$1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond?
To calculate the fair value of a bond, you need to determine the present value of the bond's future cash flows. In this case, the cash flows include the periodic coupon payments and the principal payment at maturity.
Let's break down the steps to calculate the fair value of the bond:
Step 1: Calculate the coupon payment
The coupon payment is a fixed percentage of the face value (or par value) of the bond. In this case, the bond has a face value of $1,000 and a coupon rate of 7.4%. Therefore, the annual coupon payment is calculated as:
Coupon Payment = Coupon Rate * Face Value
Coupon Payment = 7.4% * $1,000
Coupon Payment = $74
Step 2: Determine the number of periods
Since the bond has a remaining maturity of 10 years, the number of periods is 10.
Step 3: Calculate the present value of the coupon payments
To calculate the present value of the future cash flows, we need to discount each cash flow back to its present value using the required return rate. The formula to calculate the present value of a future cash flow is:
Present Value = Cash Flow / (1 + Required Return Rate) ^ Period
For the coupon payments, we will discount each annual coupon payment by using the required return rate of 9%. Since the coupon payments occur annually, we will discount each payment for the next 10 years.
Calculating the present value of the coupon payments:
Year 1: $74 / (1 + 9%)^1
Year 2: $74 / (1 + 9%)^2
Year 3: $74 / (1 + 9%)^3
...
Year 10: $74 / (1 + 9%)^10
Step 4: Calculate the present value of the principal payment
At maturity, the bondholder will receive the face value of the bond, which is $1,000. We also need to discount this payment to its present value using the required return rate and the remaining maturity.
Calculating the present value of the principal payment:
Principal Payment = $1,000 / (1 + 9%)^10
Step 5: Sum up the present values
Now, sum up the present values of the coupon payments and the principal payment to calculate the fair value of the bond:
Fair Value = Present Value of Coupon Payments + Present Value of Principal Payment
The final result will provide you with the fair value of the $1,000 face value bond for a required return of 9%.