A 7.10 percent coupon bond with 14 years left to maturity is priced to offer a yield to maturity of 7.9 percent. 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. Round your final answer to 2 decimal places.)
To calculate the change in price the bond will experience, we need to find the current price of the bond and calculate the future price of the bond using the new yield to maturity.
1. Calculate the current price of the bond:
Since the bond is priced to offer a yield to maturity of 7.9 percent, we can use the present value formula for bonds to calculate the current price.
PV = C * (1 - (1 / (1 + r)^n)) / r + (F / (1 + r)^n)
Where:
PV = present value or current price of the bond
C = coupon payment per period (7.10% * Face Value)
r = yield to maturity (7.9%)
n = number of periods left to maturity (14 years)
F = Face Value of the bond
2. Calculate the future price of the bond using the new yield to maturity:
Using the same formula as above, we can now use the new yield to maturity (7.4%) to calculate the future price of the bond.
PV_new = C * (1 - (1 / (1 + r_new)^n)) / r_new + (F / (1 + r_new)^n)
Where:
PV_new = future price of the bond
C = coupon payment per period (7.10% * Face Value)
r_new = new yield to maturity (7.4%)
n = number of periods left to maturity (13 years)
3. Calculate the change in price:
Change in price = future price - current price
Change in price = PV_new - PV
Now let's calculate the current price of the bond using the given information:
C = 7.10% * Face Value = 0.071 * F
r = 7.9% = 0.079
n = 14 years
PV = 0.071 * F * (1 - (1 / (1 + 0.079)^14)) / 0.079 + (F / (1 + 0.079)^14)
Using this formula, we can calculate the current price of the bond.
Next, let's calculate the future price of the bond using the new yield to maturity:
C = 7.10% * Face Value = 0.071 * F
r_new = 7.4% = 0.074
n = 13 years
PV_new = 0.071 * F * (1 - (1 / (1 + 0.074)^13)) / 0.074 + (F / (1 + 0.074)^13)
Using this formula, we can calculate the future price of the bond.
Finally, we can calculate the change in price:
Change in price = PV_new - PV
Calculate the difference between the future price and the current price to find the change in price. Round your final answer to 2 decimal places.