BOND VALUATION An investor has two bonds in his portfolio that have a face value
ID: 2789764 • Letter: B
Question
BOND VALUATION An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 11% annual coupon, Bond L matures in 15 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 15 more payments are to be made on Bond L. a, what will the value or the Bond L be ir the going interest rate is 5%? Round your answer to the nearest cent. What will the value or the Bond S be ir the going interest rate is 5%? Round your answer to the nearest cent. what will the value of the Bond L be if the going interest rate is 10%? Round your answer to the nearest cent. what will the value of the Bond S be if the going interest rate is 10%? Round your answer to the nearest cent. What will the value of the Bond L be if the going interest rate is 129%? Round your answer to the nearest cent. 931.89 what will the value of the Bond S be if the going interest rate is 12%? Round your answer to the nearest cent. 991.07 b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change? I. The change in price due to a change in the required rate of return increases as a bond's maturity decreases. II. Long-term bonds have greater interest rate risk than do short-term bonds. III. The change in price due to a change in the required rate of return decreases as a bond's maturity increases IV. Long-term bonds have lower interest rate risk than do short-term bonds. V. Long-term bonds have lower reinvestment rate risk than do short-term bonds. -select-Explanation / Answer
Answer a.
If Interest Rate is 5%:
Bond L:
Face Value = $1,000
Annual Coupon = 11%*$1,000 = $110
Time to Maturity = 15 years
Price of Bond = $110 * PVA of $1 (5%, 15) + $1,000 * PV of $1 (5%, 15)
Price of Bond = $110 * (1 - (1/1.05)^15) / 0.05 + $1,000 / 1.05^15
Price of Bond = $1,622.78
Bond S:
Face Value = $1,000
Annual Coupon = 11%*$1,000 = $110
Time to Maturity = 1 years
Price of Bond = $110 / 1.05 + $1,000 / 1.05
Price of Bond = $1,057.14
If Interest Rate is 10%:
Bond L:
Face Value = $1,000
Annual Coupon = 11%*$1,000 = $110
Time to Maturity = 15 years
Price of Bond = $110 * PVA of $1 (10%, 15) + $1,000 * PV of $1 (10%, 15)
Price of Bond = $110 * (1 - (1/1.10)^15) / 0.10 + $1,000 / 1.10^15
Price of Bond = $1,076.06
Bond S:
Face Value = $1,000
Annual Coupon = 11%*$1,000 = $110
Time to Maturity = 1 years
Price of Bond = $110 / 1.10 + $1,000 / 1.10
Price of Bond = $1,009.09
If Interest Rate is 12%:
Bond L:
Face Value = $1,000
Annual Coupon = 11%*$1,000 = $110
Time to Maturity = 15 years
Price of Bond = $110 * PVA of $1 (12%, 15) + $1,000 * PV of $1 (12%, 15)
Price of Bond = $110 * (1 - (1/1.12)^15) / 0.12 + $1,000 / 1.12^15
Price of Bond = $931.89
Bond S:
Face Value = $1,000
Annual Coupon = 11%*$1,000 = $110
Time to Maturity = 1 years
Price of Bond = $110 / 1.12 + $1,000 / 1.12
Price of Bond = $991.07
Answer b.
Long-term bonds have greater interest rate risk than do short-term bonds.
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