Face Value, Par and Principal: The Amount Borrowed, Owed Back and Priced Against

Face value is the stated amount a bond is written around: the rate is struck on it and it comes back at the end. Par value is that same amount used as a price reference, so a bond quoted at par is quoted at exactly its face value, above par is higher and below par is lower. Principal is what is owed. Usually one number, and not always.

A price has to be a price of something. On a bond the natural thing to measure it against is the amount the contract was written around in the first place. The amount is already in the document, already fixed, and already the base every other term refers to. Measuring the price against it is what lets one small number describe a bond no matter how large or small the borrowing was. Measurement against a fixed amount is the whole reason bond prices arrive as figures near a hundred rather than as rupee amounts, and it is why a word for the face value seen from the price side has to exist at all.

What is the face value of a bond?

Start with the thing itself, not with what people do to it. A bond is a written obligation, and inside that obligation there is a stated amount. The stated amount is the face value: the base the interest rate is applied to, and the sum the borrower has agreed to hand back when the borrowing ends. The ten year 8.50 per cent bond used all through this sequence carries a face value of Rs 1,000.00/-. The contracted coupon rateThe rate written into the document at the start and fixed there. It decides how much interest falls due and on which base. The contracted coupon rate is taken apart properly later in this sequence. of 8.50 per cent a year is struck on that Rs 1,000.00/-, giving Rs 85.00/- a year. At the tenth date the Rs 1,000.00/- itself comes back alongside the last Rs 85.00/-, and that date carries Rs 1,085.00/-.

Now the part that matters more than the definition. The face value is a term of a document, not a measurement of the world. Nobody observes it. Nobody estimates it. The face value was typed once, by the people drafting the obligation, and after that it does not move. The face value does not move when interest rates move, it does not move when the borrower has a good year or a terrible one, it does not move when the bond changes hands at a hundred different prices over its life, and it does not move when the borrower has already paid nine of the ten dates. Every one of those things can be true at once and the face value on that document is still Rs 1,000.00/-.

Here is the everyday version, and it is closer than it looks. A concert ticket has a printed value on the front. Somebody buys it at that printed value, decides they cannot go, and sells it to a friend for less. Somebody else buys the same ticket from a reseller for a great deal more because the show sold out. Through all of that, the number printed on the ticket has not changed by a single rupee. Printing is what fixed it. The printed number describes what the ticket was issued at, not what anybody paid for it, and the two get confused constantly.

Face value is a reference, and a reference has to be immovable to be useful. Immovability is not an accident of drafting; it is the reason the amount is written down at all. Three separate things on a bond need something fixed to point at. The interest calculation needs a base, or the rate has nothing to bite on. The repayment at the end needs a quantity, or the closing date has nothing to settle. And the price, the subject of the rest of this guide, needs something to be measured against, or a bond selling for Rs 879.70/- and a bond selling for Rs 8,79,700/- cannot be compared at all. One immovable number serves all three jobs.

What is Par Value, and how is it different from face value?

Par value is the same amount, looked at from the other side. When somebody says a bond is trading at par, they are not naming a second quantity that happens to coincide with the first. The speaker is saying that the price being paid has landed exactly on the face value, and is using that face value as the yardstick the price is being read against. Face value settles the amount a contract is written around; par value settles the amount a price is measured against; and on the same instrument they are one number wearing two hats.

So why give it a separate name at all, if the number is identical? Because the two words get used in completely different sentences, by different people, for different purposes. A person reading the document says face value, wanting the base the interest is struck on. A person reading a screen says par, wanting to know where the price has landed relative to that base. To a reader who has only ever met the first word, a quote of 100.00 is meaningless: a hundred is there, but not what it is a hundred of. Par is what supplies that.

A percentage of anything is already read this way. Somebody says a student scored ninety two. Ninety two out of what? Until the base is named, the number is unusable, and the moment somebody says out of a hundred it can be placed instantly against every other score ever heard. Par does that job for a bond price. Par names the base so that the number in front of it can be placed. The base happens to be the face value because that is the one quantity in the contract that never moves.

