A 1,000 face value bond has a remaining maturity of 8 years and a required return of 7%. The bond's coupon rate is 8%. What is the fair value of bond?
To find the fair value of a bond, you need to calculate the present value of its future cash flows. In this case, the future cash flows include the periodic coupon payments and the final payment at maturity.
Here's how you can calculate the fair value of the bond:
Step 1: Calculate the periodic coupon payment
The bond's coupon rate is given as 8%. Since the face value of the bond is $1,000, the annual coupon payment would be 8% of $1,000, which is $80 ($1,000 * 0.08).
Step 2: Determine the number of coupon payments over the remaining maturity
Since the remaining maturity of the bond is 8 years, there will be 8 coupon payments.
Step 3: Calculate the present value of coupon payments
To determine the present value of the coupon payments, you need to discount each payment using the required return. The formula for present value is:
PV = Coupon Payment / (1 + r)^n
Where:
- PV is the present value of the cash flow
- Coupon Payment is the coupon payment amount
- r is the required return rate
- n is the number of periods until the cash flow is received
For each coupon payment, you will discount it using the required return of 7% and the respective number of periods until the cash flow is received.
PV of coupon payments = (Coupon Payment / (1 + r)^1) + (Coupon Payment / (1 + r)^2) + ... + (Coupon Payment / (1 + r)^n)
In this case, since the remaining maturity is 8 years, you will calculate the present value of the 8 coupon payments using the required return of 7%.
Step 4: Calculate the present value of the final payment at maturity
At maturity, the bondholder will receive the face value, which is $1,000. To calculate the present value of the final payment, you discount it back to the present using the required return and the remaining maturity.
PV of final payment at maturity = Face Value / (1 + r)^n
In this case, the remaining maturity is 8 years, so you will discount the face value of $1,000 using the required return of 7%.
Step 5: Calculate the fair value of the bond
Finally, to calculate the fair value of the bond, sum up the present values of the coupon payments and the final payment at maturity.
Fair Value = Present Value of Coupon Payments + Present Value of Final Payment at Maturity
By performing these calculations, you should be able to find the fair value of the bond.