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# Bond Prices and Interest Rates

Bond Prices and Interest Rates The price of a bond is found to exist in three s: premium, discount or par. Before we answer our specific question, we must first understand what these three states stand for. The states are the basically the price of a bond in comparison to its par value i.e. if the price of the bond is greater than its par value, than it is said to be offered at a premium. This is because the rates of return being offered by these bonds are greater than the market rates of return. therefore, they are more valuable assets and hence are offered at a premium. Similarly, a bond is said to be offered at a discount on its par value, if the bond price is less than the par value which occurs in the instance when the rate of return that is offered by the bond is less than the market rate of return that is offered on other similar risk assets in the market. A bond is said to be priced at par value if the market price of the bond is equal to the par value of the value which occurs in the instance when the rate of return offered by this bond and the required rate of return for this type of asset are equal.  
Moving on, we will now look at the basic pricing mechanism for bonds. This mechanism is the standard procedure that is used for bond pricing and states that the value of a bond must be equal to the present value of all the future payments that the bond will make over the course of its maturity. This is directly in line with the no arbitrage rule as the cost of this asset and the generated revenues are being equalized in the pricing technique.   A basic formula for calculating bond price is given below:
C = coupon payment
n = number of payments
i = interest rate, or required yield
M = value at maturity, or par value
Source: http://www.investopedia.com/university/advancedbond/advancedbond2.asp
Coming to our specific question, as we can see from the mathematical equation for the derivation of bond prices, an increase in interest rates will lead to a decrease in bond prices. To understand in most simplistic terms, we can see that increasing the interest rate will decrease the present value of each specific payment that the bond will make over the course of its maturity as each value is now being discounted by a greater rate of return. Similarly, the present value of the par value of the bond is also going to decrease as that is also now being discounted by a larger interest rate. Therefore, the entire value of the bond will decrease as the interest rates increase. To put this into context, we can also see that as the required rate of return for a bond increases, its price moves from the premium entity to the par entity and then to the discount entity if interest rates keep rising. As we already know that bond prices decrease as they move from premium to discount entities, we find the theoretical backing to our earlier mathematically derived notion that bond prices fall in the face of increasing interest rates.  
Bibliography:
1. Brett M (2003) ‘ How to read Financial Pages’ Random House Business Books.
2. Arnold G (2008) ‘Corporate Financial Management’ Financial Times, Prentice Hall

Bond Prices and Interest Rates