Question

Madsen Motors's bonds have 8 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 12%; and the yield to maturity is 10%. What is the bond's current market price? Round your answer to the nearest cent.

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

Annual bond interest = 12% * $1000  = $120

Bond interest payments will be 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 yield to maturity rate, which is 10%, with 8 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 = $120, r is the rate of interest = 10% and n is the time period = 8

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

PVA = $120 * (1 - (1 + 10%)^-8 / 10%)

PVA = $120 * (1 - ( 1+ 0.10)^-8 / 0.10)

PVA = $120 * (1 - ( 1.10)^-8 / 0.10)

PVA = $120 * ((1 - 0.46650738021) / 0.10)

PVA = $120 * (0.53349261979 / 0.10)

PVA = $120 * 5.3349261979

PVA = $640.19

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 = 10%, n= time period = 8

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

$1000 = PV * (1 + 10%)⁸

$1000 = PV * (1 + 0.10)⁸

$1000 = PV * (1.10)⁸

$1000 = PV * 2.14358881

PV = $1000 / 2.14358881

PV = $466.507

Now,

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

Bond price = $640.19 + $466.507 = $1106.70