The Faulk Corp. has a 6 percent coupon bond outstanding. The Gonas Company has a

Question

The Faulk Corp. has a 6 percent coupon bond outstanding. The Gonas Company has a 12 percent bond outstanding. Both bonds have 15 years to maturity, make semiannual payments, and have a YTM of 9 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (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.) Percentage change in price of Faulk Percentage change in price of Gonas What if interest rates suddenly fall by 2 percent instead? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Percentage change in price of Faulk Percentage change in price of Gonas

Explanation / Answer

Rates rise by 2%

Percentage change in Price of Faulk= -15.749%

Percentage change in Price of Gonas=-13.79569%

Rates fall by 2%

Percentage change in Price of Faulk=20.164%

Percentage change in Price of Gonas=17.3159%

EXPLANATION

Bond Price=C/(1+r/2)+C/(1+r/2)^2+C/(1+r/2)^3.............C/(1+r/2)^30+FV/(1+r/2)^30

=2C/r*(1-1/(1+r/2)^30)+FV/(1+r/2)^30

Faulk:

Face Value=1000

Coupons=6%*1000/2=30

N=15*2=30

YTM=9%

Current Price of Faulk

=2*30/9%*(1-1/(1+9%/2)^30)+1000/(1+9%/2)^30

=755.667

Now if rates rise by 2%, then

price=2*30/11%*(1-1/(1+11%/2)^30)+1000/(1+11%/2)^30

=>price=636.656

So, % change in price=(636.656-755.667)/755.667=-15.749%

Now if rates fall by 2%, then

price=2*30/7%*(1-1/(1+7%/2)^30)+1000/(1+7%/2)^30

=>price=908.0397

So, % change in price=(908.0397-755.667)/755.667=20.164%

Similarly,

Gonas:

Face Value=1000

Coupons=12%*1000/2=60

N=15*2=30

YTM=9%

Current Price of Gonas

=2*60/9%*(1-1/(1+9%/2)^30)+1000/(1+9%/2)^30

=1244.333

Now if rates rise by 2%, then

price=2*60/11%*(1-1/(1+11%/2)^30)+1000/(1+11%/2)^30

=>price=1072.66873

So, % change in price=(1072.66873-1244.333)/1244.333=-13.79569%

Now if rates fall by 2%, then

price=2*60/7%*(1-1/(1+7%/2)^30)+1000/(1+7%/2)^30

=>price=1459.801

So, % change in price=(1459.801-1244.333)/1244.333=17.3159%

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