Question

BOND VALUATION

1.) An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 6% annual coupon. Bond L matures in 20 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 20 more payments are to be made on Bond L.

1. What will the value of the Bond L be if the going interest rate is 4%? Round your answer to the nearest cent.
   $
   
   What will the value of the Bond S be if the going interest rate is 4%? Round your answer to the nearest cent.
   $
   
   What will the value of the Bond L be if the going interest rate is 9%? Round your answer to the nearest cent.
   $
   
   What will the value of the Bond S be if the going interest rate is 9%? Round your answer to the nearest cent.
   $
   
   What will the value of the Bond L be if the going interest rate is 11%? Round your answer to the nearest cent.
   $
   
   What will the value of the Bond S be if the going interest rate is 11%? Round your answer to the nearest cent.
   $
   
2. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?
   
   1. Long-term bonds have greater interest rate risk than do short-term bonds.
   2. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
   3. Long-term bonds have lower interest rate risk than do short-term bonds.
   4. Long-term bonds have lower reinvestment rate risk than do short-term bonds.
   5. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.

Answer 1

Answer a.

Bond L:

Face Value = $1,000

Annual Coupon Rate = 6%
Annual Coupon = 6% * $1,000
Annual Coupon = $60

Time to Maturity = 20 years

If interest rate is 4%:

Price of Bond = $60 * PVIFA(4%, 20) + $1,000 * PVIF(4%, 20)
Price of Bond = $60 * (1 - (1/1.04)^20) / 0.04 + $1,000 / 1.04^20
Price of Bond = $1,271.81

If interest rate is 9%:

Price of Bond = $60 * PVIFA(9%, 20) + $1,000 * PVIF(9%, 20)
Price of Bond = $60 * (1 - (1/1.09)^20) / 0.09 + $1,000 / 1.09^20
Price of Bond = $726.14

If interest rate is 11%:

Price of Bond = $60 * PVIFA(11%, 20) + $1,000 * PVIF(11%, 20)
Price of Bond = $60 * (1 - (1/1.11)^20) / 0.11 + $1,000 / 1.11^20
Price of Bond = $601.83

Bond S:

Face Value = $1,000

Annual Coupon Rate = 6%
Annual Coupon = 6% * $1,000
Annual Coupon = $60

Time to Maturity = 1 year

If interest rate is 4%:

Price of Bond = $60 * PVIF(4%, 1) + $1,000 * PVIF(4%, 1)
Price of Bond = $60 / 1.04 + $1,000 / 1.04
Price of Bond = $1,019.23

If interest rate is 9%:

Price of Bond = $60 * PVIF(9%, 1) + $1,000 * PVIF(9%, 1)
Price of Bond = $60 / 1.09 + $1,000 / 1.09
Price of Bond = $972.48

If interest rate is 11%:

Price of Bond = $60 * PVIF(11%, 1) + $1,000 * PVIF(11%, 1)
Price of Bond = $60 / 1.11 + $1,000 / 1.11
Price of Bond = $954.95

Answer b.

Long-term bonds have higher interest rate risk than do short-term bonds.