The Coupon: The Contracted Interest Payment

The coupon is the interest a bond issuer has contracted to pay: a stated rate applied to the face amount, paid on stated dates. The coupon rate is a term of the contract and the coupon amount is a rupee figure it produces. Neither moves when the bond's price moves, and neither is the return a buyer earns.

Interest on a bond is not calculated. Interest on a bond is agreed. The document fixes a rate, fixes the amount that rate is struck on, and fixes the dates, and from that moment onwards the interest due on any one date is something to be looked up rather than worked out. Every other number that later gets called a rate on the same bond is somebody measuring something else, against a different base, for a purpose of their own. Most of the confusion around bonds is people comparing three of those numbers as though they were one, so the distinction is worth holding on to.

What is the coupon on a bond?

The coupon is the interest term of the obligation. When an issuer borrows through a bond, it does not merely promise to give the money back; it promises to pay for the use of the money in the meantime, and the coupon is that second promise written down with a number attached. The coupon has three parts and only three: a rate, the amount that rate is applied to, and a calendar of dates on which the resulting payment falls due.

A household picture is worth having in hand before any arithmetic arrives. Suppose a household borrows Rs 1,000/- from a neighbour and both sides agree, out loud, that Rs 85.00/- will be handed over every year until the money is returned. Nobody sits down each year with a calculator. Nobody rechecks what other neighbours are charging. The figure was settled once, at the start, and every year after that the household simply hands over Rs 85.00/-. If the household later comes into money, or falls on harder times, or if the neighbour sells the debt to a cousin for less than Rs 1,000/-, the Rs 85.00/- does not move. The Rs 85.00/- was fixed by an agreement, and an agreement is not revisited because circumstances changed.

A bond coupon works exactly like that, and everything that follows is a consequence of it. The ten year 8.50 per cent bond used throughout carries a face amount of Rs 1,000/-. The rate written into it reads 8.50 per cent a year. Apply that to the face amount and out comes Rs 85.00/- on each of ten dates, and the Rs 85.00/- is the coupon amount. The coupon amount does not move with the traded price, and it does not move with the identity of the holder. The first buyer, the twentieth, and anybody holding the bond on its last morning all receive the same Rs 85.00/-.

Why is the coupon agreed rather than worked out?

Because a promise that has to be recomputed is not much of a promise. The reason a lender accepts a bond at all is that the future is specified: on this date, this many rupees; on that date, that many. If the issuer could recompute the figure in response to its own profits, or the mood of the market, or the price the bond happens to be changing hands at, the lender would be holding an intention rather than an obligation, and would price it accordingly.

So the document does the arithmetic once and then stops. Three things get fixed and never move again on a conventional fixed rate bond. The first is the rate, written as a rate a year. The second is what that rate gets applied to, and it is the face amount rather than anything connected to a price. The third is the set of dates. After that, working out what is due on a given date is a lookup: find the date, read the amount, pay it.

Every rate in this guide is a rate a year, compounded once a year: one payment a year, and each payment discounted once for each year it stands away from today. A rate without its counting arrangement beside it is an incomplete instruction, and further down the same 8.50 per cent produces two different costs depending on nothing more than how often it is applied.

Where does the coupon rate stop and the coupon amount start?

The coupon rate is a term of the document, written as a rate a year on a stated base. The coupon amount is the rupee figure that term produces on a particular date. On the bond worked through here those two travel together so obediently that the words can be used interchangeably for a while: 8.50 per cent, Rs 85.00/-, 8.50 per cent, Rs 85.00/-, ten times over. Then an instrument arrives where they part company, and the sloppy habit stops working entirely.

Take the amortising variant. The variant carries the same Rs 1,000/- of face amount and the same contract rate, and nothing else has been added to it: the amount owed is paid back in ten equal slices of Rs 100/- rather than in one lump at the end, and the 8.50 per cent is struck each year on whatever is still outstanding. In the first year the base is the whole Rs 1,000/-, so the coupon amount is Rs 85.00/-. By the tenth year only Rs 100/- of the amount owed is left standing, so the coupon amount is Rs 8.50/-. The tenth payment is a tenth of the first.

