A AB DI Question 2. (20 marks) На Both Bond Sam and Bond Dave have 7...

Solution:

Since the bond are selling at par(i.e sale value and face value are same),hence interest rate(YTM) must be equal to coupon rate.Let the fair value(Maturity value) of bond is $1000

Accordingly if the interest rate rise by 2%(i.e 9%),then price of each bond is as follow;

Price of bond is the present value of coupon payable on it and its maturity value.Thus formula for calculating price of bond is;

=Coupon amount*[email protected] rate for given period+Maturity value*[email protected] interest rate for given period

Price of Bond Sam=$35*[email protected]% for 6 period+$1000*[email protected]% for 6th period

=$35*5.1579+$1000*0.7679

=$180.5265+767.90

=$948.42

%Change in price=($1000-$948.42/$1000)*100

=-5.16%

Price of Bond Dave=$35*[email protected] for 40 period+$1000*[email protected] for 40th period

=$35*18.40158+$1000*0.171929

=$644.06+171.93

=$815.98

%change in price=[($1000-$815.98)/$1000]*100

=-18.40%

b)If interest rate fall by 2%(i.e 5%),then price of;

Bond Sam=$35*[email protected]% for 6 period+$1000*[email protected]% for 6th period

=$35*5.508125+$1000*0.862297

=192.78+862.297

=$1055.08

%change in price=[($1000-$1055.08)/$1000]*100

=5.51%

Bond Dave=$35*[email protected]% for 40 period+$1000*[email protected]% for 40th period

=$35*25.10278+$1000*0.37243

=$878.59+$372.43

=$1251.02

%change in price=[($1000-$1251.02)/1000]*100

=25.10%

c)Interest rate risk is higher for Long term bond as compare to short term bond,which is clearly shown above.