Bond J is a 8 percent coupon bond. Bond K is a 12 percent coupon bond. Both bond
ID: 2777776 • Letter: B
Question
Bond J is a 8 percent coupon bond. Bond K is a 12 percent coupon bond. Both bonds have 12 years to maturity and have a YTM of 9.5 percent.
If interest rates suddenly rise by 1 percent, what is the percentage price change of these bonds? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
If interest rates suddenly fall by 1 percent, what is the percentage price change of these bonds? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
a.
If interest rates suddenly rise by 1 percent, what is the percentage price change of these bonds? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
Explanation / Answer
a) % price change with increase in interest rate of 1%
Bond J = (new price - original price ) / original price * 100
= ( J1 - OJ) / OJ * 100
= (961.7834 - 893.6306)/893.6306*100
= 7.63 %
Bond K =
(new price - original price ) / original price * 100
= ( K1 - OK) / OK * 100
= (1267.5159 - 1191.0828) / 1191.0828 * 100
= 6.42%
a) % price change with increase in interest rate of 1%
Bond J = (new price - original price ) / original price * 100
= ( J1 - OJ) / OJ * 100
= (961.7834 - 893.6306)/893.6306*100
= 7.63 %
Bond K =
(new price - original price ) / original price * 100
= ( K1 - OK) / OK * 100
= (1267.5159 - 1191.0828) / 1191.0828 * 100
= 6.42%
a) % price change with increase in interest rate of 1%
Bond J = (new price - original price ) / original price * 100
= ( J1 - OJ) / OJ * 100
= (961.7834 - 893.6306)/893.6306*100
= 7.63 %
Bond K =
(new price - original price ) / original price * 100
= ( K1 - OK) / OK * 100
= (1267.5159 - 1191.0828) / 1191.0828 * 100
= 6.42%
b) % price change with decrease in interest rate of 1%
Bond J = (new price - original price ) / original price * 100
= ( J2 - OJ) / OJ * 100
= (808.9172 - 893.6306)/893.6306*100
= - 9.48%
Bond K =
(new price - original price ) / original price * 100
= ( K2 - OK) / OK * 100
= (1114.6497 - 1191.0828) / 1191.0828 * 100
= - 6.42%
Original Status Increase of 1% Decrease of 1% 8% 12% 9% 13% 7% 11% Bond J Bond K Bond J Bond K Bond J Bond K Face Value (F) 1000 1000 1000 1000 1000 1000 Coupon Rate ' © 80 120 90 130 70 110 YTM 9.50% 9.50% 9.50% 9.50% 9.50% 9.50% Number of years (n) 12 12 12 12 12 12 YTM =( C + (F - P)/n)/(F + P)/2 Price of Share at original Status = Bond J 0.095 = (80 + (1000 -x)/12)/(1000 +x)/2 0.095 = (80 +(1000 - x)/12) * 2/1000 + x 0.095 = (960 + 1000 -x)/12 * 2 / 1000 + x 570 + 1.57 x = 1960 x = (1960 -570) /1.57 OJ = 893.6306 Price of Share at original Status = Bond K 0.095 = (120 + (1000 -x)/12)/(1000 +x)/2 0.095 = (120+(1000 - x)/12) * 2/1000 + x 0.095 = (1440 + 1000 -x)/12 * 2 / 1000 + x SE 570 + 1.57 x = 2440 x = (2440 -570) /1.57 OK = 1191.0828 Price of Share at 1% rate of increase = Bond J 0.095 = (90 + (1000 -x)/12)/(1000 +x)/2 0.095 = (90 +(1000 - x)/12) * 2/1000 + x 0.095 = (1080 + 1000 -x)/12 * 2 / 1000 + x 570 + 1.57 x = 2080 x = (2080 -570) /1.57 J1 = 961.7834 Price of Share at 1% rate decrease = Bond J 0.095 = (70 + (1000 -x)/12)/(1000 +x)/2 0.095 = (70 +(1000 - x)/12) * 2/1000 + x 0.095 = (840 + 1000 -x)/12 * 2 / 1000 + x 570 + 1.57 x = 1840 x = (1840 -570) /1.57 J2 = 808.9172 Price of Share at 1% rate of increase = Bond K 0.095 = (130 + (1000 -x)/12)/(1000 +x)/2 0.095 = (130+(1000 - x)/12) * 2/1000 + x 0.095 = (1560 + 1000 -x)/12 * 2 / 1000 + x 570 + 1.57 x = 2560 x = (2560 -570) /1.57 K1 = 1267.5159 Price of Share at 1% rate decrease = Bond K 0.095 = (110 + (1000 -x)/12)/(1000 +x)/2 0.095 = (110 +(1000 - x)/12) * 2/1000 + x 0.095 = (1320 + 1000 -x)/12 * 2 / 1000 + x 570 + 1.57 x = 2320 x = (2320 -570) /1.57 K2 = 1114.6497