Question

An investor has two bonds in his portfolio that have a face value of $1,000 and pay an 11% annual coupon. Bond L matures in 16 years, while Bond S matures in 1 year.

1. What will the value of the Bond L be if the going interest rate is 6%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 16 more payments are to be made on Bond L. Round your answers to the nearest cent.

   	6%	8%	12%
   Bond L	$	$	$
   Bond S	$	$	$

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 reinvestment rate risk than do short-term bonds.
   2. The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
   3. Long-term bonds have greater interest rate risk than do short-term bonds.
   4. The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
   5. Long-term bonds have lower interest rate risk than do short-term bonds.

Answer 1

Answer a.

Bond L:

Face Value = $1,000

Annual Coupon Rate = 11%
Annual Coupon = 11% * $1,000
Annual Coupon = $110

Time to Maturity = 16 years

If interest rate is 6%:

Price of Bond = $110 * PVIFA(6%, 16) + $1,000 * PVIF(6%, 16)
Price of Bond = $110 * (1 - (1/1.06)^16) / 0.06 + $1,000 / 1.06^16
Price of Bond = $1,505.29

If interest rate is 8%:

Price of Bond = $110 * PVIFA(8%, 16) + $1,000 * PVIF(8%, 16)
Price of Bond = $110 * (1 - (1/1.08)^16) / 0.08 + $1,000 / 1.08^16
Price of Bond = $1,265.54

If interest rate is 12%:

Price of Bond = $110 * PVIFA(12%, 16) + $1,000 * PVIF(12%, 16)
Price of Bond = $110 * (1 - (1/1.12)^16) / 0.12 + $1,000 / 1.12^16
Price of Bond = $930.26

Bond S:

Face Value = $1,000

Annual Coupon Rate = 11%
Annual Coupon = 11% * $1,000
Annual Coupon = $110

Time to Maturity = 1 year

If interest rate is 6%:

Price of Bond = $110 * PVIF(6%, 1) + $1,000 * PVIF(6%, 1)
Price of Bond = $110 / 1.06 + $1,000 / 1.06
Price of Bond = $1,047.17

If interest rate is 8%:

Price of Bond = $110 * PVIF(8%, 1) + $1,000 * PVIF(8%, 1)
Price of Bond = $110 / 1.08 + $1,000 / 1.08
Price of Bond = $1,027.78

If interest rate is 12%:

Price of Bond = $110 * PVIF(12%, 1) + $1,000 * PVIF(12%, 1)
Price of Bond = $110 / 1.12 + $1,000 / 1.12
Price of Bond = $991.07

Answer b.

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