Question

Nesmith Corporation's outstanding bonds have a $1,000 par value, a 12% semiannual coupon, 16 years to maturity, and a 16% YTM. What is the bond's 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

Semi annual bond interest = 12% * $1000 * 1/2 = $60

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 YTM, which is 16% /2 = 8%, with 16*2 = 32 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 = $60, r is the rate of interest = 8% and n is the time period = 32

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

PVA = $60 * (1 - (1 + 8%)^-32 / 8%)

PVA = $60 * (1 - ( 1+ 0.08)^-32 / 0.08)

PVA = $60 * (1 - ( 1.08)^-32 / 0.08)

PVA = $60 * ((1 - 0.08520004505) / 0.08)

PVA = $60 * (0.91479995494 / 0.08)

PVA = $60 * 11.4349994368

PVA = $686.0999

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 = 8%, n= time period = 32

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

$1000 = PV * (1 + 8%)³²

$1000 = PV * (1 + 0.08)³²

$1000 = PV * (1.08)³²

$1000 = PV * 11.7370829954

PV = $1000 / 11.7370829954

PV = $85.20

Now,

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

Bond price = $686.0999 + $85.20 = $771.30