Final answer:
The Union Local School District has bonds with a semiannual coupon rate of 2.9% and a YTM of 2.5%. This question relates to bond pricing, particularly how bond prices are adjusted in the market to reflect changes in interest rates. A bond's market value will inversely correlate with interest rates, selling at discounts or premiums to match the yield to maturity with current market rates.
Step-by-step explanation:
The question revolves around understanding the concepts related to the yield to maturity (YTM) of bonds, especially when comparing the coupon rate of the bond with the current market interest rate. The Union Local School District has bonds with a 2.9% coupon rate paid semiannually and a YTM of 2.5%. To explain the implications of these rates and the price of the bond, consider a similar scenario where a local water company issued a bond with a different interest rate. Let's assume a $10,000 bond with a 6% coupon rate issued for ten years and you're looking to buy this bond one year before maturity when the market interest rate is 9%. The value of this bond would decrease due to the increased interest rates.
It's crucial to note that the actual market price of a bond will inversely correlate with the interest rates. If the market interest rates rise above the coupon rate, the bond's price will fall below its face value. Similarly, if the interest rates fall below the coupon rate, the bond's market price will be above its face value. This happens because investors want a return that is commensurate with the current interest rates, making older bonds with a lower interest rate less attractive unless sold at a discount.
For instance, think about a hypothetical $1,000 bond with an 8% coupon rate. If the market interest rate rises, the bond price might drop to, say, $964 to attract buyers, since the new yield, which accounts for the interest payments and the capital gain, can be calculated as ($1080 - $964) /$964 = 12%. This 12% yield compensates for the lower coupon rate, matching the current interest rates.
Another way to understand this concept is by looking at the present value of the bond's future cash flows. If a two-year bond issued at $3,000 and an 8% rate yields $240 in interest annually, it will pay a total of $3,240 at the end of the second year. However, if the current market discount rate is 11%, you would calculate the present value of those payments considering the higher rate, which will give you a lower present value for the bond's worth, reflecting the rise in market interest rates.