Question

Arbitra Inc.'s current capital structure is 30% debt and 70% equity. The expected return on its debt is 5%, its equity Beta is 1.1. The riskfree rate is 2%, and the expected return on the market is 10%. Consider now the following additional information. The government of Bigland, where Arbitra Inc. is located, introduces a 40% corporate income tax rate. Arbitra Inc. (capital structure still 50% debt and 50% equity) has only one project which is expected to generate $1000 of EBIT next year, at which point the firm will shut down. c) Calculate Arbitra Inc.'s firm value using the WACC method. Given the firm value you calculated, calculate the value of the firm's debt d) Calculate Arbitra Inc.'s firm value using the APV method and show that this gives the same answer as in (iii). Hint: To show this, you need to first explicitly calculate the interest tax shield; for the calculation of the present value of the tax shield, use the expected return on the firm's assets.

Answer 1

Part (a)

r_d = r_f + Beta of debt x (r_m - r_f)

Or, 5% = 2% + B_d x (10% - 2%)

Hence, B_d = 3%/8% = 0.3750

Beta of equity = B_e = 1.1

Hence, asset beta = B_a = W_d x B_d + W_e x B_e = 30% x 0.375 + 70% x 1.1 = 0.8825

Cost of capital = r = r_f + B_a x (r_m - r_f) = 2% + 0.8825 x (10% - 2%) = 9.06%

Part (b)

asset beta = B_a = W_d x B_d + W_e x B_e

Hence, 0.8825 = 50% x 0.6 + 50% x B_e

Hence, new B_e = 1.165

Hence, expected r_e = r_f + B_e x (r_m - r_f) = 2% + 1.165 x (10% - 2%) = 11.32%

Part (c)

r_d = r_f + B_d x (r_m - r_f) = 2% + 0.6 x (10% - 2%) = 6.8%

WACC = R = W_d x r_d x (1 - T) + W_e x r_e = 50% x 6.8% x (1 - 40%) + 50% x 11.32% = 7.70%

Hence, firm's value = V = EBIT x (1 - T) / (1 + R) = 1,000 x (1 - 40%) / (1 + 7.70%) = $ 557.10

Value of debt = D = Wd x V = 50% x 557.10 = $ 278.55

Part (d)

Interest = I = D x r_d = 278.55 x 6.8% = 18.94

Hence, interest tax shield = ITS = I x T = 18.94 x 40% = $ 7.58

Value fo the firm using APV method = Value of the unlevered firm + PV of ITS = EBIT x (1 - T) / (1 + r) + ITS / (1 + r) = 1,000 x (1 - 40%) / (1 + 9.06%) + 7.58 / (1 + 9.06%) = $ 557.10

This value is same as the value of firm obtained in part (c) or part (iii)