Question

Octopus Transit has a $1,000 par value bond outstanding with 20 years to maturity. The bond carries an annual interest payment of $104, payable semiannually, and is currently selling for $1,110. Octopus is in a 35 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar.

a. Compute the yield to maturity on the old issue and use this as the yield for the new issue. (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Yield on new issue             %

b. Make the appropriate tax adjustment to determine the aftertax cost of debt. (Do not round intermediate calculations. Round the final answer to 3 decimal places.)

Cost of debt             %

Answer 1

a. The present value formula of the bond will give us the semi-annual yield which we will convert to the annual yield.

1110 = 52/(1+r) + 52/(1+r)^2 + ... + 1052/(1+r)^40.

To calculate r, we can either use excel or do it by hit-and-trial. We use excel and find that r = 4.594%.

This is the semi-annual yield, hence the annual yield will be = 4.594 x 2 = 9.1883% = 9.19%

b. The after-tax cost of debt is given as = Before-tax cost of debt x (1-T) = 9.1883 x 0.65 = 5.9724% = 5.972%.