Question

Using the following information to answer the following questions?

Both Bond A and Bond B have 8 percent coupons, make semiannual payments, and are priced at par value. Bond A has 3 years to maturity, whereas Bond B has 20 years to maturity.

a. If interest rates suddenly rise by 2 percent annually (to 10% annually right now), what would be the percentage changes in the prices of Bond A and Bond B?

b. If rates were to suddenly drop by 2 percent instead (to 6% right now), what would be the percentage changes in the prices of Bond A and Bond B?

c. What does this problem tell you about the interest rate risk of long-term bonds?

Answer 1

a:

Bond A				Bond B
Coupon	PMT	40		Coupon	PMT	40
Number of semiannual periods	Nper	6		Number of semiannual periods	Nper	40
Semiannual YTM	Rate	5		Semiannual YTM	Rate	5
After increase
Price	PV	$949.24		Price	PV	$828.41
% change		-5.08%		% change		-17.16%

b:

BOND A				BOND B
After decrease
Semiannual YTM	Rate	3		Semiannual YTM	Rate	3
Price	PV	$1,054.17		Price	PV	$1,231.15
% change		5.42%		% change		23.11%

c: This says that bonds with a higher maturity have a greater change in price due to a change in interest rates.

WORKINGS