There is a second reason the separate name earns its keep, and it is practical rather than tidy. The face value is a fact about one bond. Par, as a reference, is a position that every bond in existence shares. Every bond in the world has a par of exactly 100.00 when its price is expressed this way, whatever its face value is in rupees, whatever it pays and whoever borrowed the money. A position shared by every bond alive is what turns a quote into something comparable across instruments, and it is why the price side of this vocabulary needed a word of its own rather than borrowing the contract side word.

Why is a bond price shown as a number near a hundred?

Because rupee prices on bonds cannot be compared with each other, and quotes can. Comparability is the entire reason. The convention gets taught as a historical habit when it is in fact a designed answer to a real problem. Two borrowings cut into units of very different size will have prices of very different size, and putting those prices next to each other says nothing at all. Dividing each price by the face value it was written against, though, puts both on a scale that runs through 100.00 for every instrument that has ever existed. Now they are on the same ruler.

A quote is the rupee price divided by the face value, carried two places to the right, and it contains not one scrap of information the rupee price did not already contain. The second half of that sentence matters as much as the first. Converting to a quote is a relabelling, not an analysis. Nothing is learned in the division. The gain is comparability. Comparability is a property of the scale rather than of the bond, and a reader who thinks the quote is telling them something extra has misread a unit change as a finding.

Take the ten year 8.50 per cent bond through that division. A buyer who wants 10.50 per cent a year out of the bond will pay Rs 879.70/- for it. Rs 879.70/- divided by the face value of Rs 1,000.00/- is 0.8797. Carried two places to the right, the screen shows 87.97. One division by the face value of Rs 1,000.00/- is the whole of the convention. A buyer who will accept 6.50 per cent a year pays Rs 1,143.78/-, and the same division gives 1.14378, shown as 114.38.

Something happens in that second one that is the kind of small thing which quietly destroys a reader's confidence in their own arithmetic. Rs 1,143.78/- divided by Rs 1,000.00/- is 114.378 exactly, and 114.378 does not fit into two decimal places. The screen prints 114.38. Read the other way, that printed quote multiplied by the face value again lands on Rs 1,143.80/-, two paise above the price it started from. The printed quote is itself a rounding, so reversing it returns a number close to the price rather than the price. Two paise on one bond is nothing; on a purchase of ten thousand units it is Rs 200.00/-, and on the day somebody has to reconcile a payment against a contract note it is a discrepancy that has to be explained rather than shrugged at.

The rule this leaves is short: name the base every single time. A quote of 87.97 is not a price and is not an amount; it is 87.97 of the face value, and the sentence is incomplete until those last four words are in it. The rule sounds pedantic right up to the first time somebody produces a screen showing 87.97 and the amount leaving an account has to be worked out.

What do above par and below par actually say?

One thing. Where the price has landed relative to the face value shows how the rate a buyer is willing to accept compares with the rate the document already promises. The comparison between those two rates is the whole content of the position, and everything else people read into it has been imported from somewhere else.

The logic runs like this, and it is worth walking rather than asserting. The bond promises Rs 85.00/- a year for ten years, then Rs 1,000.00/- back. Both amounts are fixed. If a buyer will only part with money at 10.50 per cent a year, the fixed promise has to be bought cheaply enough that it works out to 10.50 per cent a year, and the only free variable left is the price. So the price falls to Rs 879.70/-, and Rs 879.70/- sits below the face value and therefore below par. If instead a buyer is content with 6.50 per cent a year, the same fixed promise can be bought expensively and still work out, so the price rises to Rs 1,143.78/- and the bond quotes above par. The position against par is a shadow cast by the difference between the rate somebody wants and the rate written into the document, and it moves only because that difference moves.

