What is the value of 15-year corporate bonds, with a coupon rate of 9%, if current interest rates on similar bonds is 8%? How much would the value change if interest rates increased to 10%? Under what conditions will this bond trade at par (face value)?
To calculate the value of a 15-year corporate bond with a coupon rate of 9% when current interest rates are 8%, you need to use the present value of a bond formula. This formula incorporates the future cash flows (coupon payments and the face value) discounted by the prevailing interest rate.
Here's how you can calculate the value of the bond when interest rates are 8%:
1. Determine the cash flow for each year: The bond has a face value (also known as par value), which is the amount paid to the bondholder upon maturity. In this case, let's assume the face value is $1,000. The annual coupon payment will be 9% of the face value, which is $90 per year for 15 years.
2. Calculate the present value of each cash flow: To calculate the present value of the annual coupon payments, you need to discount them using the prevailing interest rate. Since the coupon payments are an annuity, you can use the formula for the present value of an ordinary annuity. In this case, you would discount $90 each year for 15 years using an interest rate of 8%.
3. Calculate the present value of the face value: Since the face value is paid at the maturity of the bond, you need to discount it back to its present value using the same interest rate of 8%.
4. Add up the present values of all cash flows: Sum the present value of the coupon payments and the present value of the face value to find the total present value of the bond.
If interest rates increased to 10%, you would follow the same steps but use the new interest rate of 10% instead of 8%.
To determine under what conditions the bond will trade at par (face value), you need to compare the bond’s coupon rate to the prevailing interest rates. If the coupon rate is equal to the prevailing interest rate, the bond will trade at par. In this case, if the coupon rate is 9% and the current and future interest rates are also 9%, then the bond will trade at par. If the coupon rate is higher than the prevailing interest rates, the bond will trade at a premium. Conversely, if the coupon rate is lower than the prevailing interest rates, the bond will trade at a discount.