Homework SourseBond J has a coupon rate of 3 percent and Bond K has a coupo
Bond J has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent Both bonds have 17 years to maturity, make semiannual payments, and have a YTM of 6 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 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 BondJ Percentage change in price of Bond K 
Solution
1) Percentage change in Price of Bond J -20.98% Percentage change in Price of Bond K -17.08% Workings: Price of Bond is the Present Value of Cash flow from bond. Cash flow of bond is dicounted at the rate of YTM to find present value. Step-1:Calculation of current value of Both Bond Bond J Bond K Current Value 683 1,317 Working: a. Par Value of Both Bond $ 1,000 b. Semi annual coupon interest of : Bond J = Par Value x Semi annual coupon interest = $ 1,000 x 1.5% = $ 15 Bond K = Par Value x Semi annual coupon interest = $ 1,000 x 4.5% = $ 45 c. Cumulative discount factor of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.03)^-34)/0.03 i 3% = 21.1318 n 34 d. Discount factor of 1 = (1+i)^-n = (1+0.03)^-34 = 0.3660 e. Present Value of Bond J: Present Value of Coupon $ 15 x 21.1318 = 317 Present Value of Par Value $ 1,000 x 0.3660 = 366 Present Value of Bond J 683 f. Present Value of bond K: Present Value of Coupon $ 45 x 21.1318 = 951 Present Value of Par Value $ 1,000 x 0.3660 = 366 Present Value of Bond J 1,317 Step-2:Calculation of Price of both bond after rise of 2% in interest rate Bond J Bond K Current Value 540 1,092 Working: a. Par Value of Both Bond $ 1,000 b. Semi annual coupon interest of : Bond J = Par Value x Semi annual coupon interest = $ 1,000 x 1.5% = $ 15 Bond K = Par Value x Semi annual coupon interest = $ 1,000 x 4.5% = $ 45 c. Cumulative discount factor of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.04)^-34)/0.04 i 4% = 18.4112 n 34 d. Discount factor of 1 = (1+i)^-n = (1+0.04)^-34 = 0.2636 e. Present Value of Bond J: Present Value of Coupon $ 15 x 18.4112 = 276 Present Value of Par Value $ 1,000 x 0.2636 = 264 Present Value of Bond J 540 f. Present Value of bond K: Present Value of Coupon $ 45 x 18.4112 = 829 Present Value of Par Value $ 1,000 x 0.2636 = 264 Present Value of Bond J 1,092 Step-3:Calculation of Percentage change in price of both bond Bond J Bond K Existing Price a 683 1,317 Revised Price b 540 1,092 Percentage change c=(b-a)/a -20.98% -17.08% 2) Percentage change in Price of Bond J 28.47% Percentage change in Price of Bond K 22.44% Workings: Step-1:Calculation of Price of both bond after fall of 2% in interest rate Bond J Bond K Revised price 878 1,612 Working: a. Par Value of Both Bond $ 1,000 b. Semi annual coupon interest of : Bond J = Par Value x Semi annual coupon interest = $ 1,000 x 1.5% = $ 15 Bond K = Par Value x Semi annual coupon interest = $ 1,000 x 4.5% = $ 45 c. Cumulative discount factor of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.02)^-34)/0.02 i 2% = 24.49859 n 34 d. Discount factor of 1 = (1+i)^-n = (1+0.02)^-34 = 0.510028 e. Present Value of Bond J: Present Value of Coupon $ 15 x 24.4986 = 367 Present Value of Par Value $ 1,000 x 0.5100 = 510 Present Value of Bond J 878 f. Present Value of bond K: Present Value of Coupon $ 45 x 24.4986 = 1,102 Present Value of Par Value $ 1,000 x 0.5100 = 510 Present Value of Bond J 1,612 Step-3:Calculation of Percentage change in price of both bond Bond J Bond K Existing Price a 683 1,317 Revised Price b 878 1,612 Percentage change c=(b-a)/a 28.47% 22.44%