Which gives the tidy case in the middle for free. When the rate a buyer wants is exactly the rate the document promises, there is nothing for the price to adjust for, and the price lands on the face value. A price landing on the face value is what at par means, and it is why the ten year 8.50 per cent bond bought by somebody wanting 8.50 per cent a year costs exactly Rs 1,000.00/- and quotes exactly 100.00.

Now the harder half. A position against par is not a verdict: it does not say that a bond is cheap, that the borrower is sound, or that a buyer will do well out of it. Take those one at a time, because each of them is a real mistake somebody makes.

The position does not say cheap. Cheap means paying less than something is worth, and worth on a bond depends on what the payments are, when they arrive, and how confident a holder can be that they arrive at all. A quote of 87.97 is a fact about arithmetic that has already been agreed between a buyer and a seller. The quote says the price was set so that the fixed promise of Rs 85.00/- a year works out to 10.50 per cent a year, and where that happens to be the correct rate for a borrowing of that length carrying that risk, nothing about the bond is cheap at all.

The position does not say the borrower is in trouble. A borrower in trouble does often see its bonds quoted lower, so the intuition is not invented out of nowhere. But a bond issued years ago at a low contracted coupon rate will sit below par when rates generally are higher, with a borrower whose position has not changed by one rupee. The quote responded to the general level of rates, not to the borrower.

And it does not say what a buyer will do well from. Doing well depends on the price paid, on the borrower actually keeping the terms for the whole of the remaining life, and on where the holder puts each Rs 85.00/- as it arrives. A quote settles none of those. The document sets out what a borrower has committed to do, and what a holder ends up with belongs to the return a holder earns.

What does one instrument look like at three different quotes?

Everything in this guide so far has been a single bond described three ways, so it is worth laying the three side by side and asking what actually differs between them. The ten year 8.50 per cent bond, the instalment version of it used further down, the zero coupon bondA borrowing with one payment at one future date and no interest dates in between. What it is worth today, and why, is worked through elsewhere in this sequence. mentioned alongside it, Palash Cements Limited, an invented cement maker, and a five year government spot rate were all built for teaching, and every rupee amount below follows from their written terms.

Read the last two columns before the first four. Four numbers describe this bond and three of them are identical in all three rows: the face value stays Rs 1,000.00/-, the interest stays Rs 85.00/- a year, and Rs 1,000.00/- is handed back at the tenth date whatever anybody paid. One number moves. The price a buyer parts with runs from Rs 879.70/- to Rs 1,143.78/-. The span of Rs 264.08/-, set against a face value of Rs 1,000.00/-, is a span of 26.41 of quote. The price is the only difference in the table, and every other difference a reader thinks they see is a difference between the buyers rather than between the bonds.

A coincidence worth naming as forced arithmetic

Something in that table looks like a discovery and is not one. The quote of 87.97 sits 12.03 below par. Elsewhere in this sequence, the fall in the price of this bond when the rate a buyer wants rises by 200 basis points is worked out as 12.030 per cent. Same number. Likewise, 114.38 sits 14.38 above par, and the rise in the price when the wanted rate falls by 200 basis points is 14.378 per cent. Both pairs agree because the starting price is exactly the face value, so a percentage of the price and a distance in quote points are being measured off the same Rs 1,000.00/-, and the agreement is forced rather than found. Priced at 92.00 first, the same bond has its distance from par and its percentage move stop matching immediately. Reading a quote gap as a percentage move without checking that the starting point was par is the trap that sits here.

Which counting convention makes these three prices reproducible?

Every rate in this guide is an annual rate and every discounting step happens once a year. One payment a year, ten payments, each one pulled back to today by dividing once for each year that passes. The counting convention belongs beside the numbers rather than tucked into a note. The same Rs 85.00/- on the same ten dates, discounted twice a year instead of once, produces a different price. A reader who takes Rs 879.70/- away and cannot rebuild it will assume an error was made, when in fact half the arithmetic was missing. So: annual, throughout, and the convention is part of the quote rather than a footnote to it.

