The first (and easiest) place to start determining the value of bonds is with a unique class of bonds that never matures. These are indeed rare, but they help illustrate the valuation technique in its simplest form. Originally issued by Great Britain after the Napoleonic Wars to consolidate debt issues, the British consol (short for consolidated annuities) is one such example. This bond carries the obligation of the British government to pay a fixed interest payment in perpetuity.
The present value of a perpetual bond would simply be equal to the capitalized value of an infinite stream of interest payments. If a bond promises a fixed annual payment of I forever, its present (intrinsic) value, V, at the investor's required rate of return for this debt issue, is which, from Chapter 3's discussion of perpetuities, we know should reduce.
Thus the present value of a perpetual bond is simply the periodic interest payment divided by the appropriate discount rate per period. Suppose you could buy a bond that paid $50 a year forever. Assuming that your required rate of return for this type of bond is 12 percent, the present value of this security would.
This is the maximum amount that you would be willing to pay for this bond. If the market price is greater than this amount, however, you would not want to buy it.