A 7.10 percent coupon bond with 14 years left to maturity is priced to offer a 7.8 percent yield to maturity. You believe that in one year, the yield to maturity will be 7.4 percent. What is the change in price the bond will experience in dollars? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Change in bond price $
To calculate the change in price the bond will experience, we need to find the present value of the bond with the new yield to maturity (7.4 percent) and subtract it from the present value of the bond with the initial yield to maturity (7.8 percent).
First, let's calculate the present value of the bond with the initial yield to maturity (7.8 percent). We can use the present value formula for a bond:
PV = (C / (1 + r)^1) + (C / (1 + r)^2) + ... + (C + F) / (1 + r)^n
Where:
PV = Present value
C = Coupon payment
r = Yield to maturity
n = Number of periods
Using the given information:
C = 7.10 percent of the bond's face value
r = 7.8 percent
n = 14 years
Calculate the present value of the bond with the initial yield to maturity:
PV_initial = (0.0710 * Face value / (1 + 0.078)^1) + (0.0710 * Face value / (1 + 0.078)^2) + ... + (0.0710 * Face value + Face value) / (1 + 0.078)^14
Next, calculate the present value of the bond with the new yield to maturity (7.4 percent):
PV_new = (0.0710 * Face value / (1 + 0.074)^1) + (0.0710 * Face value / (1 + 0.074)^2) + ... + (0.0710 * Face value + Face value) / (1 + 0.074)^14
Finally, calculate the change in bond price:
Change in bond price = PV_new - PV_initial
Solving these calculations will give you the change in bond price in dollars.