Irredeemable bonds
Take the case of a ˆ1,000 irredeemable bond with an annual coupon of 8%. This financial asset offers to any potential purchaser a regular and fixed ˆ80 per year in perpetuity (i.e.
8% of the par value of ˆ1,000), but the actual price of the bond will fluctuate in response to the prevailing rate of interest. When the bond was issued, general interest rates for this risk class may well have been 8% and so the bond may have been sold at ˆ1,000. However, interest rates change over time and the ˆ80 coupon may not remain sufficient to maintain the bond price at ˆ1,000.Suppose that the current rate of interest is now 10%. Investors will no longer be willing to pay ˆ1,000 for an instrument that yields only ˆ80 per year. The current market value of the bond will fall to ˆ800 - the current value of the irredeemable bond is given by dividing the coupon rate by the current rate of interest, ˆ80/0.10. This is the maximum amount needed to pay for similar bonds given the current interest rate of 10%. We say that the bond is trading at a ‘discount' to its nominal value because it is trading below ˆ1,000.
If the coupon rate is more than the current market interest rate, the bond price will be greater than the nominal (par) value. Thus, if market rates are 6%, the irredeemable bond will be priced at ˆ1,333.33 (ˆ80/0.06). We say that it is trading at a ‘premium' to its nominal value, i.e. at more than ˆ1,000.
The formula relating the price of an irredeemable bond, the coupon and the market rate of interest is:
where Pd = price of bond, D stands for debt
C = nominal annual income (the coupon rate ? nominal (par) value of the bond) kD = market discount rate, the annual return required on bonds of similar risk and characteristics.
Also:
where Vd = total market value of all of the bonds of this type
I = total annual nominal interest of all the bonds of this type.
We may wish to establish the market rate of interest represented by the market price of the bond. For example, if an irredeemable bond offers an annual coupon of 9.5% and is currently trading at £87.50, with the next coupon due in one year, the rate of return is:
Note this formula can be used only if the next coupon is payable one year from the time of valuation. If there are coupons before then they need to be discounted separately, adding to the overall value.