The rate never moved. The base under it fell, and the payment fell with it. The fall cannot be said out loud using one word for both objects: any sentence of the form the rate fell from Rs 85.00/- to Rs 8.50/- is wrong on both counts, and a reader who hears it will conclude the issuer renegotiated something. Two objects, two words, always.

The whole schedule can be checked without going through it date by date, and the check is worth doing because it shows what the falling payments actually are. Add up the ten balances the rate is struck on: Rs 5,500/-. Apply 8.50 per cent to that sum once and out comes Rs 467.50/-, the same total the ten separate coupon amounts add to. Do it for the ordinary bullet bond, where all ten dates strike the rate on the same Rs 1,000/-, and the sum of bases is Rs 10,000/-, giving Rs 850.00/- of interest. The rate cancels clean out of the comparison, so the Rs 382.50/- between the two runs is a difference of bases and nothing else.

What falls due on each date, and what falls due on the last one?

The document fixes how many coupons there are and when each one is due. On the ten year 8.50 per cent bond there are ten of them, one a year, and the calendar is settled at the start along with everything else. Who gets paid matters more than it sounds once a bond starts changing hands, and the document settles that too: entitlement to a payment is decided by reading the register on a record dateThe cut-off date on which the register is read to decide who receives the next payment., and how that reading works in practice is covered separately.

Now the part readers get wrong more often than anything else on a bond schedule. The final coupon and the repayment of the face amount fall due on the same day, so Rs 1,085.00/- falls due on the tenth date against Rs 85.00/- on each of the nine before it. There are ten payments, not eleven. The last one is not a coupon date followed by a repayment date; it is one date with two things arriving on it. Drawn as eleven, it invents a payment the issuer never promised, and every sum taken afterwards is out by Rs 85.00/-.

Stand back from the schedule and add it up. Ten coupon amounts of Rs 85.00/- come to Rs 850.00/- of interest, and the Rs 1,000/- of face amount comes back on top, so everything the issuer has contracted to hand over is Rs 1,850.00/-. Of that, 45.95 per cent is interest and 54.05 per cent is the amount borrowed coming home. The two shares are carried to two places each precisely so they print to 100.00 between them rather than being nudged there; at one place they would read 45.9 and 54.1, a pair that lands on 100.0 by good fortune rather than because the arithmetic put it there.

What changes if the same rate is applied twice a year?

Everything in this guide runs on one coupon a year, and that is a fact about this instrument rather than a fact about bonds. Plenty of bonds pay twice a year. The counting arrangement is part of the quote, not a detail hanging off the end of it, and the cleanest way to see that is to take the same 8.50 per cent and apply it twice instead of once.

Applied twice a year, 8.50 per cent means Rs 42.50/- handed over in month six and another Rs 42.50/- at the year end. The rupees for the year still add to Rs 85.00/-, so it looks like the same deal. It is not. The holder who receives Rs 42.50/- in month six has that money for six months before the year is out, and can put it to work. Reckoned over the full year, 8.50 per cent applied twice really costs 8.6806 per cent, or 8.68 per cent to two places, and that is 18 basis points more than the printed figure. The comparison shows what a counting arrangement costs, and it is not a second convention for this instrument: this bond pays once a year, and every figure elsewhere is built on that.

The same printed number can carry two different costs, so a rate written without its counting arrangement is an unfinished instruction. The counting arrangement belongs beside the rate and the dates, not in a footnote a hurried reader will skip.

Why does one bond carry three different rates?

Here is the block the rest of this subject leans on. Take one bond, at one moment, held by one person, and three separate numbers will be called the rate. The three numbers do not contradict each other. Each is the answer to a different question, and each is only meaningful with its base attached.

The first is the contracted coupon rate: 8.50 per cent a year, struck on the Rs 1,000/- of face amount. The contracted rate belongs to the document. The same rate binds every holder the bond will ever have, and it will still read 8.50 per cent on the day the bond matures no matter what happened to prices in between.

The second is the current yield, and it belongs to a buyer rather than to the bond. The current yield is the coupon amount expressed as a rate a year on the price that buyer actually handed over. Somebody who paid Rs 879.70/- receives the same Rs 85.00/- a year, and Rs 85.00/- set against Rs 879.70/- is 9.66 per cent a year on the money they parted with. Somebody who paid Rs 1,143.78/- for the identical bond receives the identical Rs 85.00/-, and Rs 85.00/- divided into that price is 7.43 per cent a year.