A control moved between Rs 879.70/- and Rs 1,143.78/- would move the quote in exact proportion, teaching only that a division is a division and nothing else. The relationship on this subject that genuinely rewards a control is the one between the rate a buyer wants and the price they end up paying, and that control is covered under bond pricing, built on this same instrument with these same figures.

Where do face value, principal and par stop pointing at one number?

Most of the time the three words land on the same figure, which is exactly why people start using them as though they were one word. Take the ten year 8.50 per cent bond: its face value reads Rs 1,000.00/-, the amount owed comes to Rs 1,000.00/-, and par as a price reference is that same Rs 1,000.00/-. Nothing bad happens to a reader who blurs them there. The bad thing happens later, on an instrument where they come apart, and by then the habit is set. So here are three situations where they separate, all three of them ordinary rather than exotic.

The first is a borrowing that repays in slices instead of in one go. Take the ten year 8.50 per cent bond and cut its Rs 1,000.00/- into ten equal repayments of Rs 100.00/-, one at each date. The instalment schedule divides the Rs 1,000.00/- of face value into ten equal slices and adds nothing else to the document. Five years in, Rs 500.00/- has gone back, so the principal outstandingHow much of what was borrowed has still not gone back at a given moment. The size of that quantity, and the base a contracted rate is struck on, were settled earlier in this sequence under the amount borrowed. is Rs 500.00/-. The face value on that document is still Rs 1,000.00/-. A face value is a term somebody wrote, and repayment does not rewrite it. Two of the three words have now separated, and expressed against the face value the outstanding amount reads 50.00.

The second is a document that sets the closing payment above the face value. Nothing forces the sum handed back at the end to equal the sum printed as the face value; they are two separate terms of one contract and a drafter may set them apart deliberately. Where the closing payment is larger, the excess has a name, and that name is a redemption premiumThe slice by which a sum paid when a borrowing ends exceeds the amount printed in the document. How a redemption premium is agreed, and what it is for, are set out earlier in this sequence under repayment.. An illustrative two per cent on Rs 1,000.00/- gives Rs 20.00/- of premium, so Rs 1,020.00/- goes back at the end against a face value that is still Rs 1,000.00/-. The quoting convention follows the amount around: Rs 1,020.00/- expressed against the face value is 102.00, a redemption at 102.00 rather than at par.

The third is a borrowing that makes one payment at one date and nothing in between. There is no stream of interest to receive along the way, so the whole of what a lender earns has to come out of buying it for less than it hands back. Its price therefore sits below its face value from the day it is sold until the day it matures, and not by a small margin either. The single payment borrowing is worth pausing on because it breaks the intuition hardest: a bond can spend its entire life below par without one thing being wrong with it, without any rate having moved against it, and without its borrower ever having had a difficult quarter. The bond is below par by construction.

One rule survives all three cases: the face value is a term of the document, the principal is what is owed at a particular moment, and par is a price reference, so any sentence that has to be precise says which of the three it means. In ordinary conversation nobody minds. In a contract note, a covenant test, a valuation or an argument about how much somebody is owed, the three come apart and the sentence that used the words interchangeably turns out not to have said anything checkable at all.

What can a quote near par not settle?

Two things a reader keeps expecting it to settle, and it settles neither. The first is how much interest lands in the holder's account. Interest comes from striking the contracted coupon rate on the face value, and it is never struck on the price, so a buyer who paid Rs 879.70/- for the ten year 8.50 per cent bond receives the same Rs 85.00/- a year as a buyer who paid Rs 1,143.78/-. The quote had no vote in it. The second is what rate the buyer will actually earn. The earned rate depends jointly on the price paid and the schedule of payments, and the pairing is worked out under bond pricing.

