Question

ssume a corporation's bond has 14 years remaining until maturity. The coupon interest rate is 9.6% and the bond pays interest semi-annually. Assume bond investors' required rate of return on the bond is 8.3%. What would be the expected market price of this bond. (Assume a $1000 par value.) Answer to 2 decimal places.

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 = 9.6% * $1000 * 1/2 = $48

while calculating the present values, we will use semi annual rate of return as interest rate. Semi annual rate of return = 8.3% / 2 = 4.15%

We will now calculate the present value of interest payments and present value of bond maturity.

Calculation of present value of bond interest payments:

Bond interest payments will be semi annual every year, so it is an annuity. We will use the following formula to find the present value bond interest payment:

PVA = P * (1 - (1 + r)^-n / r)

where, P is the periodical amount = $4800, r is the rate of interest = 4.15% and n is the time period = 14 * 2 = 28 semi annual periods

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

PVA = $48 * (1 - (1 + 4.15%)^-28 / 4.15%)

PVA = $48 * (1 - (1 + 0.0415)^-28 / 0.0415)

PVA = $48 * (1 - (1.0415)^-28 / 0.0415)

PVA = $48 * (1 - 0.32028774371) / 0.0415)

PVA = $48 * (0.67971225629 / 0.0415)

PVA = $48 * 16.3786085853012

PVA = $786.173212

Calculation of Present value of bond at maturity:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $1000, PV = Present Value, r = rate of interest = 4.15%, n= time period = 28

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

$1000 = P * (1 + 4.15%)²⁸

$1000 = P * (1 + 0.0415)²⁸

$1000 = P * (1.0415)²⁸

$1000 = P * 3.1221925273

P = $1000 / 3.1221925273

P = $320.28774371

Now,

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

Putting the values in the above equation, we get,

Bond price = $786.173212 + $320.28774371

Bond price = $1106.46