A bond's coupon rate is equal to its yield to maturity if its purchase price is equal to its par value. The par value of a bond is its face value, or the stated value of the bond at the time of issuance, as determined by the issuing entity. Most bonds have par values of $100 or $1,000. The par value of a bond does not dictate its market price, however. Instead, the market, or selling, price of a bond is influenced by a number of factors in addition to its par. These factors include the bond's coupon rate, maturity date, prevailing interest rates and the availability of more lucrative bonds.
The coupon rate of a bond is its interest rate, or the amount of money it pays the bondholder each year, expressed as a percentage of its par value. A bond with a $1,000 par value and coupon rate of 5% pays $50 in interest each year until maturity.
A bond's maturity date is simply the date on which the bondholder receives repayment for his investment. At maturity, the issuing entity must pay the bondholder the par value of the bond, regardless of its current market value. This means that if an investor purchases a fiveyear $1,000 bond for $800, he collects $1,000 at the end of five years in addition to any coupon payments he received during that time.
The market value of bonds has a negative correlation with prevailing interest rates. As interest rates go up, the price of preexisting bonds goes down. As rates decline, current bonds with higher rates become more valuable.
For example, if a company issues a $1,000 bond with a 4% interest rate, but the government subsequently raises the minimum interest rate to 5%, then any new bonds being issued have higher coupon payments than the company's initial 4% bond. To entice investors to purchase the bond despite its lower coupon payments, the company has to sell the bond at less than its par value, which is called a discount. If, instead, interest rates drop to 3%, the preexisting 4% bond sells for more than its par value; this is called a premium.
Since the market price of bonds is so changeable, it is possible to make a profit in addition to that generated by coupon payments by purchasing bonds at a discount. The yield to maturity of a bond is the rate of return generated by a bond after accounting for its market price, expressed as a percentage of its par value. Considered a more accurate estimate of a bond's profitability than other yield calculations, the yield to maturity of a bond incorporates the gain or loss created by the difference between the bond's purchase price and its par value.
If a bond is purchased at par, therefore, then its yield to maturity is equal to its coupon rate, because the initial investment is offset entirely by repayment of the bond at maturity, leaving only the fixed coupon payments as profit. If a bond is purchased at a discount, then the yield to maturity is always higher than the coupon rate. If it is purchased at a premium, the yield to maturity is always lower.

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