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 12 years, while Bond s matures in 1 year.

a. What will the value of each bond 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 12 more payments are to be made on Bond L.

b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change?

No excel, no calulator

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 = 12 years

If interest rate is 6%:

Price of Bond = $110 * PVIFA(6%, 12) + $1,000 * PVIF(6%, 12)
Price of Bond = $110 * (1 - (1/1.06)^12) / 0.06 + $1,000 * (1/1.06)^12
Price of Bond = $110 * 8.383844 + $1,000 * 0.496969
Price of Bond = $1,419.19

If interest rate is 8%:

Price of Bond = $110 * PVIFA(8%, 12) + $1,000 * PVIF(8%, 12)
Price of Bond = $110 * (1 - (1/1.08)^12) / 0.08 + $1,000 * (1/1.08)^12
Price of Bond = $110 * 7.536078 + $1,000 * 0.397114
Price of Bond = $1,226.08

If interest rate is 12%:

Price of Bond = $110 * PVIFA(12%, 12) + $1,000 * PVIF(12%, 12)
Price of Bond = $110 * (1 - (1/1.12)^12) / 0.12 + $1,000 * (1/1.12)^12
Price of Bond = $110 * 6.194374 + $1,000 * 0.256675
Price of Bond = $938.06

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.