Question 1187352: 11. Ten years ago the Jamaica Nice Company issued a 30-year bond with a $1,000 par value. to the public. The bonds have a 10.50% annual coupon rate. If investors require a yield to maturity of 9.0% what is the current price of the bonds?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the current price of the bond:
**1. Determine the remaining years to maturity:**
* The bond was issued 10 years ago and had a 30-year maturity.
* Therefore, there are 20 years remaining until the bond matures.
**2. Calculate the annual coupon payment:**
* Coupon rate = 10.50%
* Par value = $1,000
* Annual coupon payment = 0.105 * $1,000 = $105
**3. Use the present value formula for a bond:**
The current price of the bond is the present value of all future cash flows (coupon payments and par value) discounted at the yield to maturity.
Bond Price = (C * [1 - (1 + r)^-n] / r) + (FV / (1 + r)^n)
Where:
* C = Annual coupon payment ($105)
* r = Yield to maturity (9.0% or 0.09)
* n = Number of years to maturity (20)
* FV = Face value or par value of the bond ($1,000)
**4. Plug the values into the formula:**
Bond Price = ($105 * [1 - (1 + 0.09)^-20] / 0.09) + ($1,000 / (1 + 0.09)^20)
**5. Calculate the present value of the coupon payments:**
* (1 + 0.09)^-20 ≈ 0.1784
* 1 - 0.1784 ≈ 0.8216
* $105 * 0.8216 / 0.09 ≈ $956.11
**6. Calculate the present value of the par value:**
* $1,000 / (1 + 0.09)^20 ≈ $178.41
**7. Add the present values together:**
Bond Price ≈ $956.11 + $178.41 ≈ $1,134.52
**Therefore, the current price of the bond is approximately $1,134.52.**
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