Question

10.

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 17 years, while Bond S matures in 1 year.

1. What will the value of the Bond L be if the going interest rate is 7%, 8%, and 13%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 17 more payments are to be made on Bond L. Round your answers to the nearest cent.

   	7%	8%	13%
   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 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 = 12%
Annual Coupon = 12% * $1,000
Annual Coupon = $120

Time to Maturity = 17 years

If interest rate is 7%:

Price of Bond = $120 * PVIFA(7%, 17) + $1,000 * PVIF(7%, 17)
Price of Bond = $120 * (1 - (1/1.07)^17) / 0.07 + $1,000 / 1.07^17
Price of Bond = $1,488.16

If interest rate is 8%:

Price of Bond = $120 * PVIFA(8%, 17) + $1,000 * PVIF(8%, 17)
Price of Bond = $120 * (1 - (1/1.08)^17) / 0.08 + $1,000 / 1.08^17
Price of Bond = $1,364.87

If interest rate is 13%:

Price of Bond = $120 * PVIFA(13%, 17) + $1,000 * PVIF(13%, 17)
Price of Bond = $120 * (1 - (1/1.13)^17) / 0.13 + $1,000 / 1.13^17
Price of Bond = $932.71

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 7%:

Price of Bond = $120 * PVIF(7%, 1) + $1,000 * PVIF(7%, 1)
Price of Bond = $120 / 1.07 + $1,000 / 1.07
Price of Bond = $1,046.73

If interest rate is 8%:

Price of Bond = $120 * PVIF(8%, 1) + $1,000 * PVIF(8%, 1)
Price of Bond = $120 / 1.08 + $1,000 / 1.08
Price of Bond = $1,037.04

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.