . ) remain at years 1 level.

If the firm defaults at time 1, the firm is reorganized. Because of bankruptcy costs, the operating cash-flows of F in the subsequent years (2, 3, 4 etc...) are at 70% of years 1 level.

Everyone is risk neutral. all discount rates are equal to 4%. F has one perpetual bond outstanding, with a face value of $1,000.

1) Consider a perpetual coupon with coupon C and rate r. Show that the pay off that the holder of the perpetuity bond gets at time 1 is C + C/r.

2) Check that debt is risk-free (i.e., the firm never defaults if the interest is is equal to the risk-free rate). Compute Fs debt value and equity value

3) F decides to repay existing debt (in advance) and pay a $1,000 dividend to stock-holders. This operation is financed by the emission of two new perpetual bonds, face value = market value = $1,000 (one new bond is used to repay the existing bond, the other one to pay out the dividend). The two bonds have the same seniority. Note that the two bonds will have the same interest rate. Can the interest rate be equal to 4%? Compute the interest rate i. You can show that i verifies 1000 = (0.50.5(50+0.7 (50/4%) ) + 0.5(1000 i + (1000i/4%)) )/ 1+4%

4) Compute the total wealth of shareholders after the operation. Do shareholders benefit from the operation?