The Discount Rate: What It Represents and How It Is Chosen

A discount rate is the return available on the next best use of the same money at the same risk. One is chosen to match the cash flow it will be applied to on four counts: same currency, same inflation basis, same claim, same risk. Sankalp Industrial Systems Limited, invented, assumes 12.00 per cent, and a third of a percentage point of that assumption is Rs 1,12,23,93,421 of value.

Everything below rests on one idea, and it is not an arithmetic idea. Money committed to one thing cannot be committed to another. The return the other thing would have paid, at the same risk, is the bar this thing has to clear. A discount rate is therefore a fact about the alternative rather than a fact about the business being valued, and every rule below follows from that one.

What is a discount rate actually the price of?

Start away from companies altogether. A household has Rs 5,00,000 sitting in an account. A cousin asks to borrow it for three years to extend a workshop. Before anybody can say what that promise of repayment is worth today, a completely different question has to be answered: what would that same Rs 5,00,000 have done for three years if the cousin had never asked? Not what the lender hopes it would do. The honest answer is what the money would actually have done, at the same sort of risk the loan carries.

Whatever that answer is, it is the discount rate. A discount rate is a price, and the thing being priced is waiting plus exposure. The measurement is not of the workshop; it is of what has to be given up to fund it. If the realistic alternative was a fixed deposit, the rate is low. If the realistic alternative was another cousin with a better workshop and the same chance of failing, the rate is that cousin's return. The workshop's own quality does not enter the calculation at all. Quality enters the numerator, in the cash flows, and quality must not be counted a second time in the rate.

The two halves of what is being priced get confused constantly. The first half is waiting. Even if the cousin's repayment were absolutely certain, the lender would still want something for not having the money for three years. There was always something else that money could have been doing in the meantime. The second half is exposure. The repayment is not certain, and the range of things that could go wrong is wider for a workshop extension than it is for a deposit, so the bar rises again. A discount rate is those two payments stacked into one percentage, and every honest attempt to build one is an attempt to size both halves.

Waiting and exposure together are also why a rate is never simply lifted from the nearest available number. The nearest available number usually prices only one of the halves. A deposit rate prices waiting and almost none of the exposure. A rate quoted last year prices exposure that has since changed. The question to be answered is stubbornly specific: what would this money have done, over this period, at this risk.

Companies do exactly this and just have more counterparties. Sankalp Industrial Systems Limited is funded by people who each had somewhere else to put the money. Lenders had other borrowers. Shareholders had other shares of the same riskiness. Every one of those people is quietly holding the business to the return their own alternative would have paid, and the company's discount rate is the blend of those held bars. Nobody sat down and awarded the company a rate. The rate is what the alternatives came to.

Why does the rate belong to the money and not to the business?

Two analysts can be handed the identical forecast, agree on every rupee in it, and still discount it at different rates without either of them making a mistake. The disagreement sounds arbitrary, and that is what makes it uncomfortable. The rate is not arbitrary. The rate is conditional, and the condition is whose money is being committed.

Think of two people looking at the same stall outside the same office building. One of them has cash idling. The other would have to pull money out of a workshop that is already returning something solid. The two funders are giving up different things, so the stall has one set of cash flows and two different costs of being funded. Neither of them is measuring the stall wrongly. Each is measuring a sacrifice of their own, and the two sacrifices genuinely differ.

A rate therefore travels with a pocket rather than with a letterhead. An argument about a discount rate can never be settled by looking harder at the company either. Looking harder at the company improves the forecast. The rate is settled somewhere else entirely, in a comparison the company is not a party to.

Does the rate say anything about whether the business is any good?

The rate says nothing at all about quality, and the belief that it does causes more damage than any other misunderstanding about discount rates. A high discount rate is not a verdict that a business is weak, and a low one is not a compliment.

Riskier businesses do tend to attract higher rates, so the confusion is understandable, and it is easy to slide from that into treating the rate as a quality score. A rate is not a score; it is a price for exposure, and the exposure is the funder's, not the company's. A well run business in a volatile trade can carry a high rate while a mediocre one in a dull trade carries a low one, and nothing about that ordering is a judgement on management.

