Question

GT Corporation plans to raise some capital by issuing a new 10-year bond with the par of $1,000 and 6.5% annual coupon. The finance manager asks you to do some research and provide a fair price for this bond. You know that the firm just issued a 15-year bond two years ago with the par of $1,000 and 5% semi-annual coupon. The current price for this existing bond is $985. What is the fair price of the new bond you should provide to the manager? (assuming they have the same EAR) $1,106.79 $1,097.28 $1,103.66 $ 985

Answer 1

arket price of the new bond: $1,103.66

Step-by-step explanation:

We solve for the market rate using excel goal seekor a financial calculator

Considering the current market value of the bond is equal to the present value of the coupon payment and maturity:

Coupon payment are ordinary annuity

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

While the maturity is a lump sum

`(Maturity)/((1 + rate)^(time) ) = PV`

The bond is the sum of both.

from this we got that market rate is equal to 0.0516

Now, we can determinate the presetn value of the new bond using this rate:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 32.50 (1,000 face value x 6.5% / 2)

time 20 (10 years x 2 payment per year)

rate 0.0258 (5.16% annual rate divide by 2 coverted to semiannual)

`32.5 * (1-(1+0.0258)^(-20) )/(0.0258) = PV\\`

PV $502.8400

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity: Face value of $ 1,000.00

time and rate same as the coupon payment

`(1000)/((1 + 0.0258)^(20) ) = PV`

PV 600.82

PV coupon $502.8400 + PV maturity $600.8224 = $1,103.6624