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The question is incomplete as the maturity dates are missing. The complete question is as follows,
Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 19 percent annual interest. The current yield to maturity on such bonds in the market is 11 percent. Compute the price of the bonds for these maturity dates:
a. 40 years
b. 17 years
c. 8 years
(Do not round intermediate calculations. Round your final answers to 2 decimal places. Assume interest payments are annual.)
Answer:
a.
Bond Price = $1716.084065 rounded off to $1716.08
b.
Bond Price = $1603.90355 rounded off to $1603.90
c.
Bond Price = $1411.68982 rounded off to $1411.69
Explanation:
To calculate the quote/price of the bond today, which is the present value of the bond, we will use the formula for the price of the bond. As the bond is an annual bond, we will use the annual coupon payment, number of periods and annual YTM. The formula to calculate the price of the bonds today is attached.
<u>a. 40 Years </u>
Coupon Payment (C) = 1000 * 0.19 = $190
Total periods remaining (n) = 40
r or YTM = 0.11 or 11%
Bond Price = 190 * [( 1 - (1+0.11)^-40) / 0.11] + 1000 / (1+0.11)^40
Bond Price = $1716.084065 rounded off to $1716.08
<u>b. 17 Years </u>
Coupon Payment (C) = 1000 * 0.19 = $190
Total periods remaining (n) = 17
r or YTM = 0.11 or 11%
Bond Price = 190 * [( 1 - (1+0.11)^-17) / 0.11] + 1000 / (1+0.11)^17
Bond Price = $1603.90355 rounded off to $1603.90
<u>c. 8 Years </u>
Coupon Payment (C) = 1000 * 0.19 = $190
Total periods remaining (n) = 8
r or YTM = 0.11 or 11%
Bond Price = 190 * [( 1 - (1+0.11)^-8) / 0.11] + 1000 / (1+0.11)^8
Bond Price = $1411.68982 rounded off to $1411.69
