Question

Whatever, Inc., has a bond outstanding with a coupon rate of 5.64 percent and semiannual payments. The yield to maturity is 6.1 percent and the bond matures in 15 years. What is the market price if the bond has a par value of $1,000?

Answer 1

Price of the bond can be calculated by the following formula:

Bond price = Present value of interest payment + Present value of bond payment at maturity

Semi annual bond interest = 5.64% * $1000 * 1/2 = $28.2

Bond interest payments will be semi annual every year, so it is an annuity. Bond payment at maturity is a one time payment. The interest rate that will be used in calculating the required present values will be the semi annual yield to maturity, which is 6.1% /2 = 3.05%, with 15*2 = 30 periods.

Now,

First we will calculate the present value of interest payments:

For calculating the present value, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $28.2, r is the rate of interest = 3.05% and n is the time period = 30

Now, putting these values in the above formula, we get,

PVA = $28.2 * (1 - (1 + 3.05%)^-30 / 3.05%)

PVA = $28.2 * (1 - ( 1+ 0.0305)^-30 / 0.0305)

PVA = $28.2 * (1 - ( 1.0305)^-30 / 0.0305)

PVA = $28.2 * ((1 - 0.40603186369) / 0.0305)

PVA = $28.2 * (0.59396813631 / 0.0305)

PVA = $28.2 * 19.47436512491803

PVA = $549.18

Next, we will calculate the present value of bond payment at maturity:

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $1000, PV = Present value, r = rate of interest = 3.05%, n= time period = 30

now, putting theses values in the above equation, we get,

$1000 = PV * (1 + 3.05%)³⁰

$1000 = PV * (1 + 0.0305)³⁰

$1000 = PV * (1.0305)³⁰

$1000 = PV * 2.46286089692

PV = $1000 / 2.46286089692

PV = $406.03

Now,

Bond price = Present value of interest payment + Present value of bond payment at maturity

Bond price = $549.18 + $406.03 = $955.36