Question

Bond j has a coupon rate of 5 percent. bond k has a coupon rate of 15 percent. both bonds have eight years to maturity, a par value of $1,000, and a ytm of 11 percent, and both make semiannual payments. if interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? note: a negative answer 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. if interest rates suddenly fall by 2 percent instead, what is the percentage change in the price of these bonds? note: do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.

Answer 1

When market interest rates fluctuate, the prices of existing bonds adjust through changes in their present value. A rise in interest rates decreases the present value and hence the price of a bond, while a fall in rates has the opposite effect, increasing a bond's price.

Step-by-step explanation:

The change in the price of bonds due to interest rate fluctuations can be understood by calculating their present value using different discount rates. Let's consider a simple two-year bond issued for $3,000 with an 8% coupon rate. Initially, the present value of this bond is calculated using an 8% discount rate, which is the same as the coupon rate, hence, the price of the bond would be at par, which is the face value of $3,000. However, if the discount rate increases to 11% due to a rise in market interest rates, the present value of the bond's future cash flows (interest payments and the principal repayment) would decrease, leading to a lower price for the bond.

For Bond J with a 5% coupon rate and Bond K with a 15% coupon rate, with all else being equal, an increase in interest rates by 2% would lead to a reduction in their prices because the present value of their future cash flows would become less attractive compared to new bonds issued at higher rates. Conversely, if interest rates fell by 2%, the prices of Bond J and Bond K would increase as their higher coupon payments would become more valuable compared to new bonds issued at the lower rates.