Bond J has a coupon rate of 5.7 percent. Bond S has a coupon rate of 15.7 percen
ID: 2729795 • Letter: B
Question
Bond J has a coupon rate of 5.7 percent. Bond S has a coupon rate of 15.7 percent. Both bonds have ten years to maturity, make semiannual payments, and have a YTM of 12.4 percent. Requirement 1: 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).) Percentage change in price Bond J -17.513 % Bond S -14.42 % Requirement 2: 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).) Percentage change in price Bond J % Bond S %
I need the Second Requirement!
Explanation / Answer
Original Price: Semi-annual interest payment , YTM = 12.4% (reduced to 6.2% per semi-annual) having maturity of 10 years (extended to 20 Semi-annuals)
Price = coupon interest half year * PVIFA(6.2%, 20) + Bond par value * PVIF(6.2%, 20)
Bond J = Coupon Interest rate 5.7% per annum
Price = $28.50 * 11.2860 + $1000 * 0.3003 = $621.95
Bond S = Coupon Interest rate 15.7% per annum
Price = $78.5 * 11.2860 + $1000 * 0.3003 = $1186.25
Requirement 1: If interest rates suddenly rise by 3 percent,
Bond J = Coupon Interest rate 8.7% per annum
Price = $43.50 * 11.2860 + $1000 * 0.3003 = $791.24
Bond S = Coupon Interest rate 18.7% per annum
Price = $93.50 * 11.2860 + $1000 * 0.3003 = $1355.54
Percentage of Change :
Bond J = (791.24 - 621.95) / 621.95 = + 27.22%
Bond S = (1355.54 - 1186.25) / 1186.25 = + 14.27%
Requirement 2: If interest rates suddenly fall by 3 percent instead,
Bond J = Coupon Interest rate 2.7% per annum
Price = $13.50 * 11.2860 + $1000 * 0.3003 = $452.66
Bond S = Coupon Interest rate 12.7% per annum
Price = $63.50 * 11.2860 + $1000 * 0.3003 = $1016.96
Percentage of Change :
Bond J = (452.66 - 621.95) / 621.95 = - 27.22%
Bond S = (1016.96 - 1186.25) / 1186.25 = - 14.27%