The third is the yield, and it is the one that takes everything into account. The yield is the single annual rate that discounts all ten promised payments back to the price paid. For the buyer at Rs 879.70/- that rate is 10.50 per cent a year. The yield sits above their current yield because it counts something the current yield cannot see: Rs 1,000/- comes back at the end against Rs 879.70/- handed over, and that Rs 120.30/- is part of the buyer's compensation.

Now watch those numbers as the price changes. The direction is not a coincidence, and it is worth being able to predict. The contracted rate is a flat line: 8.50 per cent whatever the price does. The measured rate falls away as a curve. The same Rs 85.00/- is being divided by a larger and larger price. The two readings coincide at exactly one price, the price equal to the face amount, and that meeting is forced rather than remarkable. At Rs 1,000.00/- the base under the contracted rate and the base under the measured rate are the same number, so of course the two answers agree. Move a rupee either side and they part, and they never meet again.

Is there a shortcut from the measured rate to the yield?

A shortcut gets close, and watching it miss is more instructive than watching it work. The idea is natural enough. A buyer at Rs 879.70/- collects Rs 85.00/- a year, and also collects Rs 120.30/- more at the end than they handed over. Spread evenly across the ten dates, the Rs 120.30/- comes to Rs 12.03/- a year, and Rs 12.03/- divided into Rs 879.70/- is 1.37 per cent a year. Added to the 9.66 per cent already being measured on the price, the shortcut says 11.03 per cent.

The yield is 10.50 per cent. The shortcut lands 53 basis points too high, and it does so for a reason worth understanding rather than memorising. Handing a reader Rs 12.03/- in year one and Rs 12.03/- in year ten as though they were equally valuable is exactly the assumption the yield refuses to make. The gap does not arrive in even slices at all; it arrives entirely on the last day, the furthest away and therefore the least valuable slot on the whole calendar. Credited evenly, it flatters the arithmetic.

Run the same shortcut on the buyer at Rs 1,143.78/- and it misses in the other direction. The buyer at Rs 1,143.78/- paid Rs 143.78/- more than the face amount and will not get it back, so the shortcut subtracts a slice instead of adding one, and it reports 6.17 per cent a year against a yield of 6.50 per cent, 33 basis points too low. A shortcut that overstates on one side of the face amount and understates on the other is not a rough version of the yield; it is a different measurement with a bias that flips. Use it to sanity check the sign and the rough size, and never to compare two bonds.

What happens to these figures when a price is rounded into a quote?

Prices on a bond get carried as a quote: the price expressed against a face amount of a hundred rather than a thousand, printed to two places. The quote travels well and usually costs nothing. Rs 879.70/- becomes 87.97, and multiplying 87.97 back by ten returns Rs 879.70/- to the paisa. Nothing is lost.

Rs 1,143.78/- does not behave. Its true quote is 114.378 and prints as 114.38, so a reader who takes the printed 114.38 and multiplies it back gets Rs 1,143.80/-. Rs 1,143.80/- is two paise more than the price it came from, and the residual is in the rounding rather than in anybody's arithmetic. Chased through the current yield it barely registers: Rs 85.00/- over Rs 1,143.78/- is 7.4315 per cent a year and Rs 85.00/- over Rs 1,143.80/- is 7.4314 per cent, a hundredth of a basis point apart, and both print as 7.43 per cent. The rate survives the rounding. The rupees do not, and when an actual payment is being reconciled rather than rates compared, two paise is two paise. Carrying the three place figure beside the two place one whenever both are in play leaves nobody wondering where the error came from.

What does a bond with no coupon at all promise?

A bond can promise a single payment at a single date and nothing whatsoever before it. A bond built that way is the zero coupon bond, and it is a complete obligation. There is a stated amount, a stated date, and a document behind both. The parties never agreed to a calendar of interest payments, so the bond carries none.

