An investor has two bonds in his portfolio that both have a facevalue of 1000 an

Question

An investor has two bonds in his portfolio that both have a facevalue of 1000 and pay a 10 percent annual coupon. Bond L matures in15 years, while Bond S matures in 1 year.
a) What will the value of each bond be if the going interest rateis 5 percent, 8 percent, and 12 percent? Assume that there is onlyone more interest payment to be made on Bond S, at it maturity, and15 more payments on Bond L.
b) Why does the longer-term bond's price vary more when interestrates change than does that of the shorter-term bond?

Explanation / Answer

Calculating Bond value if the Interest rate (YTM)is 5% Bond Value = Present Value of the voupons + Present Value ofthe face amount Bond "L": Bond Value = [C * PVIFA(5%,15)] + [F *PVF(5%, 15) ] Bond Value = [$100 * 10.3797 + $1,000 * 0.4810 Bond Value = [$1,037.97 + $481] Bond Value of "L" = $1,518.97 Bond "S": Bond Value = [C * PVIFA(5%,1)] + [F *PVF(5%, 1) ] Bond Value = [$100 * 0.9524 + $1,000 * 0.9524 Bond Value = [$95.24 + $952.40] Bond Value of "S" = $1,047.64 Calculating Bond value if the Interest rate (YTM)is 8% Bond "L": Bond Value = [C * PVIFA(8%,15)] + [F *PVF(8%, 15) ] Bond Value = [$100 * 8.5595 + $1,000 * 0.3152 Bond Value = [$855.95 + $315.20] Bond Value of "L" = $1,171.15 Bond "S": Bond Value = [C * PVIFA(8%,1)] + [F *PVF(8%, 1) ] Bond Value = [$100 * 0.9259 + $1,000 * 0.9259 Bond Value = [$92.59 + $925.90] Bond Value of "S" = $1,018.49 Calculating Bond value if the Interest rate (YTM)is 12% Bond "L": Bond Value = [C * PVIFA(12%,15)] + [F *PVF(12%, 15) ] Bond Value = [$100 * 6.8109 + $1,000 * 0.1827 Bond Value = [$681.09 + $182.70] Bond Value of "L" = $863.79 Bond "S": Bond Value = [C * PVIFA(12%,1)] + [F *PVF(12%, 1) ] Bond Value = [$100 * 0.8929 + $1,000 * 0.8929 Bond Value = [$89.29 + $829.90] Bond Value of "S" = $919.19 Hope this hleps Calculating Bond value if the Interest rate (YTM)is 5% Bond Value = Present Value of the voupons + Present Value ofthe face amount Bond "L": Bond Value = [C * PVIFA(5%,15)] + [F *PVF(5%, 15) ] Bond Value = [$100 * 10.3797 + $1,000 * 0.4810 Bond Value = [$1,037.97 + $481] Bond Value of "L" = $1,518.97 Bond "S": Bond Value = [C * PVIFA(5%,1)] + [F *PVF(5%, 1) ] Bond Value = [$100 * 0.9524 + $1,000 * 0.9524 Bond Value = [$95.24 + $952.40] Bond Value of "S" = $1,047.64 Calculating Bond value if the Interest rate (YTM)is 8% Bond "L": Bond Value = [C * PVIFA(8%,15)] + [F *PVF(8%, 15) ] Bond Value = [$100 * 8.5595 + $1,000 * 0.3152 Bond Value = [$855.95 + $315.20] Bond Value of "L" = $1,171.15 Bond "S": Bond Value = [C * PVIFA(8%,1)] + [F *PVF(8%, 1) ] Bond Value = [$100 * 0.9259 + $1,000 * 0.9259 Bond Value = [$92.59 + $925.90] Bond Value of "S" = $1,018.49 Calculating Bond value if the Interest rate (YTM)is 12% Bond "L": Bond Value = [C * PVIFA(12%,15)] + [F *PVF(12%, 15) ] Bond Value = [$100 * 6.8109 + $1,000 * 0.1827 Bond Value = [$681.09 + $182.70] Bond Value of "L" = $863.79 Bond "S": Bond Value = [C * PVIFA(12%,1)] + [F *PVF(12%, 1) ] Bond Value = [$100 * 0.8929 + $1,000 * 0.8929 Bond Value = [$89.29 + $829.90] Bond Value of "S" = $919.19

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