Bond J has a coupon rate of 4.1 percent. Bond S has a coupon rate of 14.1 percen
ID: 2779049 • Letter: B
Question
Bond J has a coupon rate of 4.1 percent. Bond S has a coupon rate of 14.1 percent. Both bonds have nine years to maturity, make semiannual payments, and have a YTM of 9.2 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 4.1 percent. Bond S has a coupon rate of 14.1 percent. Both bonds have nine years to maturity, make semiannual payments, and have a YTM of 9.2 percent.
Explanation / Answer
Answer to Requirement 1
Percentage change in Price
Bond J
-18.43%
Bond S
-14.94%
Answer to Requirement 2
Percentage change in Price
Bond J
23.74%
Bond S
18.76%
Bond J
Coupon rate = 4.1%
Coupon amount = $100 * 4.1% * 0.5 = $2.05
Time to maturity n = 9 years * 2 = 18 semi-annual periods
YTM r = 9.2% or 9.2/2 = 4.6% semi-annual rate
Current Price = $ 2.05 * [(1-(1/(1.046)^18)/0.046] + $ 100/1.046^18
= $ 2.05 * [(1-(1/2.246831)/0.046] + $100/2.246831
= $ 2.05 * [(1-0.445071)/0.046] + $ 44.5071
= $ 2.05 * 0.554929/0.046 + $ 44.5071
= $ 2.05 * 12.06367 + $ 44.5071
= $ 24.7305 + $ 44.5071
= $ 69.2376 or $ 69.24 (rounded off)
If there is sudden 3% increase in interest rates, that is required rate = 9.2+3 = 12.2% or 6.1% semi-annually
Price of Bond = $ 2.05 * [(1-(1/(1.061)^18)/0.061] + $ 100/1.061^18
= $ 2.05 * [(1-(1/2.9031997)/0.061] + $ 100/2.9031997
= $ 2.05 * [(1-0.3444475)/0.061] + $ 34.4448
= $ 2.05 * (0.6555525/0.061) + $ 34.4448
= $ 2.05 * 10.7467623 + $ 34.4448
= $ 22.0309 + $ 34.4448
= $ 56.4757 or $ 56.48 (rounded off)
Change in price of bond = $ 56.48 - $ 69.24 = -$12.76
Percentage change in Price = (-$12.76/$69.24) * 100 = -18.4286 or -18.43%
If the interest rates fall by 3%,required rate of return is 9.2-3 = 6.2% or 3.1% semi-annually
Price = $ 2.05 * [(1-(1/(1.031)^18)/0.031] + $ 100/1.031^18
= $ 2.05 * [(1-(1/1.73243111)/0.031] + $ 100/1.73243111
= $ 2.05 * [(1-0.577224)/0.031] + $ 57.7224
= $ 2.05 * (0.422776/0.031) + $ 57.7224
= $ 2.05 * 13.63794 + $ 57.7224
= $ 27.9578 + $ 57.7224
= $ 85.68
Change in price = $ 85.68 - $ 69.24 = $ 16.44
Percentage change in price = (16.44/69.24)*100 = 23.7435 or 23.74% (rounded off)
Bond S
Coupon Rate = 14.1% paid semi-annually
Coupon Payment = $ 100 * 14.1% * 0.5 = $ 7.05
Ytm = 9.2% or semi-annual rate of 4.6%
Taking the figures from the calculations above as all the other details are same
Price of the bond = $ 7.05 * 12.06367 + $ 44.5071
= $ 85.0489 + $ 44.5071
= $ 129.556 or $129.56 (rounded off)
Interest rates raise by 3%, required rate of return 9.2+3 = 12.2% or 6.1% semi-annually
Price of the bond = $ 7.05 * 10.7467623 + $ 34.4448
= $ 75.7647 + $ 34.4448
= $ 110.2095 or $ 110.21 (rounded off)
Change in Price = $ 110.21 - $ 129.56 = - $ 19.35
Percentage change in price = (-19.35/129.56)*100 = -14.9352% or -14.94% (rounded off)
Interest rates fall by 3%, required rate of return 9.2-3 = 6.2% or 3.1% semi-annually
Price = $ 7.05 * 13.63794 + $ 57.7224
= $ 96.1475 + $ 57.7224
= $ 153.8699 or $ 153.87 (rounded off)
Change in Price = $ 153.87 - $ 129.56 = $ 24.31
Percentage change in price = (24.31/129.56)*100 = 18.7635% or 18.76% (rounded off)
Percentage change in Price
Bond J
-18.43%
Bond S
-14.94%