Final answer:
The price of a $1,000 bond with a 6% coupon maturing after eight years is determined by discounting its future cash flows, which include yearly interest payments and the final principal repayment, using the current market yield of 8%. This calculation accounts for market conditions that demand a higher yield than the bond's coupon rate.
Step-by-step explanation:
Calculating the Bond's Price
When calculating the price of a bond with a coupon of 6 percent that matures after eight years, one key factor to consider is the current market interest rate or the yield required by investors. If comparable debt yields 8 percent, which is higher than the bond's coupon rate, the bond will be discounted to offer a yield that matches the market rate. To find out the bond's price, you would discount each of the bond's future cash flows, which includes annual interest payments and the principal repayment at maturity, using the 8 percent market rate of interest.
Present value calculations are used to determine what the future cash flows are worth today. For example, a simple two-year bond with an 8% coupon rate would pay $240 annually on a principal of $3,000. If the market rate is also 8%, the present value of the bond's cash flows would be equal to its par value. However, if the market rate rises to 11%, the present value would be less than the bond's face value to account for the higher yield investors can obtain elsewhere.
Applying this concept to the $1,000 bond with a 6% coupon over eight years at an 8% market rate requires the discounting of each of the bond's annual $60 interest payments and the $1,000 principal repayment at the end of the eighth year. This discounted value represents the price an investor would be willing to pay for the bond given an 8% bond yield.
Why Discount the Bond?
Bonds are discounted when the market interest rates exceed the coupon rate of the bond because the fixed interest payments are less attractive compared to new bonds issued at the higher market rate. Therefore, to provide an equivalent yield, the bond's price must be reduced. This relationship inversely affects bond prices and yields, ensuring that the yield on existing bonds remains competitive with current market rates.