Question

Moerdyk Corporation's bonds have a 15-year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (rd) is 5.30%, based on semiannual compounding. What is the bond’s price? a. $1,200.05 b. $1,164.05 c. $948.04 d. $1,224.05 e. $1,500.06

Answer 1

Option (a) 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 = 7.25% * $1000 * 1/2 = $36.25

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 5.3% /2 = 2.65%, 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 = $36.25, r is the rate of interest = 2.65% and n is the time period = 30

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

PVA = $36.25 * (1 - (1 + 2.65%)^-30 / 2.65%)

PVA = $36.25 * (1 - ( 1+ 0.0265)^-30 / 0.0265)

PVA = $36.25 * (1 - ( 1.0265)^-30 / 0.265)

PVA = $36.25 * ((1 - 0.45627995369) / 0.0265)

PVA = $36.25 * (0.54372004631 / 0.00265)

PVA = $36.25 * 20.5177375966

PVA = $743.77

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 = 2.65%, n= time period = 30

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

$1000 = PV * (1 + 2.65%)³⁰

$1000 = PV * (1 + 0.0265)³⁰

$1000 = PV * (1.0265)³⁰

$1000 = PV * 2.19163693671

PV = $1000 / 2.19163693671

PV = $456.28

Now,

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

Bond price = $743.77 + $456.28 = $1200.05