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Bonds are long-term debt securities that are issued by corporations and government entities. Purchasers of bonds receive periodic interest payments, called coupon payments, until maturity at which time they receive the face value of the bond and the last coupon payment. Most bonds pay interest semiannually. The Bond Indenture or Loan Contract specifies the features of the bond issue. The following terms are used to describe bonds.
The par or face value of a bond is the amount of money that is paid to the bondholders at maturity. For most bonds the amount is $1000. It also generally represents the amount of money borrowed by the bond issuer.
The coupon rate, which is generally fixed, determines the periodic coupon or interest payments. It is expressed as a percentage of the bond's face value. It also represents the interest cost of the bond issue to the issuer.
The coupon payments represent the periodic interest payments from the bond issuer to the bondholder. The annual coupon payment is calculated be multiplying the coupon rate by the bond's face value. Since most bonds pay interest semiannually, generally one half of the annual coupon is paid to the bondholders every six months.
The maturity date represents the date on which the bond matures, i.e., the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.
The time remaining until the maturity date when the bond was issued.
The time currently remaining until the maturity date.
For bonds which are callable, i.e., bonds which can be redeemed by the issuer prior to maturity, the call date represents the date at which the bond can be called.
The amount of money the issuer has to pay to call a callable bond. When a bond first becomes callable, i.e., on the call date, the call price is often set to equal the face value plus one year's interest.
The rate of return that investors currently require on a bond.
The rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity. Alternatively, it represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price.
The rate of return that an investor would earn if he bought a callable bond at its current market price and held it until the call date given that the bond was called on the call date.
The figure below illustrates the cash flows for a semiannual coupon bond with a face value of $1000, a 10% coupon rate, and 15 years remaining until maturity. (Note that the annual coupon is $100 which is calculated by multiplying the 10% coupon rate times the $1000 face value. Thus, the periodic coupon payments equal $50 every six months.)
Because most bonds pay interest semiannually, the discussion of Bond Valuation presented here focuses on semiannual coupon bonds.
The price or value of a bond is determined by discounting the bond's expected cash flows to the present using the appropriate discount rate. This relationship is expressed for a semiannual coupon bond by the following formula:
where
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Bond Valuation Example |
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Find the price of a semiannual coupon bond with a face value of $1000, a 10% coupon rate, and 15 years remaining until maturity given that the required return is 12%. Solution:
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A bond is considered to be a par bond when
its price equals its face value. This will occur when the coupon rate equals
the required return on the bond.
A bond is considered to be a premium bond
when its price is greater than its face value. This will occur when the coupon
rate is greater than the required return on the bond.
A bond is considered to be a discount bond when its price is less than its face value. This will occur when the coupon rate is less than the required return on the bond.
The yield to maturity on a bond is the rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity. It represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price. This is illustrated by the following equation:
where
The yield to maturity usually cannot be solved for directly. It generally must be determined using trial and error or an iterative technique. Fortunately, financial calculators make the task of solving for the yield to maturity quite simple.
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Yield to Maturity Example |
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Find the yield to maturity on a semiannual coupon bond with a face value of $1000, a 10% coupon rate, and 15 years remaining until maturity given that the bond price is $862.35. Solution:
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Many bonds, especially those issued by corporations, are callable. This means that the issuer of the bond can redeem the bond prior to maturity by paying the call price, which is greater than the face value of the bond, to the bondholder. Often, callable bonds cannot be called until 5 or 10 years after they were issued. When this is the case, the bonds are said to be call protected. The date when the bonds can be called is refered to as the call date.
The yield to call is the rate of return that an investor would earn if he bought a callable bond at its current market price and held it until the call date given that the bond was called on the call date. It represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price given that the bond is called on the call date. This is illustrated by the following equation:
where
Like the yield to maturity, the yield to call usually cannot be solved for directly. It generally must be determined using trial and error or an iterative technique. Fortunately, financial calculators make the task of solving for the yield to maturity quite simple.
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Yield to Call Example |
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Find the yield to call on a semiannual coupon bond with a face value of $1000, a 10% coupon rate, 15 years remaining until maturity given that the bond price is $1175 and it can be called 5 years from now at a call price of $1100. Solution:
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Semiannual Coupon Bonds |
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Bond Price: |
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Yield to Maturity: |
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Yield to Call: |
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Annual Coupon Bonds |
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Bond Price: |
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Yield to Maturity: |
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Yield to Call: |
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