Omnicorp is all equity financed and generates perpetual annual EBIT of $500.Assume that the EBIT,and all other cash flows,occur at year end and that we are currently at the beginning of a year.Omnicorp has 1,000 shares outstanding which trade for $3.125.The stockholders of Omnicorp require a return of 8%.Omnicorp 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 2%.Assume that the tax rate is 50%.What price does Omnicorp have to offer for repurchased shares such that the repurchase price is equal to the price that prevails after the repurchase is complete?

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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_0127_a768_8f4ad79bb5c8_TB2902_11 or P_A = 11ea7fdb_fc66_0128_a768_2b2481cfafc6_TB2902_11 Where N_B 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_0129_a768_2ba376b6c0b9_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_283a_a768_75fee24ac1d8_TB2902_11 + T × f × N_B × P_R - f × N_B × P_R or E_L = V_L - D = 11ea7fdb_fc66_283b_a768_4b8a42218f0d_TB2902_11 - (1 - T) × f × N_B × P_R And P_A = [ 11ea7fdb_fc66_283c_a768_05ec332567a4_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_283d_a768_3d8ebe4d100d_TB2902_11 - (1 - T) × f × N_B × P_R] / N_B(1 - f) Recall that V_U = 11ea7fdb_fc66_283e_a768_7fa2186aa4aa_TB2902_11 This simplifies to: P_R = 11ea7fdb_fc66_283f_a768_3d103fff68af_TB2902_11 V_U = 11ea7fdb_fc66_4f50_a768_2f507c066f56_TB2902_11 = 3,125 P_R = 11ea7fdb_fc66_4f51_a768_e72a23dd7130_TB2902_11 = $3.472 If it pays this price, then the stock price after the repurchase will be $3.472.

Omnicorp Is All Equity Financed and Generates Perpetual Annual EBIT