A 20-year, $1,000 par value bond has a 9% annual coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now
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TA MÈRE
SOIT
1000/925 X 0.25 / 1000/925^15
To find the price of the bond 5 years from now, we need to calculate the future value of both the coupon payments and the par value.
Step 1: Calculate the coupon payment:
Coupon payment = Annual coupon * Par value
Coupon payment = 9% * $1,000
Coupon payment = $90
Step 2: Calculate the future value of the coupon payments:
Future value of the coupon payments = Coupon payment * (1 + Yield to Maturity)^Number of periods
Future value of the coupon payments = $90 * (1 + 9%)^5
Future value of the coupon payments = $90 * 1.09^5
Future value of the coupon payments = $90 * 1.5386
Future value of the coupon payments = $138.47 (rounded to two decimal places)
Step 3: Calculate the future value of the par value:
Future value of the par value = Par value * (1 + Yield to Maturity)^Number of periods
Future value of the par value = $1,000 * (1 + 9%)^5
Future value of the par value = $1,000 * 1.09^5
Future value of the par value = $1,000 * 1.5386
Future value of the par value = $1,538.60 (rounded to two decimal places)
Step 4: Calculate the future price of the bond:
Future price = Future value of the coupon payments + Future value of the par value
Future price = $138.47 + $1,538.60
Future price = $1,677.07 (rounded to two decimal places)
Therefore, the price of the bond 5 years from now will be $1,677.07
To calculate the future price of the bond 5 years from now, we need to consider the current price, the coupon rate, the time remaining until maturity, and the yield to maturity.
Here are the steps to calculate the future price:
1. Calculate the annual coupon payment: The annual coupon payment can be calculated by multiplying the coupon rate (9%) by the par value ($1,000). In this case, the annual coupon payment is $90 (0.09 * $1,000).
2. Calculate the total coupon payments over the bond's remaining life: Since the bond has a remaining life of 20 years and the coupon payments are made annually, the total coupon payments will be $90 multiplied by the remaining years (20 - 5 = 15). Therefore, the total coupon payments over the bond's remaining life will be $1,350 (15 * $90).
3. Determine the yield to maturity (YTM): The yield to maturity is the rate of return an investor can expect to earn if the bond is held until maturity. Since the YTM remains at its current rate, we can assume it is constant.
4. Calculate the present value of the bond's future cash flows: To find the future price of the bond, we need to calculate the present value of the future cash flows, which consist of the remaining coupon payments and the final principal payment ($1,000). We can use the present value formula for a bond:
Future price = Present value of remaining coupon payments + Present value of principal payment
The present value of the remaining coupon payments can be calculated by discounting each individual coupon payment by the YTM. The formula for present value is:
PV = C / (1 + r) ^ n
Where:
PV = Present value
C = Cash flow
r = Discount rate (YTM)
n = Time period
Repeat this calculation for each remaining year and sum up the results.
5. Calculate the present value of the principal payment: The principal payment is $1,000, which will be received in 5 years. Calculate its present value using the same formula as in step 4.
6. Add the present value of the remaining coupon payments and the present value of the principal payment to get the present value of the future cash flows.
7. Subtract the present value of the remaining cash flows from the current price of the bond ($925) to find the future price of the bond 5 years from now.
Note: Keep in mind that future prices of bond can vary depending on market conditions and changes in interest rates. This calculation assumes the yield to maturity remains constant.