Octopus Transit has a $1000 par value bond outstanding
with 10 years to maturity. The bond carries an annual interest
payment of $84, payable semiannually, and is currently selling for
1,095. Octopus is in a 30 percent tax bracket. The firm wishes to
know what
the aftertax 30 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.
Yield on new issue?
b. Make the appropriate tax adjustment to
determine
the after tax cost of debt?
No of periods = 10 years * 2 = 20 semi-annual periods
Let us compute the Yield to Maturity (YTM)
Bond Price = Coupon / (1 + YTM / 2)period + Par value / (1 + YTM / 2)period
$1095 = $42 / (1 + YTM / 2)1 + $42 / (1 + YTM / 2)2 + ...+ $42 / (1 + YTM / 2)20 + $1000 / (1 + YTM / 2)20
Using Texas Instruments BA 2 plus calculator
SET N = 20, PMT = 42, PV = -1095, FV = 1000
CPT --> I/Y = 3.529768%
YTM = 2 * I/Y
YTM = 2 * 3.529768%
YTM = 7.059536% or 7.06%
Pre tax cost of Debt = 7.06%
After tax cost of Debt = Pre tax cost of Debt * (1 - Tax rate)
After tax cost of Debt = 7.06% * (1 - 30%)
After tax cost of Debt = 4.94%
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