assume a $1000 face value bond has a coupon rate of 8.5 percent pay interest semi-annually, ahd has an eight-year life. if investors are willingto accept a 10.25 percent rate of return on bonds of similar quality, what is the present value or worth of this bond?
To find the present value or worth of the bond, we need to calculate the present value of each cash flow (interest and principal) and sum them up. Here's how you can calculate it step by step:
1. Determine the number of periods: Since the bond pays interest semi-annually and has an eight-year life, the total number of periods will be 8 years multiplied by 2 (to account for semi-annual payments) which equals 16 periods.
2. Calculate the periodic interest rate: The annual coupon rate is 8.5%. Since the bond pays interest semi-annually, divide the coupon rate by 2 to get the periodic rate: 8.5% / 2 = 4.25% per period.
3. Calculate the discount rate: The rate of return investors are willing to accept is 10.25%.
4. Determine the periodic cash flows: The bond pays interest semi-annually, so there will be 16 semi-annual interest payments of $42.50 (4.25% of $1000) each. Additionally, at the end of the bond's eight-year life, the bondholder will receive the face value of $1000.
5. Calculate the present value of each cash flow: To calculate the present value of each interest payment, divide the cash flow by (1 + discount rate/2)^period number. For example, the present value of the first interest payment would be $42.50 / (1 + 10.25%/2)^1. Repeat this calculation for each cash flow.
6. Sum up the present values of all cash flows: Add up the present values of all the interest payments and the present value of the maturity value to determine the present value of the bond.
By following these steps, you can calculate the present value or worth of the bond.