GloboCorp is all equity financed and generates perpetual annual EBIT of $100.Assume that the EBIT,and all other cash flows,occur at year end and that we are currently at the beginning of a year.GloboCorp has 1,500 shares outstanding which trade for $0.40.The stockholders of GloboCorp require a return of 10%.GloboCorp is considering an open market stock repurchase.It plans to buy 20% of its outstanding shares.The repurchased shares will be cancelled.It will finance the repurchase by issuing perpetual bonds with a coupon rate (and yield)of 4%.Assume that the tax rate is 40%.What price does GloboCorp have to offer for repurchased shares such that the repurchase price is equal to the price that prevails after the repurchase is complete?

Question

Quizplus · Accepted Answer

The company needs to select the repurchase price, P_R, so that it is equal to the stock price that prevails after the repurchase, P_A. In other words: P_R = P_A The price after the repurchase is: P_A = 11ea7fdb_fc66_c482_a768_27122030d206_TB2902_11 or P_A = 11ea7fdb_fc66_c483_a768_55b6bcc446c0_TB2902_11 Where 11ea7fdb_fc66_c484_a768_611ff699d6ea_TB2902_11 is shares outstanding before the repurchase and f is the fraction of shares repurchased. The value of levered equity is solved using M&M Prop I with taxes: E_L = V_L - D = 11ea7fdb_fc66_c485_a768_b1796363574c_TB2902_11 + T × D - D In this example, the amount of debt is equal to the cost of the repurchase: D = f × N_B × P_R Where f × N_B is equal to the number of shares repurchased. Thus, E_L = V_L - D = 11ea7fdb_fc66_c486_a768_154e78e60b7f_TB2902_11 + T × f × N_B × P_R - f × N_B × P_R or E_L = V_L - D = 11ea7fdb_fc66_eb97_a768_e7e3d102642b_TB2902_11 - (1 - T) × f × N_B × P_R And P_A = [ 11ea7fdb_fc66_eb98_a768_e9776235053f_TB2902_11 - (1 - T) × f × N_B × P_R] / N_B(1 - f) Set P_R = P_A and solve for P_R. P_R = [ 11ea7fdb_fc66_eb99_a768_a34fd0cad25b_TB2902_11 - (1 - T) × f × N_B × P_R] / N_B(1 - f) Recall that V_U = 11ea7fdb_fc66_eb9a_a768_4310c25ebb05_TB2902_11 This simplifies to: P_R = 11ea7fdb_fc66_eb9b_a768_093e0cec6209_TB2902_11 V_U = 11ea7fdb_fc66_eb9c_a768_35150e283027_TB2902_11 = 600 P_R = 11ea7fdb_fc67_12ad_a768_bb55b9f8e0de_TB2902_11 = $0.4348 If it pays this price, then the stock price after the repurchase will be $0.4348.

GloboCorp Is All Equity Financed and Generates Perpetual Annual EBIT