Question

Laurel, Inc., and Hardy Corp. both have 6 percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $1,000. The Laurel, Inc., bond has five years to maturity, whereas the Hardy Corp. bond has 18 years to maturity.
A. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
B. If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then?

Answer 1

Answer:

A. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?

Laurel, Inc. = -8.11%

Hardy Corp. = -18.91%

B. If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then?

Laurel, Inc. = +8.98%

Hardy Corp. = +25.49%

Explanation:

bonds with 6% semiannual coupons, sold at par $1,000

Laurel, Inc. bond maturity in 5 years

Hardy Corp. bond maturity in 18 years

the current price of a bond is the sum of the present value of its face value and coupons. I will use an annuity table to calculate PV of face value and an ordinary annuity table for the coupons:

Laurel, Inc.

market rate 4% = ($1,000 x 0.8203) + ($30 x 8.9826) = $820.30 + $269.48 = $1,089.78, % change = 89.78/1,000 = 8.98%

market rate 8% = ($1,000 x 0.6756) + ($30 x 8.1109) = $675.60 + $243.33 = $918.93, % change = -81.07/1,000 = -8.11%

Hardy Corp.

market rate 4% = ($1,000 x 0.4902) + ($30 x 25.489) = $490.20 + $764.67 = $1,254.87, % change = 254.87/1,000 = 25.49%  

market rate 8% = ($1,000 x 0.2437) + ($30 x 18.908) = $243.70 + $567.24 = $810.94, % change = -189.06/1,000 = -18.91%