So how does anybody get paid for lending? By handing over less than the amount that comes back. A household lending Rs 1,000/- and receiving Rs 1,000/- ten years later has done the borrower a large favour and itself none. A household handing over a smaller sum today and collecting Rs 1,000/- on a fixed date later has been paid, and the payment sits in the gap rather than in anything arriving along the way. The compensation is real, it is contractual, and it is invisible on a payment calendar until the very last entry.

The zero coupon bond proves something about the coupon: paying it is the usual arrangement on a bond rather than a condition of being one. Every bond needs an amount owed and a date. Not every bond has interest dates in between, and a definition that treats a coupon as part of what makes a bond a bond will simply fail on the first zero it meets.

What has an issuer promised when the coupon rate is not fixed?

A document can set the coupon by a rule instead of by a number. The rule names a reference rateA published rate that a floating coupon is set against. How such a rate is put together is covered separately., adds a stated marginThe fixed addition written into a floating rule, sitting on top of whatever the reference reads on the day it is looked up. on top, and names the reset dateA date named in the document on which a floating coupon is worked out again under the same unchanged rule. on which the sum is worked out again. The coupon amount on the fourth such date is not knowable today, and nobody pretends otherwise.

Readers go wrong here in a specific way: they hear that the amount is unknown and conclude the promise is weaker. The promise is not weaker. The promise is simply about a different object. On a floating rate bond the rule is fixed and the amount is not, so the issuer has committed to something perfectly precise, and what that commitment will cost is the part left open. An issuer who applies the wrong reference, or ignores a reset date, or quietly adds to the margin, has broken the document just as thoroughly as one that failed to hand over a fixed Rs 85.00/-.

The same shape turns up in a rent agreement that says the rent moves each year with a published index rather than by a figure both sides guess at now. Neither side knows what year four costs. Both sides know exactly how year four will be worked out, and either can be held to it. Which reference may be used, and what has to be disclosed about it, belongs to the Securities and Exchange Board of India (SEBI) at sebi.gov.in, and how such a reference is constructed is covered separately.

Is a missed coupon simply a smaller coupon?

No, and the difference is the whole reason the obligation framing is worth carrying. A coupon is a contracted amount on a contracted date. If the date arrives and nothing is paid, the issuer has not paid a small amount; it has failed to do what the document required, and that failure is a defaultA failure to do something the document required. What follows one is covered separately. rather than a variation of the term. Zero is not a coupon amount. Zero is the absence of one.

Documents anticipate this. Many allow a grace periodA stretch of days after a payment date, where the document allows one, inside which paying still counts as having performed. after the date, inside which paying late still counts as performing. Many also carry an accelerationA term letting holders call for the whole amount at once instead of waiting for the remaining dates. term. Acceleration lets holders stop waiting for the remaining calendar and call for everything at once. The consequences of a missed payment are written into the same document that created the payment. A bond is therefore a stronger claim than an expectation. The consequences in detail, what a holder can actually do and what a holder ends up recovering are all covered separately. The steps an issuer has to take the moment a payment is missed belong to SEBI at sebi.gov.in.

Sit with the household picture one more time. If the neighbour is handed Rs 40.00/- instead of Rs 85.00/-, that is not a renegotiated arrangement. The arrangement is broken, with Rs 45.00/- still owed and whatever was agreed about breakage now in play. Nothing about the original terms softened; the household simply did not perform them.

What do the three rates come to on one invented instrument?

Everything above, in one place, on one bond, with every base attached. The ten year 8.50 per cent bond has Rs 1,000/- as its face amount. There are ten dates on its calendar, one a year. Written into the contract, the rate reads 8.50 per cent. The rate produces Rs 85.00/- on each date, with the tenth date carrying Rs 1,085.00/- because the last coupon amount and the repayment land together. Now put two different buyers beside it and read across.

Three rates, three bases, one promise that never changed, and any sentence saying the rate on this bond without naming a base has said nothing at all. Notice what the middle row does when the price is the face amount itself: Rs 85.00/- over Rs 1,000.00/- is 8.50 per cent, identical to the contracted rate. The match is not a coincidence and it is not a property of this bond. At that one price the two measurements are struck on the same number, so the match is forced.

Does a second instrument change any of it?

