# Valuation of Bonds/Debentures

A bond or a debenture is a long-term debt instrument or security. It is issued by business enterprises or government agencies to raise long-term capital. A bond usually carries a fixed rate of interest. It is called as coupon payment and the interest rate is called as the coupon rate. The coupon payment can be either annually or semi-annually.

A bond can be irredeemable or redeemable. Redeemable bonds have a fixed maturity date and irredeemable bonds have perpetual life with only interest payments periodically.

Valuation of Bonds/Debentures:

Basically, the value of a bond is the present value of all the future interest payments and the maturity value, discounted at the required return on bond commensurate with the prevailing interest rate and risk.

Where:

Interest 1 to n = Interests in periods 1 to n.

Unless otherwise mentioned, the maturity value of the bond is the face value.
• When the required rate of return is equal to the coupon rate, the bond value equals the par value.
• When the required rate of return is more than the coupon rate, the bond value would be less than its par value. The bond in this case would sell at a discount.
• When the required rate of return is less than the coupon rate, the bond value would be more than its par value. The bond in this case would sell at a premium.

Example:
Let us assume the face value of the bond is \$1,000 (maturity value \$1,000). The bond has a 10% coupon rate payable semi-annually and the yield to maturity (return) is 9%. The bond matures in 5 years period from now. What is the value of the bond?

Interest 1 till 10 = \$50 per semi-annual period. (\$100 annually)

n=10 because 5 years x 2 payments per period.

Yield to maturity = 9%, therefore, semi-annual YTM (return ) =9/2 = 4.5% or 0.045

Solving for the above equation, we get
Bond price = \$1,040 (rounded)

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