Question

A $1,000 par value bond has an 8% coupon rate (paid semiannually). It has 5 years remaining to maturity. If current market interest rate is 6%, what should be the current price of this bond?

a. $1,000

b. $1,268.40

c. $918.89

d. $1,085.30

Answer 1

Option (d) is correct

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 = 8% * $1000 * 1/2 = $40

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 rate, which is 6% /2 = 3%, with 5*2 = 10 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 = $40, r is the rate of interest = 3% and n is the time period = 10

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

PVA = $40 * (1 - (1 + 3%)^-10 / 3%)

PVA = $40 * (1 - ( 1+ 0.03)^-10 / 0.03)

PVA = $40 * (1 - ( 1.03)^-10 / 0.03)

PVA = $40 * ((1 - 0.74409391489) / 0.03)

PVA = $40 * (0.2559060851 / 0.03)

PVA = $40 * 8.53020283678

PVA = $341.21

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%, n= time period = 10

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

$1000 = PV * (1 + 3%)¹⁰

$1000 = PV * (1 + 0.03)¹⁰

$1000 = PV * (1.03)¹⁰

$1000 = PV * 2.19163693671

PV = $1000 / 1.34391637934

PV = $744.09

Now,

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

Bond price = $341.21+ $744.09 = $1085.30