The practical consequence is a discipline. The urge to nudge a rate because the business impressed somebody belongs in the forecast instead. If a business really is better than it first appeared, that shows up as more cash in later years or as cash that arrives more reliably. Moving the rate instead is a way of expressing an opinion twice while showing the working once.

Where does a rate come from, in one sentence?

Sankalp Industrial Systems Limited's assumed 12.00 per cent is the weighted average cost of capitalA single percentage blending what every funder of a business requires, each weighted by how much of the money that funder put up. reached by a 14.00 per cent cost of equityThe yearly percentage a shareholder wants back for putting money behind a business and standing last in the queue if anything goes wrong. Estimating one is a job of its own and is handled elsewhere in these notes. sitting alongside an after-tax cost of debtA borrower's coupon reduced by the tax that interest saves, so the real drag on a company is lighter than the rate printed in the loan agreement. of 6.00 per cent, the two of them weighted 75.0 against 25.0 on capital measured at market values.

How each of those three numbers is estimated is a substantial subject in its own right, and each is settled under the cost of capital rather than here. The estimation problem, the peer sets, the levered betaA measure of how far a share's returns swing against the wider market once the company's borrowing has been allowed for. and the argument about which weights to use each carry a full treatment there.

Only one property of that 12.00 per cent matters below: it is a chosen figure that came out of an estimate, not a figure anybody measured off an instrument. A chosen figure behaves differently from a measured one, and every argument about matching and precision below turns on that difference.

Matching test one: are the rate and the cash flow in the same currency?

Four tests decide whether a rate may be paired with a stream of cash at all. Fail any single one and the division still runs, the spreadsheet still returns a figure, and the figure is about nothing. Take them in order.

The first is the easiest to state and the easiest to breach quietly. The alternatives a rate was measured against were denominated in something, so a rate carries a currency. Rupee cash flows meet a rupee rate, and no adjustment anywhere else in the model repairs a mismatch here. The temptation arrives through the side door: a peer set assembled across borders, a required return lifted from a study conducted in a different currency, an offshore parent's internal hurdle applied to a subsidiary that bills in rupees. Each of those is a currency breach wearing ordinary clothes.

The household version is a person comparing the return on a deposit quoted in one country's money with rent received in another's and concluding one beats the other. The comparison is not close to right; it is not a comparison. Sankalp Industrial Systems Limited earns rupees, borrows rupees and is assumed to be funded by people whose alternatives are in rupees, so its 12.00 per cent is a rupee rate and it may only ever meet rupee cash.

Matching test two: are both nominal, or are both real?

Both sides of the second test look correct in isolation, and that is why it trips careful people. A cash flow forecast either has expected inflation built into it or it has been stripped out. A rate is the same. The rule is that both sides must be on the same footing, and the failure mode is a model in which a growth cell and a rate cell were filled in by two people with different habits.

A nominal forecast meets a nominal rate; a forecast with inflation removed meets a rate with inflation removed; there is no legal third pairing. The invented company's cash flows here are nominal, so they meet the nominal 12.00 per cent. Mixing the two does not produce a slightly wrong answer. The answer comes out wrong by roughly the whole compounded weight of inflation over the life of the forecast. On a stream running out past five years that weight is enormous.

The Real Discount Rate, in one sentence

A real discount rate is the same rate with expected inflation taken out of it, and it exists so that cash flows which have had inflation taken out of them have something legal to meet. On this company's assumptions, with expected inflation at 5.00 per cent, that rate is 6.6667 per cent rather than 12.00 per cent. Notice how far apart those two numbers are: this is not a rounding difference but a different rate for a different job. The full comparison of the two, including why removing inflation is done by dividing and never by subtracting, and what the shortcut costs, is covered separately.

Matching test three: whose cash is this, everyone's or the shareholders'?

The third test asks which claim the cash in hand belongs to. A stream that is available to everyone who funded the business, before lenders have taken their interest, belongs to lenders and shareholders together. A stream that is what remains after lenders have been paid belongs to shareholders alone. The two streams are different quantities, and they are entitled to different rates.

