Question

Consider the following Nestle Inc Bond: maturity: 10 years. coupon rate: 8% (paid semi-annually, face value: $1000. Your investment advisor has told you that the yield-to-maturity on this bond is 7.5%. What should be the price of this bond?

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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 = 8% * $1000 * 6 /12 = $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 yield to maturity rate, which is 7.5% /2 = 3.75%, with 10*2 = 20 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 = 3.75% and n is the time period = 20

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

PVA = $40 * (1 - (1 + 3.75%)^-20 / 3.75%)

PVA = $40 * (1 - ( 1+ 0.0375)^-20 / 0.0375)

PVA = $40 * (1 - ( 1.0375)^-20 / 0.375)

PVA = $40 * ((1 - 0.47889234205) / 0.0375)

PVA = $40 * (0.52110765795 / 0.0375)

PVA = $40 * 13.896204212

PVA = $555.85

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 = 3.75%, n= time period = 20

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

$1000 = PV * (1 + 3.75%)²⁰

$1000 = PV * (1 + 0.0375)²⁰

$1000 = PV * (1.0375)²⁰

$1000 = PV * 2.08815199613

PV = $1000 / 2.08815199613

PV = $478.89

Now,

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

Bond price = $555.85 + $478.89 = $1034.74