Question

Coupon rate for a $1000 corporate bond is 9%. This bond is paying coupon semi-annually and will mature in 9 years. If the current market yield for this bond is 8%, what would be the value of this bond?

Answer 1

Price / value 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 = 9% * $1000 * 1/2 = $45

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 market yield, which is 8% /2 = 4%, with 9*2 = 18 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 = $45, r is the rate of interest = 4% and n is the time period = 18

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

PVA = $45 * (1 - (1 + 4%)^-18 / 4%)

PVA = $45 * (1 - ( 1+ 0.04)^-18 / 0.04)

PVA = $45 * (1 - ( 1.04)^-18 / 0.04)

PVA = $45 * ((1 - 0.49362812101) / 0.04)

PVA = $45 * (0.50637187898 / 0.04)

PVA = $45 * 12.6592969747

PVA = $569.67

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 = 4%, n= time period = 18

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

$1000 = PV * (1 + 4%)¹⁸

$1000 = PV * (1 + 0.04)¹⁸

$1000 = PV * (1.04)¹⁸

$1000 = PV * 2.02581651538

PV = $1000 / 2.02581651538

PV = $493.63

Now,

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

Bond price = $569.67 + $493.63 = $1063.30