Bond price: Briar Corp is issuing a 10-year bond with a coupon rate of 7 percent. The interest rate for similar bonds is currently 9 percent. Assuming annual payments, what is the present value of the bond? (Round to the nearest dollar.)
$990
$872
$1,066
$945
872
872 is the right answer, not 990.
To calculate the present value of a bond, you need to discount the future cash flows of the bond back to their present value. In this case, the bond has a coupon rate of 7% and a time to maturity of 10 years. The interest rate for similar bonds is 9%.
To calculate the present value of the bond, you need to calculate the present value of the coupon payments and the present value of the face value (also known as the par value) of the bond.
Step 1: Calculate the present value of the coupon payments:
The bond has a coupon rate of 7%, which means it pays 7% of its face value in interest annually. Since the bond has a 10-year maturity, you will receive coupon payments for 10 years. To calculate the present value of the coupon payments, use the following formula:
Present Value of Coupon Payments = (Coupon Payment Amount / (1 + Interest Rate)) + (Coupon Payment Amount / (1 + Interest Rate)^2) + ... + (Coupon Payment Amount / (1 + Interest Rate)^n)
In this case, the coupon payment amount is 7% of the face value, and the interest rate is 9%. The time period (n) for each coupon payment is the year it is received (1 to 10 in this case).
Present Value of Coupon Payments = (0.07 * Face Value / (1 + 0.09)^1) + (0.07 * Face Value / (1 + 0.09)^2) + ... + (0.07 * Face Value / (1 + 0.09)^10)
Step 2: Calculate the present value of the face value:
At the end of the 10-year term, the bondholder receives the face value of the bond. To calculate the present value of the face value, use the following formula:
Present Value of Face Value = Face Value / (1 + Interest Rate)^n
In this case, the face value is the amount of the bond, and the time period (n) is 10 years.
Present Value of Face Value = Face Value / (1 + 0.09)^10
Step 3: Calculate the total present value:
To find the total present value of the bond, simply add the present value of the coupon payments and the present value of the face value:
Total Present Value of the Bond = Present Value of Coupon Payments + Present Value of Face Value
Now, you can calculate the present value of the bond using the given information and the formulas explained above.