Palash Cements Limited issues a bond over five annual dates at 9.10 per cent a year. Struck on Rs 1,000/- of face amount, matching the figure the credit material already uses for it, that rate produces a coupon amount of Rs 91.00/- on each of five dates. Everything worked through here transfers without alteration: rate in the document, amount in rupees, dates in a calendar, and the last date carrying the repayment alongside the final coupon amount.

Line the two up against each other and a useful thing drops out. Palash Cements carries the higher contracted rate, 60 basis points higher, and it hands over less interest in total: five payments of Rs 91.00/- is Rs 455.00/-, against ten payments of Rs 85.00/- which is Rs 850.00/-. The number of dates does at least as much work as the rate does, so the bond with the lower contracted rate pays Rs 395.00/- more interest. Interest is 31.27 per cent of everything Palash Cements has promised, against 45.95 per cent on the ten year bond. A contracted rate read on its own, with no calendar beside it, is not a quantity of interest.

One more label needs keeping straight. The 9.10 per cent is a contracted coupon rate, struck on a face amount. Money placed with the government now and handed back in one payment five years out carries a spot rate, and at that five year node it reads 6.90 per cent a year, on the same annual compounding used everywhere else here. A contracted coupon rate and a spot rate are different objects with different bases, and the 2.20 percentage points between them, or 220 basis points, is a subject covered separately.

Who reaches for which of the three, and what for?

Start with the household, where the mistake is easiest to see. A retired couple living on the interest from their savings care about one thing above all: how much money arrives, and when. For them the coupon amount is the operative figure. Rs 85.00/- a year on each bond held, arriving on a known date, is what pays for the month it arrives in. Whether the rate that produced it is 8.50 per cent on the face amount or 9.66 per cent on what they paid does not change what lands in the account.

A lender or an analyst assessing the issuer looks at the same coupon from the other side. To them Rs 85.00/- a year is an outgoing the issuer has committed to, on a fixed calendar, whatever else happens to it. Ten dates at Rs 85.00/- plus Rs 1,000/- at the end is Rs 1,850.00/- the issuer has to find, and a rate on its own does not tell them how much of it falls due next year. The lender wants the amount and the calendar.

Somebody deciding what to pay for a bond today needs the third number and cannot use either of the other two. The yield is the only one of the three that puts every promised payment and the price in the same sentence, and that is exactly what a buyer is choosing between. The current yield is genuinely useful to that buyer as well, but for a narrower purpose: it says what the running cash return on their outlay is, and that matters if they need income every year rather than a total at the end. Take the ten year 8.50 per cent bond, bought at Rs 879.70/-: those two answers are 9.66 per cent and 10.50 per cent, and a buyer who needs annual income and a buyer who needs a total are looking at different ones on purpose.

The habit that survives all three cases is the one repeated throughout: the base goes beside the rate every single time. In a note, in a table header, in a message to a colleague. The habit costs four words and removes the entire class of argument that starts with two people quoting different numbers for the same bond.

Who sets the five requirements the bond document does not settle?

Five things touched here are not settled by the bond document at all. How interest builds up between two payment dates, on what counting convention. How and when the money must actually be paid across to holders. Which facts must be disclosed about a floating coupon and the reference it is set against. How interest received on a bond is taxed once it reaches a holder. And what an issuer is required to do the moment a payment is missed.

Each of those is set by an authority, and each is revised by that authority whenever it decides to revise it. A copy of the current version looks finished, ages without any visible sign, and eventually states something untrue with complete confidence. The table below therefore carries the name of the body that fills each row inside the empty space where the row's contents would sit.

The blank is the accurate answer, and the name beside it is the part that stays true. The tax row is the one most readers would most like filled in, and precisely the one left blank: a stale tax treatment is not a small error, it is the kind that changes what somebody does with their money.

How can the arithmetic here be checked by hand?

The arithmetic stays on paper, where every step of it can be checked: 8.50 per cent of Rs 1,000/- is Rs 85.00/-, Rs 85.00/- over Rs 879.70/- is 9.66 per cent a year, and the rate that discounts all ten payments back to Rs 879.70/- is 10.50 per cent a year.

Palash Cements Limited, the ten year 8.50 per cent bond, the amortising variant built from it and the zero coupon bond set beside it are invented.
Educational material. Not advice on any investment, tax, budget or market position.