Both bond A and bond B have 7.8 percent coupons and are priced at par value. Bon
ID: 2638460 • Letter: B
Question
Both bond A and bond B have 7.8 percent coupons and are priced at par value. Bond A has 9 years to maturity, while bond B has 16 years to maturity.
Asume if interest rates suddenly rise by 2.2 percent, what is the percentage change in price of bond A and bond B? (Round your answer to 2 decimal places. Negative answers should be indicated by a minus sign. Omit the "%" sign in your response.)
b.) Assume if interest rates suddenly fall by 2.2 percent instead, what would the percentage change in price of bond A and bond B? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Please give detailed solutions. Not just answers. Thanks
Both bond A and bond B have 7.8 percent coupons and are priced at par value. Bond A has 9 years to maturity, while bond B has 16 years to maturity.
Explanation / Answer
Let par value be $1000
Since the price is equal to the par value,that means the yiled is equal to the coupan rate i.e 7.8%
a) % change in price of bond A if interest rates suddenly rise by 2.2%:
New yield = 10%
Coupon = $78
New Price of Bond A = 78*((1-(1+10%)^(-9))/10%)+1000/(1+10%)^9
=$873.30
% change in price = (873.30-1000)/1000
=-12.67
% change in price of bond B if interest rates suddenly rise by 2.2%:
New Price of Bond B = 78*((1-(1+10%)^(-16))/10%)+1000/(1+10%)^16
=$827.88
% change in price = (827.88-1000)/1000
=-17.21%
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b) % change in price of bond A if interest rates suddenly falls by 2.2%:
New yield = 5.6%
Coupon = $78
New Price of Bond A = 78*((1-(1+5.6%)^(-9))/5.6%)+1000/(1+5.6%)^9
=$1152.28
% change in price = (1152.28-1000)/1000
=15.23%
% change in price of bond B if interest rates suddenly falls by 2.2%:
New Price of Bond B = 78*((1-(1+5.6%)^(-16))/5.6%)+1000/(1+5.6%)^16
=$1228.57
% change in price = (1228.57-1000)/1000
=22.86%
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