A 10-year bond of face value 100 CCU and coupon rate of 8% was issued exactly six years ago. If the yield to maturity today is 7%, what would be the price of the bond today?
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To calculate the price of the bond today, we need to find the present value of the future cash flows.
Step 1: Calculate the annual coupon payment:
Coupon payment = Face value x Coupon rate
Coupon payment = 100 CCU x 8% = 8 CCU
Step 2: Determine the number of years remaining until maturity:
Years remaining until maturity = Total bond maturity - Number of years passed
Years remaining until maturity = 10 years - 6 years = 4 years
Step 3: Calculate the present value of the coupon payments:
PV of coupon payments = Coupon payment x (1 - (1 + Yield to maturity)^(-Years remaining until maturity)) / Yield to maturity
PV of coupon payments = 8 CCU x (1 - (1 + 7%)^(-4)) / 7%
Step 4: Calculate the present value of the face value:
PV of face value = Face value / (1 + Yield to maturity)^Years remaining until maturity
PV of face value = 100 CCU / (1 + 7%)^4
Step 5: Calculate the price of the bond today:
Price of the bond = PV of coupon payments + PV of face value
You can plug the numbers into the formulas to obtain the final price of the bond today.
To calculate the price of the bond, we need to discount the future cash flows of the bond at the current yield to maturity (YTM) rate. Here's how you can calculate the price of the bond:
Step 1: Determine the future cash flows
The bond has a 10-year maturity and a coupon rate of 8%. This means it pays an annual coupon payment of 8% of its face value, which is 100 CCU. So every year for the next four years (until maturity), the bond will pay a coupon payment of 8 CCU.
Step 2: Calculate the present value of the coupon payments
To calculate the present value of each coupon payment, you need to discount it back to the present using the yield to maturity rate of 7%. Since there are four coupon payments left (from the current year until maturity), we will discount each payment accordingly.
Year 7:
PV of the coupon payment = Coupon payment / (1 + YTM)^t
PV of the coupon payment = 8 / (1 + 0.07)^1 = 7.48 CCU
Year 8:
PV of the coupon payment = Coupon payment / (1 + YTM)^t
PV of the coupon payment = 8 / (1 + 0.07)^2 = 7.00 CCU
Year 9:
PV of the coupon payment = Coupon payment / (1 + YTM)^t
PV of the coupon payment = 8 / (1 + 0.07)^3 = 6.54 CCU
Year 10 (maturity):
PV of the coupon payment = Coupon payment + Face Value / (1 + YTM)^t
PV of the coupon payment = 8 + 100 / (1 + 0.07)^4 = 93.34 CCU
Step 3: Calculate the present value of the face value (maturity payment)
To calculate the present value of the face value payment, we need to discount it back to the present using the yield to maturity rate. Since the bond will mature in four years, we will discount the face value of 100 CCU accordingly.
PV of the face value (maturity payment) = Face Value / (1 + YTM)^t
PV of the face value (maturity payment) = 100 / (1 + 0.07)^4 = 78.50 CCU
Step 4: Calculate the total price of the bond
The total price of the bond is equal to the sum of the present values of the coupon payments and the present value of the face value.
Total Price of the Bond = PV of the coupon payments + PV of the face value
Total Price of the Bond = 7.48 + 7.00 + 6.54 + 93.34 + 78.50 = 192.86 CCU
Therefore, the price of the bond today would be approximately 192.86 CCU.