The Carter Company's bond mature in 10 years have a par value of 1,000 and an annual coupon payment of $80. The market interest rate for the bond is 9%. What is the price of these bonds
The coupon rate on the bond, (interest/principal at maturity) = 8%
Since prevailing market interest rate is higher, the bond is worth more than its "par" or maturity value of 1000, assuming it is highly rated or guaranteed.
The formula you need to do the calculation can be found at
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It is bascially the present value of future interest rates plus the principal at maturity, based upon the actual interst rate in the market for that ten-year term.
I meant to say the bond is worth LESS than 1000 because the coupon rate is less than the market rate. The website I gave you has the correct formula. Use the version based on annual rather than semiannual payments.
To calculate the price of the bonds, we can use the formula for the present value of a bond. The formula is as follows:
Price of Bond = (Coupon Payment / (1 + Market Interest Rate)^1) + (Coupon Payment / (1 + Market Interest Rate)^2) + ... + (Coupon Payment + Par Value / (1 + Market Interest Rate)^n)
In this case, the Coupon Payment is $80, the Market Interest Rate is 9%, and the Par Value is $1,000. The bond matures in 10 years.
Using the formula, we can calculate the price of the bonds:
Price of Bond = (80 / (1 + 0.09)^1) + (80 / (1 + 0.09)^2) + ... + (80 + 1000 / (1 + 0.09)^10)
To simplify the calculation, we can use a financial calculator or spreadsheet software. Alternatively, we can break down the calculation into steps.
Step 1:
Calculate the present value of each coupon payment:
Coupon Payment / (1 + Market Interest Rate)^n
For the example, we will calculate the present value for each year using the given values:
Year 1: 80 / (1 + 0.09)^1 = 73.39
Year 2: 80 / (1 + 0.09)^2 = 67.19
...
Year 10: (80 + 1000) / (1 + 0.09)^10 = 693.06
Step 2:
Sum up the present values of all coupon payments:
73.39 + 67.19 + ... + 693.06 = 953.23
So, the price of the bonds is approximately $953.23.