An investor has two bonds in his portfolio that both have a face value of $1,000

Question

An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 11% annual coupon. Bond L matures in 11 years, while Bond S matures in 1 year. Assume that only one more interest payment is to be made on Bond S at its maturity and that 11 more payments arc to be made on Bond L. a. What will the value of the Bond L be if the going interest rate is 6%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 6%? Round your answer to the nearest cent. $ What will the value of the Bond L be if the going interest rate is 8%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 8%? Round your answer to the nearest cent. $ What will the value of the Bond L be if the going interest rate is 14%? Round your answer to the nearest cent. $ What will the value of the Bond S be if the going interest rate is 14%? Round your answer to the nearest cent. $ b. Why docs the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change? I. Long-term bonds have lower reinvestment rate risk then do short-term bonds. II. The change in price due to a change in the required rate of return increases as a bond's maturity decreases. III. Long-term bonds have greater interest rate risk then do short-term bonds. IV. The change in price due to a change in the required rate of return decreases as a bond's maturity increases. V. Long-term bonds have lower interest rate risk then do short-term bonds.

Explanation / Answer

A. Formula: Bond Value = C {[1-(1+(YTM))-t/(YTM)] + [F / (1+ (YTM))t]

Value of bonds with 6% interest rate:

B0 =?
C = $1,000 x 11% = $110
F = $1,000
YTM = 6% (Going interest rates)
t = 11

Value of Bond L= $110*{[1-(1+(0.06))-11/(0.06)] + [$1,000 / (1+ (0.06))11] = $1,394

B0 =?
C = $1,000 x 11% = $110
F = $1,000
YTM = 6% (Going interest rates)
t = 1

Value of Bond S= $110*{[1-(1+(0.06))-1/(0.06)] + [$1,000 / (1+ (0.06))1] = $1,047

Value of bonds with 8% interest rate:

B0 =?
C = $1,000 x 11% = $110
F = $1,000
YTM = 8% (Going interest rates)
t = 11

Value of Bond L= $110*{[1-(1+(0.08))-11/(0.08)] + [$1,000 / (1+ (0.08))11] = $1,214

B0 =?
C = $1,000 x 11% = $110
F = $1,000
YTM = 8% (Going interest rates)
t = 1

Value of Bond S= $110*{[1-(1+(0.08))-1/(0.08)] + [$1,000 / (1+ (0.08))1] = $1,028

Value of bonds with 14% interest rate:

B0 =?
C = $1,000 x 11% = $110
F = $1,000
YTM = 14% (Going interest rates)
t = 11

Value of Bond L= $110*{[1-(1+(0.14))-11/(0.14)] + [$1,000 / (1+ (0.14))11] = $836

B0 =?
C = $1,000 x 11% = $110
F = $1,000
YTM = 14% (Going interest rates)
t = 1

Value of Bond S= $110*{[1-(1+(0.14))-1/(0.14)] + [$1,000 / (1+ (0.14))1] = $974

B. Long-term bonds have greater interest rate risk then do short-term bonds.

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