The sharpest version of it runs like this. Because the quote describes where a price landed against a contract term and says nothing about what that contract term is, two bonds both quoted at 100.00 can pay completely different amounts of interest. A quote sorts nothing on its own: it is a position, and a position cannot say what it is a position on. Palash Cements Limited borrows for five years, and the rate typed into that document reads 9.10 per cent. Struck on Rs 1,000.00/- of face value, that comes to Rs 91.00/- a year. The ten year 8.50 per cent bond, on the same Rs 1,000.00/- of face value, pays Rs 85.00/-. Both of them quoted at 100.00 would be sitting at the identical position on the identical scale while paying Rs 6.00/- a year apart.

With the two rates side by side, labelling them properly is the discipline the whole of this subject area runs on. The 8.50 per cent and the 9.10 per cent are contracted coupon rates, written into two documents and struck on face values. The 6.90 per cent used elsewhere for a five year government borrowing is a spot rate. A spot rate is the rate for money placed today and returned at one single future date, and it is not a coupon on anything. Palash Cements borrowing at 9.10 per cent against that 6.90 per cent spot rate sits 2.20 percentage points above it, or 220 basis points, one basis point being a hundredth of a percentage point. A fourth kind of rate belongs to this subject area. A forward rate covers a stretch of time that begins on some future date rather than today. Because a forward rate is derived from the two spot rates that straddle its stretch, it cannot be stated until both of those are on the table. Every rate here says which of the four kinds it is, and the reason is that they land close together and are completely different objects.

Who reaches for a quote during a working day, and what do they do with it?

Four people use this number, and none of them uses it the way a textbook diagram suggests. Start with the person doing the least glamorous job, the one most often bitten. A settlement clerk has a contract note showing a quote, and has to work out the rupees that will leave an account on the completion day. The clerk takes the quote, multiplies by the face value, multiplies by the number of units, and then adds the slice of interest accumulated since the previous payment fell due. Interest built up between two payment dates is set out under accrued interest. The quote is an input to what changes hands and is never the same thing as what changes hands, and the considerationThe sum that actually leaves a buyer's account on the completion day. The consideration need not equal a quoted price, and what sits between the two is covered separately in this sequence. is what the clerk has to get right to the paisa.

Then a treasury officer at a company with surplus cash, choosing between two offers. Both are shown as quotes, and that is precisely why quotes exist: the two borrowings may be cut into different unit sizes, and the rupee prices would be uncomparable. But the officer cannot stop at the quote. Because two identical quotes describe two positions and not two bargains, the officer has to open both documents and read the contracted coupon rate, the remaining life and the closing terms. The quote gets the two instruments onto one scale; reading the terms is what decides between them.

Third, somebody in a household buying a bond for the first time through a broker. The buyer sees 87.97 on a screen and braces for something near a hundred rupees. The amount actually leaving the account is Rs 879.70/- for each Rs 1,000.00/- unit, plus whatever interest has accumulated, so ten units come to Rs 8,797.00/- and not to a few hundred. The jolt is the same as reading a share price without checking how many shares come in a lot, and one question removes it entirely: a hundred of what?

Fourth, a lender or a regulated holder deciding what to show a holding at in its own books. The carrying figure is a rule rather than a judgement, it is not the same thing as the price a screen shows, and the rule is kept and revised by the authority named in the block below. The same discipline applies at the primary marketThe first sale, where the money a lender puts up actually reaches the borrower. Later sales pass between lenders and the borrower is not a party to them. stage, where what an issue may be offered at against its face value is a matter of rules rather than of arithmetic.

Who decides what a bond may be offered at, and how its price must be shown?

Everything above this line is arithmetic on an invented contract, and arithmetic keeps. The four items below do not keep. Each one is maintained by an authority whose job it is to change it when it needs changing, so the current wording sits at the address given for it rather than in the middle column.

The quoting convention is the item on this list most likely to be written down wrongly, precisely because it feels like arithmetic rather than like a rule. Dividing a price by a face value is arithmetic. Which price, rounded how far, shown against what, and disclosed alongside what else is a convention, it sits with an authority, and it is not arithmetic at all. The seam between those two is where rules start being stated with the confidence earned doing division.