Question

Octopus Transit has a $1,000 par value bond outstanding with 10 years to maturity. The bond carries an annual interest payment of $96, payable semiannually, and is currently selling for $1,101. Octopus is in a 40 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)-Yield on new issue

· The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value

· The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.

· The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 9.60% x ½]	PMT	48
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [10 Years x 2]	N	20
Bond Price/Current Market Price of the Bond [-$1,101]	PV	-1,101

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the semi-annual yield to maturity on the bond (1/Y) = 4.055%.

The semi-annual Yield to maturity = 4.055%.

Therefore, the annual Yield to Maturity of the Bond = 8.11% [4.055% x 2]

“Hence, the Yield on new issue will be 8.11%”

(b)-The after-tax cost of debt

The firm’s after-tax cost of debt on the Bond is the after-tax Yield to maturity (YTM)

The After-tax cost of debt = Annual Yield to maturity on the bond x (1 – Tax Rate)

= 8.11% x (1 – 0.40)

= 8.11% x 0.60

= 4.87%

“Hence, the after-tax cost of debt will be 4.87%”