Final answer:
To determine the price of Kilgore Natural Gas's bonds for different maturities, present value calculations considering the coupon rate, yield to maturity, and time to maturity are used. The prices for bonds with 30 years, 15 years, and 1 year until maturity will differ based on the provided market interest rate (yield to maturity) of 12 percent. For a 1-year maturity, the bond's price would not exceed $964 when the market interest rate is 12%.
Step-by-step explanation:
Kilgore Natural Gas has a $1,000 par value bond that pays 9 percent annual interest. The current yield to maturity for similar bonds in the market is 12 percent. To calculate the price of the bond for different maturities, we can use the formula for the present value of a bond:
P = C * (1 - (1 + r)^-n) / r + F / (1 + r)^n,
where P is the price of the bond, C is the annual coupon payment, r is the yield to maturity (market interest rate), n is the number of years to maturity, and F is the face value of the bond.
For a 30-year maturity:
C = $1,000 * 9% = $90
r = 12% or 0.12
n = 30
F = $1,000
Plugging these values into the formula gives us the price of the bond for a 30-year maturity.
For a 15-year maturity:
n = 15
Using the same formula, we can calculate the price for a 15-year maturity by changing the value of n.
For a 1-year maturity:
n = 1
As mentioned, the expected payment from the bond one year from now is $1,080. However, since the market interest rates are now at 12%, you would not pay more than the present value of that payment at the market interest rate, which is $964 as per the formula:
$964 * (1 + 0.12) = $1,080
Therefore, the price for a bond with a 1-year maturity should not exceed $964.