1 answer

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

Question:

A AB DI Question 2. (20 marks) На Both Bond Sam and Bond Dave have 7 percent coupons, make semi-annual payments, and are pric

A AB DI Question 2. (20 marks) На Both Bond Sam and Bond Dave have 7 percent coupons, make semi-annual payments, and are priced at par value. Bond Sam has 3 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? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

Answers

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.

.

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