Question

Arnell Industries has $ 30 million in permanent debt outstanding. The firm will pay interest only on this debt.​ Arnell's marginal tax rate is expected to be 30 % for the foreseeable future. a. Suppose Arnell pays interest of 9 % per year on its debt. What is its annual interest tax​ shield? b. What is the present value of the interest tax​ shield, assuming its risk is the same as the​ loan? c. Suppose instead the interest rate on the debt were 6 %. What is the present value of the interest tax shield in this​ case?

Answer 1

a. Debt = $30 million , Interest rate = 9% per year , Tax rate = 30%

Annual Interest on debt = Debt x interest rate = 30 million x 9% = $2.7 million

Annual interest tax shield = Annual interest on debt x tax rate = 2.7 million x 30% = 0.81 million = 0.81 x 1000000 = $810000

b. We know that current debt is permanent, tax rate and interest rate are continue to be expected in future, therefore annual interest tax shield will form a perpetuity

Present value of perpetuity or Annual interest tax shield = Annual interest tax shield / Discount rate

In this question Discount rate = interest rate = 9%

Present value of Annual interest tax shield = 810000 / 9% = 9000000 =$ 9 million

b. Interest rate = 6%

Annual interest = 30 million x 6% = $2.4 million.

Annual interest tax shield = 2.4 million x 30% = $0.72 million = $720000

Discount rate = interest rate = 6%

Present value of interest tax shield = 720000 / 6% = 12000000 = $12 million