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Interaction between bond value, market interest rate, coupon rate

Let us understand the variables which affect the value of the bonds. It depends on many factors such as coupon rate, market rate of return, maturity period, and redemption payment. As the interest rate varies, the bond value also changes. The variability in interest rate is known as interest rate risk. It may be defined as the probability that the bond prices will fall because of increase in general level of interest rates. This type of risk may be found in all types of bonds.

The degree of interest rate risk associated with a specific bond is basically a function of time to maturity, i.e., the number of years till maturity. This interest rate risk is higher in case of bonds of longer maturity as compared to the bonds of shorter maturity. The reason for this is that the bond with a longer maturity is more exposed to variations in interest rates. This also explains as to why the short-term bonds have lower rate of interest than the long-term bonds. Thus, if a firm has issued bonds of different maturity periods, then even if the face value and coupon rates are same, the bonds of different maturity periods will have different degrees of interest rate risk and, hence, different bond values. Bond valuation behavior with respect to different variables has been discussed below:

Bond valuation and required rate of return

If the required rate of return or the market interest rate, and the coupon rate are equal, the bond value will be equal to the par value. If the required rate of return is more than the coupon rate, the bond value is less than the par value and vice-versa.

The required rate of return is basically the opportunity cost which depends upon the market rates of interest. So, when there is a change in market interest rates, the required rate of return changes and it ultimately affects the bond values.

It should be noted that required rate of interest and bond values move inversely. At higher discount rate, the present value of the future cash inflows to be received by the investor is lower. On the other hand, if the market rate of interest falls, the discount rate will also decrease resulting in higher present values. So, the bond values will rise. This inverse relationship between the interest rates and bond valuation provides the basis as to why the bond prices change. However, the exact amount of change will depend upon the time to maturity and the coupon rate. •   Bond valuation and time to maturity

If the required rate of return is different from the coupon rate, the time to maturity also affects the value of the bond. The value of the bond approaches its par value as the time maturity approaches its maturity date. One may also note that longer the time to maturity of a bond, greater is the change in its value in response to a given change in its required rate of return.

Thus, we may infer as follows:

If the coupon rate and required rate of return are equal, the bond will sell at par value or face value because the investor receives fair compensation for the time value of money in the form of interest receipts. However, if the coupon rate is lower than the required rate of return, the coupon payment alone will not suffice. The investor will require a capital gain as well. In other words, an investor should at least be able to get a return what he/she can earn elsewhere. So, to earn a fair return, the investors need to earn price appreciation. The bond will, therefore, sell at less than its face value to provide a built-in capital gain on the investment.

References:

Rustagi, Dr. R.P., Investment Management: Theory and Practice (2008)

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