Bond J has a coupon rate of 4.3 percent. Bond S has a coupon rate of 14.3 percen
ID: 2775198 • Letter: B
Question
Bond J has a coupon rate of 4.3 percent. Bond S has a coupon rate of 14.3 percent. Both bonds have eleven years to maturity, make semiannual payments, and have a YTM of 9.6 percent.
If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds?(Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)
If interest rates suddenly fall by 3 percent instead, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)
Bond J has a coupon rate of 4.3 percent. Bond S has a coupon rate of 14.3 percent. Both bonds have eleven years to maturity, make semiannual payments, and have a YTM of 9.6 percent.
Explanation / Answer
Answer to Requirement 1
Percentage change in prices
Bond J
-20.42
Bond S
-16.37
Answer to Requirement 2
Percentage change in prices
Bond J
27.51
Bond S
21.33
Bond J
Coupon rate = 4.3% semi-annual payment
Coupon amount = $ 1000 * 4.3% * 0.50 = 21.50
Time to maturity = 11 years or 11* 2 = 22 semi-annual periods
YTM = 9.6%
Semi Annual discount rate = 9.6%/2 = 0.048
Price of the Bond = 21.50 * [1-(1/(1.048)^22]/0.048 + 1000 / 1.048^22
= 21.50 *[1-1/2.8050992]/0.048 + 1000/2.8050992
= 21.50 * (1-0.356494)/0.048 + 1000 * 0.356494
= 21.50 * 13.406375 + 356.494 = 288.2371 + 356.494 = 644.73 (rounded off)
If interest rate suddenly rise by 3% then YTM = 9.6+3 = 12.6% or 6.3% semi annually
Price of the Bond = 21.50 * [1-(1/(1.063)^22]/0.063 + 1000 / 1.063^22
= 21.50 * [1-1/3.8347]/0.063 + 1000 / 3.8347
= 21.50 * [1-0.260777]/0.063 + 1000 * 0.260777
= 21.50 * 0.739223/0.063 + 260.777
= 21.50 * 11.73386 + 260.777 = 252.278 + 260.777 = 513.05 (rounded off)
Net change in price = 513.05 – 644.73 = -131.68
% change in price = (-131.68/644.73) * 100 = - 20.42%
If interest rate suddenly falls by 3% then YTM = 9.6-3 = 6.6% or 3.3% semi annually
Price of the Bond = 21.50 * [1-(1/(1.033)^22]/0.033 + 1000 / 1.033^22
= 21.50 * [1-1/2.0427]/0.033 + 1000 / 2.0427
= 21.50 * [1-0.48955]/0.033 + 1000 * 0.48955
= 21.50 * 0.510452/0.033 + 489.55
= 21.50 * 15.4682 + 489.55 = 332.57+489.55 = 822.12 (rounded off)
Net change in price = 822.12 – 644.73 = 177.39
% change in Price = (177.39/644.73)*100 = 27.51%
Bond S
Coupon rate = 14.3% semi-annual payment
Coupon amount = $ 1000 * 14.3% * 0.50 = 71.50
Time to maturity = 11 years or 11* 2 = 22 semi-annual periods
YTM = 9.6%
Semi Annual discount rate = 9.6%/2 = 0.048
Price of the Bond = 71.50 * [1-(1/(1.048)^22]/0.048 + 1000 / 1.048^22
= 71.50 * 13.406375 + 356.494 = 958.556 + 356.494 = 1315.05
If interest rate suddenly rise by 3% then YTM = 9.6+3 = 12.6% or 6.3% semi annually
Price of the Bond = 71.50 * [1-(1/(1.063)^22]/0.063 + 1000 / 1.063^22
= 71.50 * 11.73386 + 260.777 = 838.971 + 260.777 = 1099.75 (rounded off)
Net change in price = 1099.75 – 1315.05 = -215.30
% change in price = (-215.30/1315.05) * 100 = - 16.37%
If interest rate suddenly falls by 3% then YTM = 9.6-3 = 6.6% or 3.3% semi annually
Price of the Bond = 71.50 * [1-(1/(1.033)^22]/0.033 + 1000 / 1.033^22
= 71.50 * 15.4682 + 489.55 = 1105.976 +489.55 = 1595.53 (rounded off)
Net change in price = 1595.53 – 1315.05 = 280.48
% change in Price = (280.48/1315.05)*100 = 21.33%
Percentage change in prices
Bond J
-20.42
Bond S
-16.37