Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent
ID: 2782775 • Letter: B
Question
Bond J has a coupon rate of 5 percent and Bond K has a coupon rate of 11 percent. Both bonds have 14 years to maturity, make semiannual payments, and have a YTM of 8 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (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.) Percentage change in price of Bond J Percentage change in price of Bond K 1% What if 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 Bond JExplanation / Answer
Formula for Bond price is:
Present Bond price = C1/(1+r) + C2/(1+r)2+...+ C28/(1+r)28 + FV/(1+r)28
C1, C2, ...C28 are semi-annual coupons. Discount rate "r" is yield to maturity.
Let us assume that the face value (FV) of bond is $ 100.
Coupon payment of bond J is 5% i.e. coupon payment = $ 5 . Semi-annual payment = $5/2 = $ 2.5
Coupon payment of bond J is 11% i.e. coupon payment = $ 11 . Semi-annual payment = $11/2 = $ 5.5
Since its a semi-annual bond, the yield to maturity will also be halved. SO, YTM = 4%
Price of bond J = $ 75
Price of bond K = $ 125
(1) Increase in interest rates by 2%. This implies that YTM increases to 10%.
Price of bond J = $ 62.75
Price of bond K = $ 107.45
% change in price of bond J = [ (62.75 - 75)/75 ] * 100 = - 16.33 %
% change in price of bond K = [ 107.45 - 125)/125 ] * 100 = - 14.04 %
(2) Decrease in interest rates by 2%. This implies that YTM decreases to 6%.
Price of bond J = $ 90.62
Price of bond K = $ 146.91
% change in price of bond J = [ ( 90.62 - 75)/75 ] * 100 = 20.83 %
% change in price of bond K = [ (146.91 - 125)/125 ] * 100 = 17.53 %