Step-by-step explanation:
To calculate the change in price the bond will experience in dollars, we need to compare the bond's price at the current yield to maturity (8.0 percent) with its price at the expected yield to maturity in one year (7.6 percent).
Let's denote the current price of the bond as P_0 and the price of the bond in one year as P_1.
We are given the following information:
- Coupon rate (annual interest rate): 7.30 percent
- Years left to maturity: 16 years
- Current yield to maturity: 8.0 percent
- Expected yield to maturity in one year: 7.6 percent
First, we need to calculate the future cash flows of the bond and then discount them back to their present value at the new yield to maturity.
Step 1: Calculate the coupon payment at the current yield to maturity:
Coupon payment = Coupon rate * Face value
Coupon payment = 0.0730 * Face value
Step 2: Calculate the present value of future cash flows at the current yield to maturity:
P_0 = [Coupon payment * (1 - (1 + Yield to Maturity)^(-Number of Years to Maturity))] / Yield to Maturity + [Face value / (1 + Yield to Maturity)^Number of Years to Maturity]
Step 3: Calculate the coupon payment in one year (at the new yield to maturity):
Coupon payment in one year = 0.0730 * Face value
Step 4: Calculate the present value of future cash flows at the new yield to maturity:
P_1 = [Coupon payment in one year * (1 - (1 + Expected Yield to Maturity)^(-Number of Years to Maturity + 1))] / Expected Yield to Maturity + [Face value / (1 + Expected Yield to Maturity)^(Number of Years to Maturity - 1)]
Step 5: Calculate the change in price:
Change in price = P_1 - P_0
Now, let's plug in the values and calculate:
P_0 = [0.0730 * Face value * (1 - (1 + 0.08)^(-16))] / 0.08 + [Face value / (1 + 0.08)^16]
P_0 = [0.0730 * Face value * (1 - 0.23826)] / 0.08 + [Face value / 2.77309]
P_0 = [0.0555442 * Face value] + [0.36048 * Face value]
P_0 = 0.4160242 * Face value
P_1 = [0.0730 * Face value * (1 - (1 + 0.076)^(-15))] / 0.076 + [Face value / (1 + 0.076)^15]
P_1 = [0.0730 * Face value * (1 - 0.2145877)] / 0.076 + [Face value / 2.5712026]
P_1 = [0.05739066 * Face value] + [0.38904185 * Face value]
P_1 = 0.44643251 * Face value
Change in price = P_1 - P_0
Change in price = (0.44643251 * Face value) - (0.4160242 * Face value)
Change in price = 0.03040831 * Face value
Since we don't have the face value of the bond, we cannot provide the change in price in dollars. However, you can now multiply the result by the face value of the bond to get the change in price in dollars.