Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 10 percent
ID: 2811732 • Letter: K
Question
Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 10 percent annual interest. The current yield to maturity on such bonds in the market is 15 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.
Compute the price of the bonds for these maturity dates: (Do not round intermediate calculations. Round your final answers to 2 decimal places. Assume interest payments are annual.)
a. 30 years
b. 17 years
c. 2 years
Explanation / Answer
Interest received every year = $1000 * 10% = $100
Redeemable value = $1000
Present Value Factor = Current yield to maturity = 15%
a. Price of the bond if the maturity is 30 years
Present Value of Bond = Present value of Interest received for 30 years + Present value of redeemable value of bond at the end of 30th year
= Present value of $100 for 30 years + Present Value of $1000 at the end of 30th year
= ($100 * Present value interest factor annuity of 15% for 30 years) + ($1000 * Present value factor of 15% for 30th year)
= ($100 * 6.565979) + ($1000 * 0.015103)
= $656.5979 + $15.103
= $671.70
b. Price of the bond if the maturity is 17 years
Present Value of Bond = Present value of Interest received for 17 years + Present value of redeemable value of bond at the end of 17th year
= Present value of $100 for 17 years + Present Value of $1000 at the end of 17th year
= ($100 * Present value interest factor annuity of 15% for 17 years) + ($1000 * Present value factor of 15% for 17th year)
= ($100 * 6.047161) + ($1000 * 0.0929258)
= $604.7161 + $92.9258
= $697.64
c. Price of the bond if the maturity is 2 years
Present Value of Bond = Present value of Interest received for 2 years + Present value of redeemable value of bond at the end of 2nd year
= Present value of $100 for 2 years + Present Value of $1000 at the end of 2nd year
= ($100 * Present value interest factor annuity of 15% for 2 years) + ($1000 * Present value factor of 15% for 2nd year)
= ($100 * 1.625708) + ($1000 * 0.7561436)
= $162.5708 + $756.1436
= $918.7144
Note: Here present value interest factor annuity is the cummulative present value factors for the given years ( that is the grand total of all the present value factors)
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