Consider a bond that pays an annual coupon of 5 percent and that has three years remaining until maturity. Assume the term structure of interest rates is flat at 6 percent. How much does the bond price change over the next twelve-month interval if the term structure of interest rates does not change?
Click on the arrows to vote for the correct answer
A. B. C. D.A
The bond price change is computed as follows: Bond Price Change =
New Price "" Old Price = (5/1.06 + 105/1.062) - 5/1.06 + 5/1.062 + 105/1.063 = 0.84.
To calculate the bond price change over a twelve-month interval, we need to understand the relationship between bond prices and interest rates.
When interest rates change, the prices of fixed-rate bonds tend to move in the opposite direction. In this case, the bond pays an annual coupon of 5 percent, which is fixed. If interest rates increase, the bond's fixed coupon becomes less attractive compared to newly issued bonds that offer higher coupon rates, resulting in a decrease in the bond's price. Conversely, if interest rates decrease, the bond's fixed coupon becomes more attractive relative to new bonds, leading to an increase in the bond's price.
Given that the term structure of interest rates is flat at 6 percent and the bond has three years remaining until maturity, we can calculate the bond price change as follows:
First, we need to determine the present value of the bond's future cash flows. The bond pays an annual coupon of 5 percent, so each year the bondholder will receive 5 percent of the face value as a coupon payment. At the end of the third year, the bondholder will receive the face value of the bond.
Since the term structure of interest rates is flat at 6 percent, we can discount each cash flow using this rate. The present value of the coupon payments is calculated as follows:
Year 1: Coupon payment = 5% x Face Value PV(Coupon1) = Coupon1 / (1 + Interest Rate)^1
Year 2: Coupon payment = 5% x Face Value PV(Coupon2) = Coupon2 / (1 + Interest Rate)^2
Year 3: Coupon payment = 5% x Face Value + Face Value (maturity payment) PV(Coupon3) = Coupon3 / (1 + Interest Rate)^3
To calculate the bond price, we sum up the present value of all the cash flows:
Bond Price = PV(Coupon1) + PV(Coupon2) + PV(Coupon3)
Next, we calculate the bond price change over the next twelve-month interval by adjusting the cash flows. Since there are three years remaining until maturity, the next twelve-month interval will cover the second and third years.
To calculate the bond price change, we need to calculate the present value of the adjusted cash flows for the second and third years. We adjust the coupon payments for the remaining two years and recalculate the bond price using the same formula as above.
Finally, we subtract the new bond price from the original bond price and divide it by the original bond price to determine the percentage change:
Bond Price Change = (New Bond Price - Original Bond Price) / Original Bond Price
Now, let's calculate the bond price change step by step:
Original Bond Price: PV(Coupon1) = 5% x Face Value / (1 + 6%)^1 PV(Coupon2) = 5% x Face Value / (1 + 6%)^2 PV(Coupon3) = (5% x Face Value + Face Value) / (1 + 6%)^3
Bond Price = PV(Coupon1) + PV(Coupon2) + PV(Coupon3)
New Bond Price: PV(Adjusted Coupon2) = 5% x Face Value / (1 + 6%)^1 PV(Adjusted Coupon3) = (5% x Face Value + Face Value) / (1 + 6%)^2
Adjusted Bond Price = PV(Coupon1) + PV(Adjusted Coupon2) + PV(Adjusted Coupon3)
Bond Price Change = (Adjusted Bond Price - Original Bond Price) / Original Bond Price
By plugging in the numbers and performing the calculations, we find that the bond price change over the next twelve-month interval is approximately