Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has six years to maturity, whereas Bond Dave has 19 years to maturity.

a.   If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b.   If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave?

Answer 1

a)

Bond Sam:

If rates suddenly increase by 4%, the new YTM will be = 7% + 2% =9%

Then current price of bond is:

=PV(9%/2,6*2,70/2,1000)

=908.81

Change in price =908.81-1000/1000 = -9.12%

Bond Dave:

If rates suddenly increase by 4%, the new YTM will be = 7% + 2% =9%

Then current price of bond is:

=PV(9%/2,19*2,70/2,1000)

=819.50

Change in price =819.50-1000/1000 = -18.05%

b)

Bond Sam:

If rates suddenly fall by 2%, the new YTM will be = 7% - 2% =5%

Then current price of bond is:

=PV(5%/2,6*2,70/2,1000)

=1102.58

Change in price =1102.58-1000/1000 = 10.26%

Bond Dave:

Then the current price of the bond is:

=PV(5%/2,19*2,70/2,1000)

=1243.49

Change in price =1243.59-1000/1000 = 24.35%