An investor has two bonds in his portfolio that have a face value of $1,000 and
ID: 1170092 • Letter: A
Question
An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond matures in a year while Bonds matures i ·er. Assume that only one more interest payment is to be made on Bond S at its maturity and that 20 more payments are to be made on Bond L. a, what will the value of the Bond L be if the going interest rate is 5967 Round your answer to the nearest cent. what will the value of the Bond S be if 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 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 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 decreases as a bond's maturity increases. II. Long-term bonds have lower interest rate risk than do short-term bonds III. Long-term bonds have lower reinvestment rate risk than do short-term bonds IV. The change in price due to a change in the required rate of return increases as a bond's maturity decreases. V. Long-term bonds have greater interest rate risk than do short-term bonds. Select-+Explanation / Answer
Answer a.
Bond L:
Face Value = $1,000
Annual Coupon = 10% * $1,000 = $100
Time to Maturity = 20 years
If Interest Rate is 5%:
Current Price = $100 * PVIFA(5%, 20) + $1,000 * PVIF(5%, 20)
Current Price = $100 * (1 - (1/1.05)^20) / 0.05 + $1,000 / 1.05^20
Current Price = $1,623.11
If Interest Rate is 8%:
Current Price = $100 * PVIFA(8%, 20) + $1,000 * PVIF(8%, 20)
Current Price = $100 * (1 - (1/1.08)^20) / 0.08 + $1,000 / 1.08^20
Current Price = $1,196.36
If Interest Rate is 14%:
Current Price = $100 * PVIFA(14%, 20) + $1,000 * PVIF(14%, 20)
Current Price = $100 * (1 - (1/1.14)^20) / 0.14 + $1,000 / 1.14^20
Current Price = $735.07
Bond S:
Face Value = $1,000
Annual Coupon = 10% * $1,000 = $100
Time to Maturity = 1 years
If Interest Rate is 5%:
Current Price = $100 * PVIF(5%, 1) + $1,000 * PVIF(5%, 1)
Current Price = $100 / 1.05 + $1,000 / 1.05
Current Price = $1,047.62
If Interest Rate is 8%:
Current Price = $100 * PVIF(8%, 1) + $1,000 * PVIF(8%, 1)
Current Price = $100 / 1.08 + $1,000 / 1.08
Current Price = $1,018.52
If Interest Rate is 14%:
Current Price = $100 * PVIF(14%, 1) + $1,000 * PVIF(14%, 1)
Current Price = $100 / 1.14 + $1,000 / 1.14
Current Price = $964.91
Answer b.
The change in price due to a change in the required rate of return increases as a bond’s maturity increases.
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