Question

Tax Shields. You live in a world without transaction or information costs and with a fixed real investment policy (all positive NPV projects are undertaken regardless of the firm’s capital structure). Unfortunately, the government is still around to tax you. Your RV rental firm is deciding between raising $10 million via common stock or $10 million via a twenty-year coupon bond with a face value of $10 million. The coupon rate on the bond would be 10% and the corporate tax rate is 35%. What is the present value of the tax shield generated by issuing the bond instead of common stock?

Answer 1

Target Capital to be Raised = $ 10 million and Face Value of Bond = $ 10 million, As the amount raised (or to be raised which is achieved) is equal to the bond's face value, the bond sells at par and its coupon rate equals it yield to maturity.

Yield to Maturity = Cost of Debt = Coupon Rate = 10 % and Corporate Tax Rate = 35 %

Further, the debt remains constant at $ 10 million, as the entire face value (entire debt) is repaid only upon the bond's maturity. Time to Maturity = 20 years. A constant debt ensures a constant cost of debt and a constant value of the interest tax shield.

Annual Interest Expense = Cost of Debt x Face Value of Bond = 0.1 x 10 = $ 1 million

Interest Tax Shield = Tax Rate x Annual Interest Expense = 0.35 x 1 = $ 0.35 million

Total Present Value of Interest Tax Shield = 0.35 x (1/0.1) x [1-{1/(1.1)^(20)}] = $ 2.97975 million ~ $ 2.98 million