Bond Duration & Perpetuity Formula   

      When we talk about perpetuity of a bond, we are discussing whether the security pays a fixed or variable coupon at regular intervals forever or in perpetuity. If the coupon is variable, it is said to be a floating rate perpetuity.

       To make it simpler -- we all know that annuities from a bond will not last forever. However, if there are series of equal payments at regular intervals and these payments continue forever, it is called as perpetuity.

        Today we use a formula to calculate the present value of a perpetuity and the formula is as follows:

PVP = PMT/k 

        In the formula, “PMT” refers to the amount of equal payment and “k” is the interest rate. This formula is mostly used to calculate price of a bond or stock, or it is used to calculate the fair price value of a company.

      Many analysts use bond duration analysis and perpetuity. It is a well known fact that interest rates keep changing but the cash flow from a bond stays the same because the coupon rate and maturity date are stated at the time the bond is issued. This means that the value of the bond keeps fluctuating -- when interest increases, the value of the bond decreases. And, when interest rates decrease, the value of the bond increases. This is why people who are investing in bonds want to know more about bond duration analysis and perpetuity, and analysts supply them with this information. However, to get the value of a bond on a particular date, the analyst must know the period remaining until maturity, the face value, the coupon and the market interest rate. It is only when you are armed with this information, you will get an exact figure.


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