Final answer:
The yield to maturity (YTM) is the annualized return on a bond held to maturity, considering all scheduled payments. Bond prices vary inversely with interest rate changes: when rates go up, bond prices fall; when rates go down, prices rise. Present value calculations, using market interest rates, determine a bond's current market value based on its future cash flows.
Step-by-step explanation:
The calculation of a bond's yield to maturity (YTM) is a way to determine the annualized rate of return that an investor will receive if the bond is held until its maturity date and all coupon and principal payments are made as scheduled. The concept of present value is essential when discussing the value of future payments in today's dollars, which is central to the calculation of YTM. A bond's price will fluctuate in response to changes in interest rates: if interest rates increase, the bond's price will fall to remain competitive with new bonds issued at the higher rates, and similarly, if interest rates decrease, the price of a bond will increase.
Understanding the risk involved with bonds and the influence of market interest rates is critical. For instance, if a bond is considered risk-free, its price would likely be at par value (the original price at which it was issued, usually $1,000) and pay a fixed interest (the coupon rate) until maturity. However, if market interest rates rise above the bond's coupon rate, the bond's selling price would need to decrease to make it appealing to investors who could otherwise invest in new bonds at higher rates. To calculate the present discounted value of the future cash flows from a bond (which include the periodic coupon payments and the return of principal at maturity), you apply the present value formula. This involves discounting each future payment by a discount rate, which is typically the market interest rate relevant for the bond's duration and risk profile. The sum of these discounted cash flows gives you the bond's current market value.