 ### What is Coupon Bond Valuation?

The Coupon Bond Valuation formula determines the present value (or par value) of a coupon paying bond. Interest is paid to the investor in increments over the bond’s life as it matures in the form of coupons. If a bond’s coupon rate is higher than its yield to maturity rate (YTM), the bond is considered to be selling at premium. Should the coupon rate be lower than the yield to maturity, the bond is considered to be selling at a discount. Bonds that have an equal coupon and YTM rate are considered to trade at par. As a bond’s par value and interest rates are considered set, bond valuation helps investors determine whether a bond should be purchased by allowing them to compare their calculated return value of a bond with the actual selling price of a bond.

### Coupon Bond Valuation Variables

Bonds are debt instruments that provide a steady income stream in the form of coupon payments to investors over the course of the life of a bond. At the date of maturity of a bond, the bond’s face value is paid to the investor. The variables for calculating the par value of a coupon bond are as follows:

#### Coupon Payment (C)

The amount a bond pays in coupon instalments annually, often considered a form of interest. This value can be worked out by multiplying the coupon rate by the face value of a bond. For instance, a coupon payment on a bond with a face value of \$1000 and a coupon rate of 7% would equate to a \$70 annual coupon payment. Should a bond pay coupons on a more regular basis than annually, this payment should be divided by the number of payments expected to be paid per annum.

#### Yield to Maturity (r)

The Yield to Maturity is the discount rate of return on a bond that is purchased by an investor. If a bond is expected to make payments more regularly than annually, this rate should be divided by the number of payments expected per annum when applying to a coupon bond formula.

#### Time to Maturity (t)

Time to maturity is the number of periods the coupon bond will make payments before it matures. For an annual coupon bond of 5 years, the time to maturity would be 5, however should the bond make semi-annual payments (2 p/a) over 5 years, the time to maturity would be 10 for a semi-annual coupon bond.

#### Face Value of Bond (F)

The face value, or par value, of a bond is the value investors expect to receive back from the bond issuer for the bond at the time of maturity.

#### Value of Coupon Bond (V)

The Value of a Coupon Bond is the value of a bond to investors after considering yield to maturity, face value, time to maturity, and coupon payments. It is the present value of a bond after compensating for coupon “interest” payments.

### How to Calculate the Coupon Bond Valuation

The calculation of the value of a coupon bond factors in the annual, semi-annual, etc. nature of coupon payments and the yield to maturity. Let’s consider an annual coupon bond with a face value of \$1000, a coupon rate of 7%, a yield to maturity of 8%, and a time to maturity of 5 years. Already it can be seen that this bond is being sold at a discount as the coupon rate is lower than the yield to maturity. In this example, the value of the coupon bond is calculated as follows:

V = C * ((1-1/(1+r)t) / r) + (F/(1+r)t)

V = 70 * (1-1/1.085)/0.08 + (1000/1.085)

V = \$960.07

The bond value is \$960.07, which is lower than the face value of the bond and expected as it is sold at discount. This is the value an investor would expect to pay for a bond with the denoted variable values. ### Advantages of Coupon Bond Valuation

The concept of coupon bond valuation is very important as bonds form an indispensable part of the capital markets, and as such investors and analysts are required to understand how the different factors of a bond behave in order to determine its intrinsic value. Similar to share valuation, the value of a bond is helpful in understanding whether it is a suitable investment for a portfolio and consequently forms an integral part of bond investment.

### Coupon Bond Valuation Summary

Coupon bond valuation is integral for determining the value of a bond for the purpose of portfolio investment by investors. Coupon bond valuation requires values for face value, yield to maturity, time to maturity, and coupon rate. A bond with a coupon rate higher than its yield to maturity is selling at premium, a coupon rate lower than its yield to maturity is selling at discount, and a coupon rate equal to its yield to maturity is selling at par value. ### Coupon Bond Valuation with On Equation Finance Calculator

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