Monrrow Company's bonds mature in 8 years, have a par value of $1,000, and make an annual coupon interest payment of $65. The market requires an interest rate of 7.7% on these bonds. What is the bond's price?
multiple choice answers
a. 865.13
b. 1,097.69
c. 1,069.79
d. 930.25
e. 762.80
what is the correct answer
To calculate the price of a bond, you can use the present value formula. The present value of a bond is the sum of the present values of its future cash flows. In this case, the cash flows consist of the annual coupon payments and the face value payment at maturity.
1. First, calculate the present value of the annual coupon payments.
- The bond has a coupon interest payment of $65 and matures in 8 years.
- The market interest rate is 7.7% or 0.077 in decimal form.
- Use the present value of an ordinary annuity formula: PV = C * (1 - (1 + r)^(-n)) / r, where PV is the present value, C is the coupon payment, r is the interest rate, and n is the number of periods.
- Substitute the values: PV_coupon = 65 * (1 - (1 + 0.077)^(-8)) / 0.077
2. Next, calculate the present value of the face value payment at maturity.
- The face value of the bond is $1,000.
- Since this payment occurs only at maturity, we need to calculate the present value using the formula: PV = F / (1 + r)^n, where PV is the present value, F is the face value, r is the interest rate, and n is the number of periods.
- Substitute the values: PV_face_value = 1000 / (1 + 0.077)^8
3. Finally, calculate the bond's price by summing up the present values of the coupon payments and the face value payment:
Bond price = PV_coupon + PV_face_value
Plug in the values and calculate to find the bond's price.