Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, an
ID: 2710948 • Letter: B
Question
Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent what is the percentage change in the price of Bond Sam and Bond Dave? (Negative amounts 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.) If rates were to suddenly fell by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round Intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g.. 32.16.)Explanation / Answer
For both Sam and Dave,
Let P =price of Bond=1000, c=coupon on Bond=8%*1000/2=40, y be the current market rate of interest=8%(as both the bonds are priced at par) and FV= par value=1000,
Sam time to maturity=3yrs thus total periods=T=2*3=6
Dave time to maturity=20 yrs thus total periods=T=2*20=40
interest rate rises to 10% by 2%,
y=10%,Price of Sam Bond=(2*40/.10)(1-1/(1+.10/2)6)+1000/(1+.10/2)6
Price of Sam Bond=(2*40/.10)*(1-0.746)+746.215=949.243
% change in price of Bond Sam=(949.243-1000)/1000=-5.08%
y=10%,Price of Dave Bond=(2*40/.10)(1-1/(1+.10/2)40)+1000/(1+.10/2)40
Price of Dave Bond=(2*40/.10)*(1-0.142045)+142.045=828.409
% change in price of Bond Dave =(828.409-1000)/1000=-17.16%
if interest rate declines to 6% by 2%,
y=6%,Price of Sam Bond=(2*40/.06)(1-1/(1+.06/2)6)+1000/(1+.06/2)6
Price of Sam Bond=(2*40/.06)*(1-0.837484)+837.484=1054.172
% change in price of Bond Sam=(1054.172-1000)/1000=5.42%
y=10%,Price of Dave Bond=(2*40/.06)(1-1/(1+.06/2)40)+1000/(1+.06/2)40
Price of Dave Bond=(2*40/.06)*(1-0.3065568)+306.5568=1231.148
% change in price of Bond Dave =(1231.148-1000)/1000=23.12%
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