Bond J has a coupon rate of 5.5 percent Bond S has a coupon rate of 15.5 percent
ID: 2760852 • Letter: B
Question
Bond J has a coupon rate of 5.5 percent Bond S has a coupon rate of 15.5 percent. Both bonds have eight years to maturity, make semiannual payments and have a YTM of 12 percent. Requirement 1: If interest rates suddenly use by 3 percent. that is the percentage change m 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).) Requirement 2: The interest rates suddenly fall by 3 percent instead. What 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).)Explanation / Answer
requirement 1
Bond J
Yield to maturity = 5.5 + (100 - price/8) / (100 + price/2)
0.12 = (44 +100 - price ) / 8 * 2 / (100+ price)
0.12 = 144 - price /4 * 1 / (100 + price)
0.12 = (144 - price) / (400 + 4 price)
48 + 0.48price = 144 - price
0.48 price +1 price = 144 - 48
price = 96 / 1.48
price = $64.86
increase in rate = 3%
new rate = (5.5 % +3%)
= 8.5%
Yield to maturity = 8.5 + (100 - price/8) / (100 + price/2)
0.12 = (68+100 - price ) / 8 * 2 / (100+ price)
0.12 = 168 - price /4 * 1 / (100 + price)
0.12 = (168 - price) / (400 + 4 price)
48 + .48 price = 168 - price
1.48 price = 120
price = 81.08
Percentage change in price = (81.08 - 64.86)/ 64.86
= 16.22/64.86
= 25.01%
Bond S
Yield to maturity = 15.5 + (100 - price/8) / (100 + price/2)
0.12 = (124 +100 - price ) / 8 * 2 / (100+ price)
0.12 = 224 - price /4 * 1 / (100 + price)
0.12 = (224 - price) / (400 + 4 price)
48 + .48 price = 224 - price
1.48 price = 176
price = $118.92
increase in rate = 3%
new rate = (15.5 % +3%)
= 18.5%
Yield to maturity = 18.5 + (100 - price/8) / (100 + price/2)
0.12 = (148+100 - price ) / 8 * 2 / (100+ price)
0.12 = 248 - price /4 * 1 / (100 + price)
0.12 = (248 - price) / (400 + 4 price)
48 + .48 price = 248 - price
1.48 price = 200
price = $135.14
Percentae change in price = (135.14 - 118.92 )/ 118.92
=16.22 / 118.92
=13.64%