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 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.

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 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 13%? Round your answer to the nearest cent.
   $
   
   What will the value of the Bond S be if the going interest rate is 13%? 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. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
   2. Long-term bonds have lower interest rate risk than do short-term bonds.
   3. Long-term bonds have lower reinvestment rate risk than do short-term bonds.
   4. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
   5. Long-term bonds have greater interest rate risk than do short-term bonds.

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 = 15 years

If interest rate is 4%:

Price of Bond = $120 * PVIFA(4%, 15) + $1,000 * PVIF(4%, 15)
Price of Bond = $120 * (1 - (1/1.04)^15) / 0.04 + $1,000 / 1.04^15
Price of Bond = $1,889.47

If interest rate is 10%:

Price of Bond = $120 * PVIFA(10%, 15) + $1,000 * PVIF(10%, 15)
Price of Bond = $120 * (1 - (1/1.10)^15) / 0.10 + $1,000 / 1.10^15
Price of Bond = $1,152.12

If interest rate is 13%:

Price of Bond = $120 * PVIFA(13%, 15) + $1,000 * PVIF(13%, 15)
Price of Bond = $120 * (1 - (1/1.13)^15) / 0.13 + $1,000 / 1.13^15
Price of Bond = $935.38

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 4%:

Price of Bond = $120 * PVIF(4%, 1) + $1,000 * PVIF(4%, 1)
Price of Bond = $120 / 1.04 + $1,000 / 1.04
Price of Bond = $1,076.92

If interest rate is 10%:

Price of Bond = $120 * PVIF(10%, 1) + $1,000 * PVIF(10%, 1)
Price of Bond = $120 / 1.10 + $1,000 / 1.10
Price of Bond = $1,018.18

If interest rate is 13%:

Price of Bond = $120 * PVIF(13%, 1) + $1,000 * PVIF(13%, 1)
Price of Bond = $120 / 1.13 + $1,000 / 1.13
Price of Bond = $991.15

Answer b.

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