Cash that everybody has a claim on meets the blended 12.00 per cent; cash that only shareholders see meets the 14.00 per cent cost of equity. Pairing shareholder cash with the blended rate is the common breach, and it is expensive in a specific and instructive way: the blend already contains the lenders' 6.00 per cent, weighted at a quarter, so discounting shareholder cash at 12.00 per cent charges the reader for lenders who have already been paid inside the numerator. The lenders get counted twice, once as an outflow and once as a discount.

The household picture is a shop's takings against the shopkeeper's takings. Takings before the landlord and the supplier are paid is one number. The amount left for the household is another. Nobody would apply the household's standard of living to the first figure. Both quantities are called cash flow, both are positive and both sit in adjacent rows, so the equivalent slip in a model is routine.

Matching test four: whose risk is the rate carrying?

The fourth test is the one people believe they have passed and have not. A discount rate has to carry the risk of the cash flow in front of it. Not the risk of the organisation that happens to hold it, not the risk appetite of the person doing the arithmetic, and not an average risk taken across a collection of unlike things.

Sankalp Coatings Private Limited, invented, is the 75.0 per cent held subsidiary of the same group, and it is a steadier business than the group as a whole. Its own cost of capital is 11.25 per cent, not 12.00 per cent. The rate follows the risk of the cash, not the name on the letterhead. How that 11.25 per cent is built belongs to the cost of capital. A lower risk stream inside a group legitimately carries a lower rate than the group average, and the difference is not decorative.

Seventy-five basis pointsA basis point is a hundredth of one percentage point. Forty of them make 0.40 per cent. sounds like nothing. On the five-year stream worked through here, swapping 12.00 per cent for 11.25 per cent and changing nothing else lifts the answer to Rs 24,00,52,45,513. The addition is Rs 2,72,38,66,419, a gain of 12.80 per cent. The gain sizes a 75 basis point difference on this one stream. Valuing the subsidiary itself would need the subsidiary's own forecast.

Red marks exactly one thing in every drawing above and below: a figure or a route that claims more than its inputs can support. Where two things are merely different and neither is wrong, both are drawn in neutral fills.

How hard does the rate actually pull?

Now the measurement. A claim about leverage that is not measured is just an adjective. Sankalp Industrial Systems Limited is forecast to produce free cash for the whole business of Rs 98,00,00,000 in Year 1, rising by Rs 18,00,00,000 in each of the next four years to Rs 1,70,00,00,000 in Year 5, followed by a terminal valueA stand-in figure for everything a business earns beyond the last year anybody troubled to forecast, expressed at that last year's date. of Rs 29,25,00,00,000 standing at the end of Year 5. At 12.00 per cent, taking each year's cash at the year end under the convention called year-end discountingA convention treating a whole year's cash as though it landed on the very last day of that year rather than trickling in through it., the answer is Rs 21,28,13,79,094.

Now hold every cash flow, the 5.00 per cent growth assumption and the discounting convention exactly where they are, and move only the rate. Take it down by 33 basis points, from 12.00 to 11.67 per cent. The same model returns Rs 22,40,37,72,515. A third of one percentage point of a chosen rate is worth Rs 1,12,23,93,421 on this invented company. Set beside the starting Rs 21,28,13,79,094, that gain is 5.27 per cent. The input moved by 2.75 per cent of itself and the output moved by 5.27 per cent of itself, so on these assumptions the value is a little under twice as responsive as the rate that produced it.

The responsiveness is not a quirk of this company. It follows from where the money sits in time. But first, look at where the Rs 1,12,23,93,421 actually came from: the split is more instructive than the total.

Why do the far years feel the rate most?

Two things are working at once, and most people have met only the first, so the two are worth separating.

The first is ordinary compounding in reverse. A rupee arriving in Year 1 is divided by the rate once. A rupee arriving in Year 5 is divided by it five times. Change the rate a little and the fifth division amplifies the change four more times than the first one does. Compounding in reverse is familiar from any discount factor table.

