Question

Both Bond Bill and Bond Ted have 11.2 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 4 years to maturity, whereas Bond Ted has 21 years to maturity. Both bonds have a par value of 1,000.

If rates were to suddenly fall by 3 percent instead, what would be the percentage change in the price of bills bills bonds?

Answer 1

Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 11.2 percent. If the YTM suddenly falls to 8.2 percent:

PBill= $56(PVIFA4.1%,8) + $1,000(PVIF4.1%,8) = $1,100.58

PTed= $56(PVIFA4.1%,42) + $1,000(PVIF4.1%,42) = $1,298.23

ΔPBill% = ($1,100.58 – 1,000) / $1,000 = 0.10058 or +10.06%

ΔPTed% = ($1,298.23 – 1,000) / $1,000 = 0.29823 or +29.82%

All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates.