Thursday, December 17, 2009

Bond Valuation

We know that when a government or a company borrows money from the public, it does so by issuing bonds. Naturally, a bond is a piece of paper (legal of course), that signifies debt.

Bonds are usually long - term borrowings, say 10 - 15 years. Needless to say that during the term of a bond, the borrowing party will pay interest to the lending party. The rate of interest at which this interest is paid is known as the coupon rate of interest and it remains the same for the term of the bond (at least for a straight bond). The principal amount on which the interest is calculated is called the Face Value or the Maturity Value of the bond. The interest payments are made periodically, either annually or semi - annually and are called coupon payments.

The value (or price) of a bond responds to the market interest rate. If market interest rates rise, the value of a bond falls and vice - versa. This is pretty intuitive. Suppose, you have a bond that pays you a 7% p.a. interest rate. You are quite happy with it until one day you find that the going market interest rate on similar financial instruments is 8.5% p.a. You get grumpy and want to sell off your bond and re - invest your money at the higher interest rate. The only problem is that you may not find a ready buyer for a bond that pays 7% at a time when other instruments are offering 8.5%. Since you want to sell and the buyers are not that forthcoming, you may have to plead the buyers and maybe give them a bargain price for your bond. The price would therefore fall. The reverse is true for when the market interest rates are lower than the coupon rate on your bond. Then, you have something valuable because you have a financial instrument that gives you more interest income as compared to other instruments on the market. Should you need to sell such a bond, it can fetch you a lucrative price.

Simply put, the market interest rate can also be called  the Required rate of return.  Let us call it k. If the coupon rate is higher than k, the price of a bond rises and is above the Face value of the bond.(Premium Bond). If the coupon rate is less than k, the price of a bond falls and is below the Face value of the bond. (Discount Bond) And if by chance, the coupon rate is equal to k, the bond sells for its face value.

The premium or discount on a bond reduces with time, i.e.; as we move closer to the maturity date, the price of the bond gets closer and closer to its face value, such that on the maturity date, the price is equal to the face value.

Mathematically speaking, the value of a bond is the present value of its coupon payments and face value (maturity value). The video below demonstrates how to find a bond's value:

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