Bond valuation is a method used to determine the expected trading price of a bond. The expected trading price is calculated by adding the sum of the present values of all coupon payments to the present value of the par value (no worries, the bond value calculator on this page performs all of the calculations for you, and shows its work).

Since the value of a bond is equal to the sum of the present values of the par value and all of the coupon payments, we can use the Present Value of An Ordinary Annuity Formula to find the value of a bond (as generated by the Bond Valuation Calculator lower down on this page).

Present Value of Ordinary Annuity Formula |
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$$ B0 = \frac c2 * \frac { \left [ 1- \left [ \frac {1}{1+i/2^{nk}} \right] \right ]}{i/k} +p_{(1+i/k)^{nk}} $$ |

Variables |

C = coupon payment (Par Value * Coupon Rate) |

n = number of years |

i = market rate, or required yield |

k = number of coupon payments in 1 year |

P = value at maturity, or par value |

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:

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.

This is illustrated by the following equation |
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$$ B0 = \frac c2 \left[ 1-\left(1+ {YTM \above 1pt 2} \right)^{-2t} \above 1pt {YTM \above 1pt 2} \right ] + {F \above 1pt \left(1+ {YTM \above 1pt 2} \right)^{2t}}$$ |

Variables |

B0 = the bond price, |

C = the annual coupon payment, |

F = the face value of the bond, |

YTM = the yield to maturity on the bond, and |

t = the number of years remaining until maturity. |

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:

This is illustrated by the following equation. |
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$$ B0 = \frac c2 \left[ 1-\left(1+ {YTC \above 1pt 2} \right)^{-2d} \above 1pt {YTC \above 1pt 2} \right ] + {CP \above 1pt \left(1+ {YTC \above 1pt 2} \right)^{2d}}$$ |

Variables |

B0 = the bond price, |

C = the annual coupon payment, |

CP = the call price, |

YTC = the yield to call on the bond, and |

CD = the number of years remaining until the call date. |

SELECT CALCULATOR | |

Par value / Face value ($): | |

Bond price ($): | |

Coupon rate (%): | |

Coupon rate compounding interval: | |

Current market rate of similar bonds (%): | |

Years to maturity (#): | |

Call price: ($): | |

Years until call date: | |

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