Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 12% annual coupon. Bond L matures in 10 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 10 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 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 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 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.
   $   
   
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 lower interest rate risk than do short-term bonds.
   2. Long-term bonds have lower reinvestment rate risk than do short-term bonds.
   3. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
   4. Long-term bonds have greater interest rate risk than do short-term bonds.
   5. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

Answer 1

Answer a.

Bond L:

Face Value = $1,000

Annual Coupon Rate = 12%
Annual Coupon = 12% * $1,000
Annual Coupon = $120

Time to Maturity = 10 years

If interest rate is 6%:

Price of Bond = $120 * PVIFA(6%, 10) + $1,000 * PVIF(6%, 10)
Price of Bond = $120 * (1 - (1/1.06)^10) / 0.06 + $1,000 / 1.06^10
Price of Bond = $1,441.61

If interest rate is 9%:

Price of Bond = $120 * PVIFA(9%, 10) + $1,000 * PVIF(9%, 10)
Price of Bond = $120 * (1 - (1/1.09)^10) / 0.09 + $1,000 / 1.09^10
Price of Bond = $1,192.53

If interest rate is 14%:

Price of Bond = $120 * PVIFA(14%, 10) + $1,000 * PVIF(14%, 10)
Price of Bond = $120 * (1 - (1/1.14)^10) / 0.14 + $1,000 / 1.14^10
Price of Bond = $895.68

Bond S:

Face Value = $1,000

Annual Coupon Rate = 12%
Annual Coupon = 12% * $1,000
Annual Coupon = $120

Time to Maturity = 1 year

If interest rate is 6%:

Price of Bond = $120 * PVIF(6%, 1) + $1,000 * PVIF(6%, 1)
Price of Bond = $120 / 1.06 + $1,000 / 1.06
Price of Bond = $1,056.60

If interest rate is 9%:

Price of Bond = $120 * PVIF(9%, 1) + $1,000 * PVIF(9%, 1)
Price of Bond = $120 / 1.09 + $1,000 / 1.09
Price of Bond = $1,027.52

If interest rate is 14%:

Price of Bond = $120 * PVIF(14%, 1) + $1,000 * PVIF(14%, 1)
Price of Bond = $120 / 1.14 + $1,000 / 1.14
Price of Bond = $982.46

Answer b.

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