The second is the divisor inside the tail, and it is far more violent. Everything after the last forecast year is condensed into a single figure by dividing a cash flow by the rate less the growth. On this company that divisor is 12.00 less 5.00, standing at 7.00 points. Shave a third of a percentage point from the rate and the divisor drops to 6.67. The subtraction leaves a small number behind, and the rate is then measured against that small number rather than against itself, so a small change in the rate becomes a proportionally much larger change in the tail.

The two together give the shape below. Value against rate is not a straight line. The curve steepens as the rate falls. The divisor keeps shrinking, so the same 33 basis points buys progressively more the lower down the curve the starting point already is. Measured on this company: moving from 12.00 to 11.67 per cent adds Rs 1,12,23,93,421. The identical move higher up buys much less: at 15.00 per cent the model returns Rs 14,50,43,31,357, and taking the same 33 basis points off lifts it to Rs 15,04,14,91,024, an addition of Rs 53,71,59,667. The identical change in the input is worth a little over twice as much at one end of the range as at the other. The doubling is a property of this stream and this growth assumption rather than a law, and it holds because the tail is large and the divisor is small.

How precise can a discount rate honestly be?

Less precise than the two decimal places everybody writes it to. The imprecision is not a criticism of anybody's arithmetic; it is a statement about what the inputs can support. A rate is assembled out of estimates, and estimates have widths. Writing 12.00 per cent rather than 12 per cent is a display convention, and it is a harmless one right up to the moment somebody reads the two zeroes as evidence.

The same thing happens at the other end. Solving for the rate that makes this model return a particular round figure does not give a round rate; it gives something like 11.671 per cent. Rounding that to the two decimals the convention allows moves the answer by tens of lakhs. The rate is quoted to a precision the estimate behind it cannot support, and the output inherits that false precision multiplied by the leverage measured above.

So what should be done instead? Fewer decimals in the rate fix nothing. The fix is at the output, and it has a specific shape.

Take the same model out two hundred basis points either side of the assumption. At 10.00 per cent it returns Rs 30,37,68,23,490. At 14.00 per cent it returns Rs 16,25,52,19,153. The two ends are Rs 14,12,16,04,337 apart. Measured against the figure sitting between them, that width comes to 66.36 per cent, and quoting the middle alone hides every bit of it. A width is not a verdict that the range is too wide or that the model is bad. The width says what four hundred basis points of assumption are worth, and it leaves the reader in a position to argue about the assumption. Arguing about the assumption is the only argument worth having.

Who actually uses this, and what do they use it for?

Four desks reach for a discount rate in a normal week and none of them is doing quite the same job.

A lender uses one to price the promise in front of it. The credit team is not valuing the borrower; it is asking what return its own money would fetch elsewhere at that credit quality, and then testing whether this borrower's covenantsPromises written into a loan agreement, binding the borrower to keep doing some things and to avoid others until the borrowing has been repaid in full. and cash cover justify accepting it. When Sankalp Industrial Systems Limited's working capital facilityA revolving credit line a business draws on to fund stock and unpaid customer bills, usually renewed each year rather than repaid on a fixed schedule. comes up for annual renewal, that comparison is what moves the rate on it, not the company's own view of its prospects.

An equity analyst uses one as the single lever that turns a forecast into a value. The analyst's first duty is therefore to publish the rate rather than bury it. A forecast published without its rate is not a valuation: the reader can neither reconstruct it nor argue with it.

A company treasury or board uses one as a hurdle rateThe smallest percentage return a proposal has to beat before a board is willing to let the money go. for new spending. A hurdle rate is the closest thing to the household version: the board is asking what else the same rupees could have done inside the business, and refusing anything that clears less. How projects are then ranked against that hurdle, and what happens when two of them conflict, is a capital budgeting subject and is covered elsewhere.

A household uses one without naming it. Deciding whether to prepay a loan is exactly this arithmetic: the return on prepaying is the loan rate that stops being paid, and the decision turns on whether any other use of that money, at comparable risk, beats it. All four are answering the same question in different clothes: what the money would have done somewhere else.

Sankalp Industrial Systems Limited and Sankalp Coatings Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.