Question

Interest Rate RISK Bond Sam and Bond Dave both have 6 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. Bond Sam bond has five years to maturity, whereas the Bond Dave bond has 18 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? (A negative answer should be indicated by a minus sign. Do not round Intermedlate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

The value of Bond Sam and Bond Dave will decrease with an interest rate rise, with longer-term Bond Dave being more sensitive to this change due to its longer maturity. To provide an example with numbers, let's consider a two-year bond issued at $3,000 with an 8% interest rate. Initially, the present value of the bond's payments would be calculated using the original 8% discount rate. If interest rates rise to 11%, the present value of those same payments would be discounted at the higher rate, resulting in a lower current value of the bond.

Step-by-step explanation:

When interest rates rise, the price of existing bonds typically falls, since newer bonds are likely to be issued at the higher current interest rates, making existing bonds with lower rates less attractive. For both Bond Sam and Bond Dave, which have a 6 percent coupon rate and are priced at par, a 2 percent increase in interest rates would lead to a decrease in the bond prices; however, the percentage change in the price of these bonds would depend on their remaining time to maturity. Since Bond Dave has a longer duration with 18 years until maturity, it will be more sensitive to changes in interest rates compared to Bond Sam, which only has 5 years to maturity.

The bond pricing formula indicates that bond price is inversely related to the yield to maturity. Therefore, if we calculate the new price of the bonds with the increased interest rates using the present value of future cash flows, we can determine by what percentage each bond's price has changed. Usually, longer-term bonds experience larger price swings in response to interest rate changes than shorter-term bonds.

To provide an example with numbers, let's consider a two-year bond issued at $3,000 with an 8% interest rate. Initially, the present value of the bond's payments would be calculated using the original 8% discount rate. If interest rates rise to 11%, the present value of those same payments would be discounted at the higher rate, resulting in a lower current value of the bond.