Perpetual bond

Every ordinary bond does two things for its holder: it pays a coupon on a schedule, and on a fixed date it returns the face value and stops existing. A perpetual bond only does the first thing. It has no maturity date — the XXI-A workbook's own words are that such a bond "does not have any maturity date" and "exists forever."

That one missing feature changes how it has to be valued. An ordinary bond's price is the present value of a finite stream of coupons plus one final repayment of face value. A perpetual bond's price is the present value of coupons that, in principle, never stop — there is no repayment date to discount back to today.

The workbook's general approach to bond valuation (Chapter 4) sums the present value of every future cash flow at the investor's required rate of return. For a bond with a finite maturity, that sum has a last term — the discounted face value on the maturity date.

A perpetual bond removes that last term. What is left is an unchanging coupon stream with no end, and the present value of a constant stream discounted forever at a constant rate has a simple closed form: price equals the annual coupon divided by the required yield. There is no face-value term to add, because there is no date on which it is ever repaid.

Price of a perpetual bond = Annual coupon (Rs) ÷ Required yield (as a decimal)

The XXI-A workbook does not carry a worked perpetual-bond valuation, so the figures below are illustrative, applying the workbook's own present-value approach to a bond that never matures.

An Indian bank issues a perpetual bond — the kind banks issue to count toward regulatory capital, commonly called an AT1 bond — with a face value of Rs 10,00,000 and an annual coupon of 8.5%, i.e. Rs 85,000 a year, payable forever unless the bank calls the bond.

If an investor's required yield for a bond of this credit quality is 9%:

Price = Rs 85,000 ÷ 0.09 = Rs 9,44,444

The bond is worth less than its Rs 10,00,000 face value at this yield, because the 9% required return exceeds the 8.5% coupon — the same logic as any bond trading at a discount, just with no maturity date to eventually pull the price back to par.

If yields fall to 7.5%, the same Rs 85,000 coupon is worth more relative to what the market now demands:

Price = Rs 85,000 ÷ 0.075 = Rs 11,33,333

A one-percentage-point move in yield moves a perpetual bond's price by far more than it would move an ordinary five-year bond's price, precisely because there is no approaching maturity date to anchor the price back toward face value.

Chapter 4 (Investing in Fixed Income Securities) introduces the perpetual bond in one line, alongside the zero-coupon bond, as an example of how a cash-flow pattern changes what a bond is worth. The examinable point is conceptual: a bond with no maturity date is valued as coupon divided by yield, and its price is correspondingly more sensitive to a change in yield than a bond that matures on a fixed date.

• No maturity date means no face-value repayment is ever discounted into the price. Students used to ordinary bond pricing keep adding a face-value term out of habit; a true perpetual bond has none.
• "Perpetual" describes the issuer's obligation, not the holder's holding period. Perpetual bonds are typically listed and can be sold to another investor at any time.
• A callable perpetual bond can still be repaid early if the issuer exercises a call option, even though it has no fixed maturity — perpetual and callable are separate features that commonly appear together in bank capital bonds.
• Price is far more sensitive to a yield change than a dated bond of similar coupon, because there is no approaching maturity to pull the price toward par as time passes.